GPS World

Category: Research & Development

  • Innovation: Quo vademus

    Innovation: Quo vademus

    Future automotive GNSS positioning in urban scenarios

    By Martin Escher, Mirko Stanisak and Ulf Bestmann

    INNOVATION INSIGHTS with Richard Langley
    INNOVATION INSIGHTS with Richard Langley

    WHERE ARE WE GOING with GNSS positioning? There have been many advances in satellite-based positioning over the past couple of decades and there are more to come.

    Probably the most significant advance, affecting the most users, has been the further miniaturization of GNSS chipsets and modules. Virtually every mobile phone now includes a GPS component. Developers have also made these embedded devices more sensitive so that they can work with smaller, less efficient antennas. Furthermore, GPS satellites are now being launched with additional, more capable signals and already high-end receivers are starting to use these signals. Once full constellations transmitting these signals are in place, consumer devices will likely make use of them as well.

    Another very important advance in GNSS positioning has been the development of additional GNSS constellations and multi-GNSS receivers capable of using their signals. Actually, it’s been a multi-GNSS world for quite a while now. The Russians began development of GLONASS shortly after work began on fielding GPS and both systems achieved full operational capability in the mid-1990s. Unfortunately, due to financial problems following the break-up of the Soviet Union, the number of operating GLONASS satellites fell to the single digits making the system virtually unusable. However, with renewed government support, GLONASS has once again become a viable GNSS and many consumer and professional receivers can track and use GLONASS signals along with those of GPS.

    In the 1990s, we also saw the development of the U.S. Wide Area Augmentation System, transmitting GPS correction and integrity information from geostationary satellites on the GPS L1 (and subsequently L5) frequency. Other compatible satellite-based augmentation systems followed, including the European Geostationary Navigation Overlay Service, Japan’s Multi-Functional Transport Satellite Satellite-based Augmentation System, India’s GPS Aided GEO Augmentation System, and Russia’s System for Differential Correction and Monitoring. Besides enhancing integrity, the data transmitted by the satellites of these systems improves GPS pseudorange-based positioning accuracy, sometimes to below the one-meter level.

    Starting about 15 years ago, we have seen the development of additional autonomous GNSSs, joining GPS and GLONASS. The European Galileo system is under construction as is China’s BeiDou system. And although only providing regional coverage, we should also mention Japan’s Quasi-Zenith Satellite System and the Indian Regional Navigation Satellite System. While all of the new systems are still in development and full constellations are still some years away from completion, the signals from the satellites already in orbit can be used to supplement those received from GPS and GLONASS satellites to improve positioning and navigation availability for some difficult navigation scenarios.

    One of the most difficult situations requiring a continuous positioning capability is driving in built-up areas where buildings and other objects can block the signals from a number of GPS satellites such that GPS-only positioning becomes impossible. Even if four or more satellites are in view of the satellite navigation receiver’s antenna, those satellites might have unfavorable geometry, resulting in significantly degraded positioning accuracy. However, if the receiver can access the signals of two or more GNSSs, then position fixes might be available where none were possible with GPS alone, and the accuracies of marginal fixes might be improved.

    In this month’s column, we take a look at some early work in using multi-GNSS plus additional sensors for navigating in the heart of the city of Braunschweig, Germany (the birth place of Johann Friedrich Carl Gauss, the inventor of least squares and the father of modern geodesy), and how the additional signals can help us to get where we’re going.

    In the near future, we will see the introduction of more and more next-generation advanced driver assistance systems (ADASs) targeting the field of automated or autonomous driving. These systems will have to be considered as safety critical. In contrast to conventional localization systems, they will have to guarantee a higher overall accuracy and integrity to their target applications. Of course, the overall performance of any localization system is mostly limited by its behavior during the worst conditions.

    Such behavior is a very limiting factor especially for an ADAS that uses a GNSS such as GPS. The accuracy and integrity of GNSS depend on the quality and availability of satellite signals. The more signals that are available, the greater are the accuracy and integrity. However, as GNSS signals can be blocked easily, the worst-time behavior is difficult to characterize, especially in challenging urban scenarios important for an ADAS.

    To face these challenges, additional sensors such as inertial measurement units (IMUs) or odometers can be used for positioning as well. These sensors can increase the availability and accuracy for situations where GNSS-based positioning is not available. Additionally, the characteristics of these sensors are complementary to satellite navigation. The combination of these sensors with satellite navigation thus has the potential to achieve a positioning accuracy and integrity superior to that of single-system performance.

    As the number of GNSS measurements is crucial for a precise position fix, the parallel use of different GNSS constellations can improve the overall performance significantly.

    Four global satellite-positioning systems are now available. The American GPS and the Russian GLONASS have been in operation for years and are already used in a wide variety of applications. Additionally, newer systems like the European Galileo and the Chinese BeiDou systems are under construction. Even though these systems do not have continuous worldwide availability at the moment, their currently available satellites can already be included in multi-constellation GNSS positioning. Once more satellites are in orbit, the benefit of multi-constellation GNSS will increase even further.

    In this article, we take a look at the current performance of multi-constellation GNSS positioning in an urban scenario, contrasting it with GPS-only positioning as well as GNSS positioning aided by additional sensors.

    Satellites in orbit

    To characterize multi-constellation GNSS performance, stationary GNSS data has been collected using different receivers in Braunschweig, Germany. GNSS data from GPS, GLONASS, Galileo and BeiDou was recorded over a 14-hour window on November 20, 2015.

    Based on the broadcast ephemeris data and the receiver’s position, the availability of GNSS measurements was calculated for the duration of the campaign. TABLE 1 shows the number of all satellites of the different constellations as well as the minimum and maximum number of available satellites for each system during the recording period down to an elevation angle of 0°.

    Table 1. Number of satellites in orbit and in view during a 14-hour window.
    Table 1. Number of satellites in orbit and in view during a 14-hour window.

    FIGURE 1 shows the satellite availability for the measurement campaign. To obtain a position fix using a single GNSS constellation, range measurements to at least four satellites of this constellation must be acquired. Thus, assuming optimal reception of GNSS signals, single-constellation positioning was possible for the full observing window using only GPS, only GLONASS and only BeiDou satellites. On the other hand, Galileo-only position fixes were not possible at any time due to the low number of simultaneously visible satellites.

    FIGURE 1. Satellites in view from Braunschweig, Germany.
    FIGURE 1. Satellites in view from Braunschweig, Germany.

    However, combining measurements from different GNSS constellations in parallel — multi-constellation GNSS — provides the most benefit.

    Multi-Constellation GNSS

    All major GNSS constellations operate independently and use different reference frames for position and time. To combine measurements of different GNSS constellations, the correct handling of the diverse reference frames needs to be ensured.

    On the one hand, the different coordinate systems have to be taken into account. However, the differences between the position frames is usually kept to within a few centimeters and can thus be neglected for most standalone-GNSS applications.

    On the other hand, the handling of the different system time scales requires a specific approach. Even though the inter-system biases (that is, the differences between the system time scales) are usually kept within a few nanoseconds, the influence of the inter-system offsets must not be ignored for most applications and have to be taken into account for a combined position solution.

    The most common approach is to extend the estimated state vector with a distinct clock error for each used constellation. For a combined position solution incorporating GPS, GLONASS, Galileo and BeiDou, the state vector used for the least-squares estimation could look like this:

    Inn-E1.  (1)

    Each pseudorange measurement only contributes to its respective clock-error component.

    Of course, as the values of more unknown variables have to be estimated, the number of necessary GNSS measurements increases, too. To calculate a combined position solution including GPS, GLONASS, Galileo and BeiDou for the above-mentioned example, seven variables must be estimated. This means that at least seven independent GNSS measurements are necessary at each epoch. However, if no satellite of a specific constellation is available, the state vector can also be adapted to not estimate the corresponding clock error. In this way, the availability of a multi-constellation GNSS solution is always higher or, in the worst case, equal to that of the single-constellation GNSS solutions.

    By being able to use more than just one GNSS constellation, the geometric distribution of the satellites over the sky is improved, resulting in a lower dilution of precision (DOP). A lower DOP value usually indicates a better mapping of range measurement precision into the position precision. However, as the different GNSS constellations are currently in different states of maturity, the range precision varies significantly. Thus, a multi-constellation position solution is not necessarily more accurate than a single-constellation solution, but will benefit from an improved overall availability and integrity.

    Such a capability is particularly important for safe operations in constrained scenarios like urban canyons, which are a common challenge for automotive applications. Compared to currently prevailing GPS-only positioning, multi-constellation GNSS has the potential to enable safety-of-life services, which will require a high level of integrity in the automotive domain.

    Tight coupling

    To take even greater advantage of multi-GNSS positioning in challenging environments, the combination with additional sensors can improve the overall positioning performance significantly. The Institute of Flight Guidance at the Technische Universität Braunschweig has developed a tightly coupled GPS fusion system, which incorporates measurements of a close-to-market IMU and odometer sensors for reliable urban car positioning.

    This system is capable of using raw data from a reference station receiver to generate differential GNSS corrections. These differential corrections must be free from reference-receiver clock error before they can be used by the tightly coupled system (rover-receiver clock-bias update by pseudorange positioning, rover-receiver clock-drift update by Doppler frequency velocity estimation, and clock-bias prediction by clock drift).

    Inn-E2.  (2)

    As shown in Equation 2, the system calculates the residuals for each pseudorange (PSR) received by the reference receiver based on the well-known reference antenna positionIn-x-ant and the current satellite position as calculated using its broadcast ephemerisIn-xj-sant . While calculating the residuals, it involves the atmospheric effects ε j computed by the Klobuchar ionosphere delay model and a modified Hopfield tropospheric delay model.

    These residuals must be corrected by the satellite clock errors In-dj-sat (also calculated using the broadcast ephemeris). The arithmetic average of the corrected residuals is used as an estimate for the reference receiver clock error (see Equation 3). This approach is sufficient for most applications, but it is also possible to use additional algorithms to estimate the clock error more accurately.

    In-Eq3  .  (3)

    To generate reference receiver clock error-free pseudorange corrections, the residuals are calculated a second time. Only the estimated clock error of the reference receiver is removed in the second set of residuals:

    In-Eq4  .  (4)

    The assumption was made that these residuals correct all satellites, all atmospheric errors and the inter-system time errors.

    With this assumption, the tightly coupled system uses the corrected residuals as pseudorange corrections for the ranges measured by the rover receiver. Using the corrected pseudoranges, the tightly coupled system can estimate the rover receiver’s clock error for positioning:

    In-Eq5  .  (5)

    In this way, the inter-system offsets are eliminated as well. Corrected multi-constellation GNSS measurements can thus be processed by estimating one receiver clock error only.

    Simulation of obstacles

    The performance of satellite navigation is affected directly by the distribution of the useable GNSS satellites over the sky. The more GNSS satellites are spread out over the sky, the lower the DOP value and the better the positioning accuracy. For reference, FIGURE 2 shows a sky plot of unconstrained GNSS with perfect reception of all GNSS satellites during the measurement period of 14 hours. Combining the satellites of all four GNSS core constellations (GPS, GLONASS, Galileo and BeiDou), up to 30 satellites are usable at the same time.

    FIGURE 2. Sky plot of GNSS satellites (GPS, GLONASS, Galileo and BeiDou) at Braunschweig.
    FIGURE 2. Sky plot of GNSS satellites (GPS, GLONASS, Galileo and BeiDou) at Braunschweig.

    Of course, this is an optimized scenario that can only be achieved using high-quality antennas without any obstacles in the vicinity. Many applications, including urban automotive situations, do not have a comparable reception of GNSS data, and will suffer from blocked satellites and multipath reception.

    Therefore, we created a simulation of surrounding obstacles to predict the behavior of GNSS positioning in challenging urban scenarios. In this simulation, all buildings are represented by endless walls with constant height. A satellite is assumed to be invisible if its line of sight crosses the wall.

    To get a first impression of the usability of this approach, we took GNSS measurements in front of the Institute of Flight Guidance in Braunschweig.

    Using this scenario, the same simulation of optimal visibility using ephemeris data has been conducted again. As shown in FIGURE 3, large portions of the sky are blocked by the simulated obstacles.

    FIGURE 3. Sky plot with valid (thick lines) and invalid (thin lines) measurements.
    FIGURE 3. Sky plot with valid (thick lines) and invalid (thin lines) measurements.

    Of course, the blockages also affect the number of visible satellites as shown in FIGURE 4. Instead of 23 to 31 satellites for the unconstrained scenario, only 11 to 18 satellites are now visible.

    FIGURE 4. Comparison of satellite visibility with and without simulated obstacles.
    FIGURE 4. Comparison of satellite visibility with and without simulated obstacles.

    In a following step, we validated the theoretical predictions of the visible GNSS satellites against the reception by a GNSS receiver of the available signals at the simulated position.

    Validation of simulation

    For a validation of the obstacle simulation, data from a high-grade receiver was used for the validation of the simulation. This modern GNSS receiver is able to track signals from all GNSS constellations (GPS, GLONASS, Galileo and BeiDou) on different GNSS frequencies with a data rate of up to 100 Hz. The BeiDou reception, however, was only acquired recently before the recording of the data and unfortunately suffered from bad BeiDou tracking performance.

    The receiver was connected to a multi-frequency antenna. This GNSS antenna was installed at the back of the roof of the research car. A sky plot of the tracked signals is shown in FIGURE 5.

    FIGURE 5. Tracked signals of the high-end receiver.
    FIGURE 5. Tracked signals of the high-end receiver.

    A comparison of the simulated (Figure 3) and the actual (Figure 5) sky plots shows a very good agreement between the simulations and the measurements. There are, however, some spots in the sky plot where the real GNSS receiver is able to track satellites that are behind a building. This can be explained by the reception of signals through the windows of the building. Thus, the signal-quality indication based on the receiver’s signal-to-noise measurements of these spots is quite bad in these situations.

    As described before, we experienced some problems with the BeiDou reception of the high-grade receiver. Thus, we used an additional single-frequency GNSS receiver. This receiver is capable of providing raw L1 GNSS data of two constellations simultaneously and was configured to track GPS and BeiDou satellites. In this way, an additional sky plot showing GPS and BeiDou reception in the same setup could be generated. The visible BeiDou satellites are shown in light blue in FIGURE 6 and are in accordance with the simulated visibility.

    FIGURE 6. Valid signals sky plot of the single-frequency receiver data.
    FIGURE 6. Valid signals sky plot of the single-frequency receiver data.

    In general, the sky plots identify significant differences compared to the simulated ones as even in regions blocked by buildings some satellites can still be tracked. The contour of the building, however, can still be seen in the signal strength plot in FIGURE 7.

    FIGURE 7. Signals strength sky plot of the single-frequency data.
    FIGURE 7. Signals strength sky plot of the single-frequency data.

    This result is an indication that the single-frequency receiver can track some satellites blocked by the buildings using diffracted or reflected signals, but, of course, resulting in worse positioning accuracy.

    It goes without saying that the various receivers we used are designed with contrary goals in mind. High-performance GNSS receivers are optimized to provide accurate position solutions for high-demanding applications. Thus, the receiver attempts to suppress multipath effects as much as possible to obtain precise and accurate position solutions. The single-frequency receiver, on the other hand, is closer to the low-price, high-volume class of receivers for portable devices, and is optimized to provide valid position output even in challenging environmental situations. Thus, the receivers must not be compared directly because they are designed for completely different purposes.

    Simulating urban canyons

    To assess the overall multi-GNSS performance in urban scenarios, we conducted driving tests in the city center of Braunschweig. Driving through city centers is particularly challenging for any positioning algorithm because of various potential sources of errors. Instead of only using suburban commuter roads, the route we chose represents the most challenging situations for the city center. Most of the roads are surrounded by multi-story buildings (typically up to six floors) very close to the driving lanes. This is – especially for European cities – a common and challenging urban scenario for satellite navigation. An example of such a scenario is shown in FIGURE 8.

    FIGURE 8. Dimensions of representative urban scenario.
    FIGURE 8. Dimensions of representative urban scenario.

    To quantify the impact of the limited GNSS availability due to buildings and other obstacles, we simulated a scenario with walls on both sides of the road. With the road running in a north-south direction, we simulated buildings within a distance of 14 meters and a height of 15 meters. The simulated effect on a GNSS receiver in the middle of the street due to blocked satellites in this scenario is shown in FIGURE 9. Satellites with an elevation angle of up to 65° can be obstructed by the buildings.

    FIGURE 9. Sky plot for obstacle simulation of urban canyon.
    FIGURE 9. Sky plot for obstacle simulation of urban canyon.

    In this scenario, more than half of the sky is blocked by buildings, making satellite navigation quite challenging. Additionally, Braunschweig is located at about 52° north latitude and is close to the inclination of most GNSS constellation orbits (GPS 55°, Galileo 56°, BeiDou MEO 55°). Only GLONASS satellites can be seen in the far northern part of the sky from time to time due to their inclination of 65°.

    Using GPS satellites only, fewer than four satellites are available for long periods of time. On the other hand, using a combination of all constellations, up to 14 satellites can be used even for this constraining scenario. Most of the time, at least seven satellites are visible, allowing a multi-constellation GNSS position solution.

    Downtown positioning

    To assess the practical benefit of multi-constellation GNSS in urban scenarios, we conducted a test drive in downtown Braunschweig using our research car. This area is dominated by narrow roads with multi-story buildings on both sides of the road. Using recorded data from different GNSS receivers and other sensors, multiple positioning solutions were obtained by post-processing the recorded data to compare the different positioning performances.

    As a baseline for comparison, a GPS-only position solution was calculated. This result represents the current state-of-the-art navigation systems for most production cars. All valid GPS-only position fixes are shown in FIGURE 10. For large portions of the test drive, no GPS-only position solution was possible because of insufficient GPS measurements.

    FIGURE 10. GPS-only standalone positioning fixes for test drive in Braunschweig.
    FIGURE 10. GPS-only standalone positioning fixes for test drive in Braunschweig.

    To quantify the benefit of multi-constellation GNSS compared to GPS-only, a combined position solution was calculated using the same data as before. There was a significant improvement in the availability compared to the GPS-only position solution.

    However, even when using multiple GNSS constellations, some areas with no valid GNSS fixes still exist. The GNSS availability can be improved further by using differential corrections from a GNSS reference receiver. The correction data is available in the research car using 4G mobile telecommunication links to different service providers. Each provider uses a network of GNSS receivers to calculate differential corrections. However, all commercially available services are currently limited to GPS and GLONASS. Thus, another stationary multi-constellation GNSS reference receiver at the Institute of Flight Guidance generated correction data for the test drives. As the baselines are short in this scenario (not longer than 10 kilometers), no significant spatial decorrelation is expected.

    As the majority of possible inter-system offsets are already eliminated using the differential corrections of identical receiver types, a multi-constellation solution can be calculated here even with as few as four GNSS satellites in view. This is shown in FIGURE 11. In this way, the achieved availability increased again.

    FIGURE 11. Differentially corrected multi-constellation positioning fixes for test drive in Braunschweig.
    FIGURE 11. Differentially corrected multi-constellation positioning fixes for test drive in Braunschweig.

    Finally, using all the information available in the car, a hybrid position solution based on differentially corrected GNSS, inertial navigation and the test vehicle’s odometer has been calculated.

    In sections without any GNSS positioning aiding (marked red in FIGURE 12), the inertial navigation system was used in dead-reckoning mode. As these outages lasted only for short periods of time, the accuracy of the combined position remained usable for the duration of the test. In this way, an accurate position solution could be calculated for the whole test drive using this tightly coupled positioning algorithm.

    FIGURE 12. Tightly coupled positioning trajectory for test drive in Braunschweig.
    FIGURE 12. Tightly coupled positioning trajectory for test drive in Braunschweig.

    With increasing positioning complexity, the computational burden increased as well. For a tightly coupled system integrating the measurements of the different sensors, significantly more calculations must be performed in real time than for current GPS-only standalone positioning. However, even today these computations can be easily made using embedded devices.

    Conclusions and outlook

    For this article, the achievable positioning performance of multi-constellation GNSS has be analyzed with a special emphasis on urban automotive applications. Simulations of constrained environments have been compared with real data and show good agreement. Multi-constellation GNSS outperforms GPS-only positioning, especially in situations where large portions of the sky are blocked by obstacles, because significantly more satellites remain usable. Multi-constellation GNSS has thus the potential to be an important part of future safety-of-life positioning and navigation applications.

    However, a few challenges still exist. Some GNSS constellations have not reached their full operational capabilities as not all satellites are in orbit yet (Galileo and BeiDou). Additionally, the ranging errors of these systems are expected to decrease with improved navigation message accuracy and receiver performance.

    The availability of numerous GNSS constellations results in new requirements for the receivers as well. Even though most manufacturers of GNSS equipment already support the additional systems with some products, the majority of currently used GNSS receivers is limited to one or two constellations, especially in mass-market applications. In addition, the reception quality of the newer systems is not always on the same level as GPS or GLONASS because of the limited experience that manufacturers have with Galileo and BeiDou. This, we hope, will change in the near future.

    Acknowledgments

    This article is based on the paper “Future Automotive GNSS Positioning in Urban Scenarios” presented at The Institute of Navigation 2016 International Technical Meeting, held in Monterey, Calif., Jan. 25–28.

    Manufacturers

    The high-grade receiver used in our tests was a Septentrio AsteRx3. The receiver was connected to a NovAtel GPS-703-GGG antenna. The single-frequency receiver we used was a u-blox LEA-M8T GNSS receiver with firmware version 2.3. Additionally, we used a NovAtel OEM6 multi-GNSS receiver and an Analog Devices ADIS16375BMLZ IMU.

    MARTIN ESCHER holds a Dipl.-Ing. in electrical engineering from the Technische Universität (TU) Braunschweig in Braunschweig, Germany, and has been employed as a research engineer at the Institute of Flight Guidance (IFF) since 2010.

    MIRKO STANISAK is a research assistant and Ph.D. candidate at the IFF of TU Braunschweig. He received his Dipl.-Ing. in mechanical engineering in 2009 and since then has worked on various GNSS-related topics.

    ULF BESTMANN received his Dr.-Ing. in mechanical engineering from the TU Braunschweig in 2010. He is employed at the IFF of TU Braunschweig, where he is head of the navigation department.

    Further Reading

    • Authors’ Conference Paper

    “Future Automotive GNSS Positioning in Urban Scenarios” by M. Escher, M. Stanisak and U. Bestmann in Proceedings of ITM 2016, the 2016 International Technical Meeting of The Institute of Navigation, Monterey, Calif., Jan. 25–28, 2016, pp. 836–845.

    • Multi-Constellation GNSS Measurements

    “Precise Point Positioning with Galileo Observables” by R.M. White and R.B. Langley in Proceedings of the 5th International Colloquium on Scientific and Fundamental Aspects of the Galileo Programme, Braunschweig, Germany, Oct. 27–29, 2015.

    “Accuracy and Reliability of Multi-GNSS Real-Time Precise Positioning: GPS, GLONASS, BeiDou, and Galileo” by X. Li, M. Ge, X. Dai, X. Ren, M. Fritsche, J. Wickert and H. Schuh in Journal of Geodesy, Vol. 89, 2015, pp. 607–635, doi: 10.1007/s00190-015-0802-8.

    “Getting a Grip on Multi-GNSS: The International GNSS Service MGEX Campaign” by O. Montenbruck, C. Rizos, R. Weber, G. Weber, R. Neilan and U. Hugentobler in GPS World, Vol. 24, No. 7, July 2013, pp. 44–49.

    “Precise Positioning with Galileo Prototype Satellites: First Results” by R.B. Langley, S. Banville and P. Steigenberger in GPS World, Vol. 23, No. 9, Sept. 2012, pp. 45–49.

    “Performance Evaluation of Integrated GPS/GIOVE Precise Point Positioning” by W. Cao, A. Hauschild, P. Steigenberger, R.B. Langley, L. Urquhart, M. Santos and O. Montenbruck in Proceedings of ITM 2010, the 2010 International Technical Meeting of The Institute of Navigation, San Diego, Calif., Jan. 25–27, 2010, pp. 540–552.

    “The Future Is Now: GPS + GNSS + SBAS = GNSS” by L. Wanninger in GPS World, Vol. 19, No. 7, July 2008, pp. 42–48.

    • Tightly-Coupled GPS Fusion System

    “A GPS/Galileo Tightly-Coupled Localization System for Safety-Relevant Automotive Assistance Systems” by H.-G. Büsing, M. Escher, T. Scheide and P. Hecker in Proceedings of ION GNSS 2011, the 24th International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Ore., Sept. 19–23, 2011, pp. 356–362.

    • Geometry Effects on GNSS Positioning

    “Dilution of Precision” by R.B. Langley in GPS World, Vol. 10, No. 5, May 1999, pp. 52–59.

  • Innovation: Flying safe

    Innovation: Flying safe

    GNSS robustness for unmanned aircraft systems

    By Joshua Stubbs and Dennis M. Akos

    When siting the antenna of a GNSS receiver or designing a GNSS-based navigation system, electromagnetic compatibility is an important concern. This is particularly true for airborne platforms. In this month’s cover story, we take a look at how radio-frequency interference can impact GNSS equipment on unmanned aircraft systems and how robustly the equipment can navigate those systems.

     

    INNOVATION INSIGHTS with Richard Langley
    INNOVATION INSIGHTS with Richard Langley

    WHAT’S THE WEAKEST THING ABOUT GNSS? Literally, it’s the signals. The strength of GNSS signals is notoriously low as anyone who has tried to operate a consumer-level device inside a steel and concrete building can readily attest. Unlike mobile phone signals, GNSS signals are too weak to survive the attenuation of walls, floors, and ceilings and so typically cannot provide a dependable signal indoors for most receivers.

    Even outdoors, the signals can be significantly attenuated by dense wet foliage and completely blocked by buildings and other objects. The GPS C/A-code signal generated by the transmitter in a satellite is approximately 27 watts. If such a transmitter were operated on Earth it would provide a decent signal even inside a nearby building. First responders, for example, can communicate with each other using portable transceivers with even lower-powered transmitters.

    However, GPS satellites are about 20,000 kilometers away at their closest and the signals they transmit spread out as they travel to the Earth and even with the directivity of the satellite transmitting antenna, by the time the signals reach the surface of the Earth, their power density is only on the order of 10-13 watts per square meter. And that’s outdoors.

    This signal is so weak that it is buried in the receiver’s background noise, which is similar to what you hear when you tune an AM radio between stations. So how can GPS possibly work with such a weak signal? The received signal is actually spread out over several megahertz of radio-frequency spectrum by the pseudorandom noise ranging code. It is this known noise-like code that allows receivers to determine the biased-ranges to satellites and from those ranges determine their positions. Knowing the code, the receiver de-spreads the weak received signal, concentrating it and lifting it above an acceptably low background noise.

    All is fine and well as long as the received signal density doesn’t drop much below the 10-13 watts per square meter level but also the background noise level mustn’t rise much above the acceptable level for which the receiver is designed. Both of these criteria are reflected in the carrier-to-noise-density ratio, or C/N0, of the signal. Why might the noise level change? The noise comes from the receiver itself as well as from naturally produced electromagnetic radiation from the sky, the ground, and objects in the receiving antenna’s vicinity. The sky noise includes so-called cosmic noise from the sun, Milky Way galaxy, other discrete cosmic objects and radiation left over from the Big Bang as well as radiation from our atmosphere. For the most part, the noise from these sources is small but occasionally the sun can have a radio outburst that can significantly increase the noise level at GNSS frequencies and actually overpower the GNSS signals as happened with GPS in December 2006.

    But the noise level can also be impacted by human-made electrical devices in the vicinity of a GNSS receiver’s antenna. This radio-frequency interference, or RFI, can come from devices such as radio transmitters, microwave ovens, motors, relays, ignition systems, switching power supplies and light dimmers. So, when siting the antenna of a GNSS receiver or designing a GNSS-based navigation system, electromagnetic compatibility is an important concern. This is particularly true for airborne platforms. In this month’s column we take a look at how RFI can impact GNSS equipment on unmanned aircraft systems and how robustly can the equipment navigate those systems.

    As the number of unmanned aircraft systems (UAS; also called unmanned aerial vehicles and drones) in use is increasing across many sectors, there is an interest in understanding the robustness of the GNSS engine used on UAS. With UAS being integrated into the National Airspace System (NAS), questions arise about what kind of navigation system should be used on UAS, and to what degree it should be standardized. Conventional aircraft typically use a certified GNSS receiver for navigational purposes, and as UAS will share the sky with conventional aircraft in the future, it is not unreasonable that UAS will use similar receivers.

    The first part of this article provides background on the status of GNSS standards for UAS. In the second part, we discuss why radio-frequency interference (RFI) can be expected on some UAS, together with what issues the RFI could cause for the GNSS engine. A simple experiment to determine the presence of RFI in the GPS L1 band due to proximity of a GPS antenna to electronics is presented in this section as well. The third part of the article discusses real-time kinematic (RTK) positioning for UAS purposes. In terms of accuracy, RTK positioning often provides the best results. The robustness of RTK measurements is questionable, though, because the technique relies on carrier-phase measurements. We present a case study, which shows some of the issues of using RTK positioning for UAS, in this part of the article, too.

    GNSS standards for UAS

    GNSS, and especially GPS, have been used in aviation for quite some time. The GPS receivers used for aviation have to guarantee a certain level of performance to be used, and are certified by the manufacturer to deliver said performance.

    The Federal Aviation Administration (FAA) is working on integrating UAS into the NAS. The development of UAS has been quick and has led to a lack of standardization for UAS, something that does exist for traditional manned aircraft. This has led to operators in most cases having to file for exemptions from the existing rules in order to use UAS. It is the ambition of the FAA to transition from issuing exemptions to issuing certifications of UAS once an agreement on regulations has been reached. There are still a number of challenges associated with a full integration of UAS into the NAS, including regulatory, procedural and technical challenges.

    The Wide Area Augmentation System (WAAS) was the first operational space-based augmentation system, intended to increase the robustness and reliability of GPS for aviation purposes. The WAAS Minimum Operational Performance Standards (MOPS) document (see Further Reading) specifies what kind of performance GPS plus WAAS provides to aviation users.

    The MOPS requirements have been carefully examined and extended. The maximum in-band interference levels for aviation have been theoretically analyzed. As long as signal and interference levels are within the specified ranges, the required performance should be expected.

    These levels, combined with the WAAS MOPS, provide the aviation community with the standardization required for manned aircraft operations where lives can be at stake if something were to go wrong with a navigation system. A Volpe National Transportation Systems Center report (see Further Reading) recommends the use of certified GPS receivers for applications where GPS is a critical system. This is not yet a requirement for UAS, and the question remains unanswered as to whether this will be a requirement for UAS in the future.

    Traditional aviation uses required navigation performance (RNP), a performance-based navigation approach, to assess what type of navigation systems can be used for different phases of flight. For example, while an aircraft is en route, an RNP of 2 nautical miles is required, meaning the actual position of the aircraft cannot deviate more than 2 nautical miles from a reported position. It should be noted that RNP takes the entire system into consideration, from the space-segment to the receiver to the capabilities of the aircraft.

    GNSS receivers used on manned aircraft have to be certified to deliver the RNP for each phase of flight for which they are used. Receiver autonomous integrity monitoring (RAIM) is used to ensure that faulty measurements do not affect the position and navigation solution. Due to the nature of RAIM, more satellites are required than the traditional minimum of four. If GNSS supplements other systems on board the aircraft, RAIM may be used to only monitor the quality of the system, and it will report when performance is below the required minimum. This form of RAIM requires a minimum of five satellites.

    However, if the aircraft depends on GNSS for navigation, RAIM must be able to determine if a particular satellite is providing incorrect or subpar data. This requires one additional satellite, bringing the minimum number of satellites that have to be in view of the receiver’s antenna up to six (two more than non-RAIM GNSS operation).

    However, using RAIM requires additional computational power, which one might not be able to provide on board a UAS due to size, weight and power limitations. It has been suggested that a GNSS system coupled with an inertial navigation system (INS) could be used for UAS navigation. A micro-electro-mechanical system (MEMS) INS would be very small, would not require a lot of power, and could improve the performance of a UAS navigation system. A GNSS plus MEMS INS approach may well be able to provide the robustness needed for UAS. However, the analysis of such a system is outside the scope of this article.

    Some basic considerations should be taken into account for a UAS GNSS positioning system. Integrity should be prioritized over accuracy if the system is used for navigational purposes. Low-altitude operations could bring on problems of sky blockage. The proposed solution to this is to use a receiver capable of using multiple constellations to ensure that as many satellites as possible are in view.

    Radio frequency interference

    Radio frequency interference, or RFI, is the interference caused by electromagnetic waves interacting with a system they were not intended to interact with. A familiar case of RFI can be experienced when a cellular phone is placed in close proximity to an AM radio. A distinctive sound can sometimes be heard, which is the sound of RFI interacting with the radio.

    Many forms of RFI exist. The interference can be in-band, that is, originating on frequencies transmitted within the band occupied by a desired signal, or out-of-band where the center-frequency of the interfering signal lies outside the band used by the desired signal but it can have a nonlinear impact on the components in the front end of the GNSS receiver. In some cases. the bandwidth of the interference is very small (narrowband), and in some cases the bandwidth is quite large (broadband). Depending on the type of interference, the affected systems will react differently.

    RFI can, for obvious reasons, be expected from intentional radiators, such as equipment broadcasting signals near the GNSS signal frequencies, or other equipment that emits harmonics that lie close to the GNSS frequencies. These sources are documented, and the effects of them can be mitigated through proper planning and analysis.

    However, electrical equipment can produce RFI that is not intended to be emitted — a so-called unintentional radiator. The Federal Communications Commission (FCC) Part 15 regulations define an unintentional radiator as “a device that intentionally generates radio frequency energy for use within the device, or that sends radio frequency signals by conduction to associated equipment via connecting wiring, but which is not intended to emit RF energy by radiation or induction.” Such devices are allowed to emit signal levels up to 300 or 500 microvolts per meter (depending on the class of the device) in the GNSS bands, as measured three meters away from the device.

    Although most GNSS frequencies are protected, the risk for intentional or unintentional RFI exists. Some elements of the GPS system have been designed to mitigate interference effects, and GPS remains a relatively robust system. However, there are still sources that could interfere with the GPS signals, such as out-of-band transmissions, harmonics of airborne or ground-based transmitter equipment, radar transmitters or even local oscillators in nearby equipment.

    In 1996, under a presidential decision directive, a commission to investigate a broad range of infrastructure vulnerabilities, including vulnerabilities to GPS, was set up. The commission found that GPS is in fact vulnerable to unintentional disruptions, from both human-made and naturally occurring sources. The commission recommended using certified GPS receivers for critical applications. The commission further recommended monitoring, reporting and locating unintentional RFI sources.

    One of the potential issues with RFI in a GNSS engine is that it can cause false local correlation peaks, which could cause the code-tracking loop and the carrier-tracking loop to diverge from the main correlation peak.

    RFI in the UAS GNSS Engine. On smaller UAS, space restrictions could lead to electronic components being placed in close proximity to each other. As stated earlier, some of these components could be producing RFI in the GNSS bands. If the RFI is strong enough to significantly raise the noise floor, the GPS signals could effectively be drowned out by noise. UAS that rely primarily on GNSS for navigation will risk losing navigational capabilities during such occurrences.

    With no external interference present, the noise floor should be at the receiver’s thermal noise floor. The presence of interference could be indicated by the raising of the noise floor above the level of the thermal noise.

    FIGURE 1 shows a simple setup for testing the hypothesis that electronics found on a common UAS could produce harmful RFI in the GPS engine. Some of the onboard equipment was a flight-controller, a 915-MHz communication link and a 2.4-GHz communication link.

    FIGURE 1. Setup to test for GPS RFI.
    FIGURE 1. Setup to test for GPS RFI.

    A GPS antenna was placed outside and inside the UAS at common antenna locations. The antenna was connected to a high-performance GPS single-frequency-receiver evaluation kit and a spectrum analyzer. To enhance the effects and signals, a 40-dB inline amplifier was connected before the signal was split.

    Three tests were carried out in this case study:

    • In a reference test, the antenna was placed on the outside of the airframe and the UAS was not powered on.
    • With the UAS power remaining off, the antenna was placed inside the airframe to see how much the signal was attenuated (see FIGURE 2).
    • With the antenna still inside the airframe, the UAS was powered on and all systems on the UAS were running.
    FIGURE 2. Inside the UAS (including the GPS antenna).
    FIGURE 2. Inside the UAS (including the GPS antenna).

    The results from the receiver can be seen in FIGURES 3 and 4. Figure 3 shows that the number of satellites being tracked by the GPS receiver did not change between tests.

    FIGURE 3. Satellites tracked by the evaluation-kit receiver.
    FIGURE 3. Satellites tracked by the evaluation-kit receiver.
    FIGURE 4. C/N0 values for different antenna and power configurations.
    FIGURE 4. C/N0 values for different antenna and power configurations.

    However, Figure 4 shows C/N0 for each test, and a clear difference can be seen (up to 10-dB difference from the case where the antenna was in the same location but with the UAS on and off). While this difference did not affect the receiver’s ability to provide a position solution, the accuracy was likely degraded due to the RFI. In a real-world scenario, this could lead to the user not noticing the presence of RFI, since the receiver is still able to output a position.

    TABLE 1 shows some metrics calculated from the GPS receiver data. The table clearly shows a drop in C/N0 values when the UAS is powered on.

    Table 1. Calculated values.
    Table 1. Calculated values.

    The results from the spectrum analyzer further show the effects of turning the UAS and its equipment on. FIGURE 5 shows the frequency spectrum using an average of 50 sweeps centered at 1575.42 MHz (GPS L1) with a bandwidth of 30 MHz for the case when the antenna was inside the airframe and the UAS was switched off. Due to improper initial calibration, the absolute values of the measurements are incorrect, and should be increased by 9 dBm. However, the relative measurements are still valid. FIGURE 6 shows the same setup for the spectrum analyzer but with all the UAS equipment on with the same caveat about the absolute values.

    By comparing Figures 5 and 6, it is clear that the noise floor rises significantly when the UAS and its equipment is switched on. The GPS “bump” that was visible in the center of Figure 5 is no longer visible when the UAS is switched on in Figure 6.

    FIGURE 5. RF spectrum when the antenna is inside the airframe, UAS switched off. See text concerning y-axis scale.
    FIGURE 5. RF spectrum when the antenna is inside the airframe, UAS switched off. See text concerning y-axis scale.
    FIGURE 6. RF spectrum when the antenna is inside the airframe, UAS switched on (all systems running). See text concerning y-axis scale.
    FIGURE 6. RF spectrum when the antenna is inside the airframe, UAS switched on (all systems running). See text concerning y-axis scale.

    RTK Positioning

    RTK positioning is a high-accuracy GNSS positioning method that involves a base station and one or more rovers. The receivers operate in two distinct modes, fix or float. When a receiver is in float mode, the number of integer wavelengths in the carrier-phase measurements has not been resolved yet. In fixed mode, these have been resolved. This is also known as ambiguity resolution. The accuracy is greatly improved if ambiguities are resolved to their correct integer values. During dynamic cases (and even sometimes during static cases), the receiver may change between the two modes repeatedly.

    RTK for UAS. RTK positioning can be very useful for UAS, as it can provide a better accuracy in a lot of cases compared to traditional positioning. It can be used for navigational purposes, or for positioning of scientific payloads carried on board a UAS.

    RTK use on UAS is currently limited, in part due to the number of challenges associated with it. These include the size and weight issue for smaller UAS. Space is limited on board smaller UAS, and the available payload is also limited. RTK systems require more equipment than a regular GNSS system and therefore require more space and weight.

    There is also the issue of cost for smaller UAS. To get quick, high-precision RTK positioning, a dual-frequency receiver is desirable, but such a system is often expensive and could deny a wide sector of the market access to such receivers. Researchers have performed some experiments with an L1-only RTK receiver and show that it could be possible to use such a system for UAS.

    The experiments to be discussed in this article assume that the receivers being tested are candidates for possible UAS use. The high-performance GPS single-frequency-receiver evaluation kit used in the RFI tests is considered the prime candidate, as it is a common receiver found on UAS and is relatively cheap and lightweight.

    As shown in the previous RFI section, it is possible for RFI to be present and for it to lower the C/N0 without affecting the number of satellites tracked. This could lead to the user being initially unaware of the RFI, and could potentially be a problem for RTK positioning as carrier-phase measurements are more easily disrupted.

    Dynamic RTK Experiment. We performed an experiment to evaluate the performance of RTK in a real-world scenario that could be comparable to the use of RTK on a UAS. A comparison between RTK positioning and standard pseudorange-based positioning, essentially the GPS Standard Positioning Service (SPS), was also carried out for one of the receivers. RFI effects were not measured during the experiment.

    Almost all post-processing (and some data capturing) was done using RTKLIB, a free and open source GNSS software suite. RTKLIB is modular and can be used at any stage in GNSS applications. The software is available at rtklib.com.

    Three receivers were compared: the previously discussed high-performance GPS single-frequency-receiver evaluation kit; a low-cost, high-performance GPS receiver with RTK functionality; and a professional-grade multi-GNSS multi-frequency RTK survey receiver. As the low-cost receiver is marketed for UAS use, it was of interest to see how the receiver compared to the others in a dynamic case. The evaluation-kit receiver was of interest due to similar receivers often being used on UAS today. The professional-grade receiver was of interest since it is a high-end receiver capable of receiving multiple constellations and frequencies. The experiment was performed to simulate some of the conditions that might be experienced on UAS. The most approximate test vehicle that was available at the time was a car.

    The receivers were set up to capture GPS signals only. The low-cost and evaluation-kit receivers are only capable of receiving the L1 signal, and were set up accordingly. The professional-grade receiver was set up to capture the L1, L2 and L5 signals. A truth reference for the test vehicle was needed for comparison, and for this we used a multi-frequency receiver with an inertial measurement unit (IMU). The benefit of the IMU is that it contains gyros and accelerometers that can capture very precise movements at times when GNSS signals might not be available (during periods of sky blockage for example).

    However, due to the gyros drifting, the IMU needs to be updated with GNSS data every few minutes to give an accurate solution. The receiver was configured to capture GPS L1+L2+L5, GLONASS L1+L2 and WAAS. The GNSS data was then post-processed in precise point positioning (PPP) mode with data from several nearby stations. The GNSS PPP data was then smoothed and combined with the IMU data to form a GNSS PPP plus IMU solution. It was assumed that the GNSS receiver and IMU gave a correct solution at all times. A diagram of the setup can be seen in FIGURE 7.

    FIGURE 7. Diagram of the setup of dynamic RTK experiment.
    FIGURE 7. Diagram of the setup of dynamic RTK experiment.

    The car with the equipment was driven around the town and campus at the University of Colorado in Boulder. The path included a parking lot (a wide open area), parts of a highway (an open area), major roads (open area with parts covered by trees), residential areas (with many trees covering the sky) and a parking garage (with complete sky blockage). The parking garage was entered towards the end of the experiment.

    The receiver data was post-processed using an RTKLIB setup to process the data as if it was received in real time. A multi-frequency multi-GNSS receiver was set up with a roof-mounted antenna at the University of Colorado to collect data for the duration of the experiment, and this data was later used as base-station data for the RTK calculations.

    The low-cost receiver had a hard time regaining a position solution, while the evaluation-kit receiver did slightly better. The professional-grade receiver only lost a clear position for about 10 seconds. This behavior agrees with expectations: the low-cost receiver is new and is being updated regularly with new software, and the evaluation-kit receiver is known for being able to perform well under poor conditions. The professional-grade receiver has the support of additional GPS signals, which could explain why it was the first to regain a good position solution.

    TABLE 2 shows some of the values calculated from the experiment, which further confirms that the evaluation-kit receiver is able to calculate a position more often than the professional-grade receiver, but a more inaccurate position. In the table, “availability” is defined as how many data points the receiver was able to capture, divided by how many would have been captured if the receiver could capture data at all times. “RTK solution” is how often the captured data was sufficient to calculate an RTK solution. “Fix solution” is defined as how often the ambiguities could be resolved out of the available RTK data points, and “float solution” is how often the ambiguities could not be resolved out the available RTK data points. The comparison of the results using SPS versus the RTK technique for the evaluation-kit receiver is interesting. Using RTK increases the accuracy only slightly, but not as much as anticipated before the test was performed.

    Table 2. Tabulated results from the dynamic RTK experiment (N/A = not applicable).
    Table 2. Tabulated results from the dynamic RTK experiment (N/A = not applicable).

    Conclusions

    GNSS is viable for UAS navigation, but it remains to be seen how policymakers will decide to regulate its use for this application. Many existing and emerging technologies could prove useful in increasing not only the reliability, but also the accuracy, of the GNSS engine on board a UAS.

    Although UAS share many similarities with traditional manned aircraft, by their nature they are unmanned and would not pose the same immediate risk for significant loss of life if an accident were to occur. This, coupled with the fact that UAS can vary greatly in size and operational requirements, leaves the possibility open to using different certification requirements of GNSS navigation for different UAS.

    RFI. The RFI experiment showed a considerable impact on C/N0 from the evaluation-kit receiver. While the number of satellites tracked remained constant between tests, it is possible that during slightly different operating conditions (different UAS and/or receivers, other onboard equipment and so on), the impact could have been more severe.

    RTK for UAS. RTK systems are complex, but they have some clear advantages to traditional pseudorange-based standalone GNSS, with regard to accuracy. From the results of using the evaluation-kit receiver during the dynamic RTK experiment, it seems as though it would be only advantageous if RTK could be used on a UAS. The only visible difference between the SPS and RTK operation in the experiment was a slight increase in accuracy. The availability of the measurements (that is, how much data was available) was the same for when the receiver used SPS versus RTK. However, the slight increase in accuracy might not be sufficient to compel operators to use the RTK technique for UAS navigation, as additional equipment and setup will be required.

    However, when using a receiver with more frequencies, such as the professional-grade receiver, we saw a great increase in accuracy. This receiver was quite large and heavy, and is most likely outside the budget considerations for many smaller UAS setups. It is also likely that using a dual-frequency receiver that is similar to the evaluation-kit receiver in size and weight could improve accuracy, and this should be tested in the future.

    Further investigations should be performed to determine if the RTK technique could be used successfully for UAS navigation. A natural next step would be to place an RTK setup on an actual UAS and to test how RFI affects the RTK measurements.

    Acknowledgments

    This article is based on the paper “GNSS/GPS Robustness for UAS” presented at The Institute of Navigation 2016 International Technical Meeting. The research was carried out in cooperation with the Research and Engineering Center for Unmanned Vehicles in the Department of Aerospace Engineering Sciences at the University of Colorado, Boulder.

    JOSHUA STUBBS has an M.Sc. in space engineering, with a focus on aerospace, from Luleå University of Technology in Sweden. In 2015, he did his master’s thesis work at the University of Colorado, Boulder, where he focused on GNSS applications for UAS.

    DENNIS M. AKOS completed his Ph.D. degree in electrical engineering at Ohio University, Athens, Ohio, within the Avionics Engineering Center. He is a faculty member with the Aerospace Engineering Sciences Department at the University of Colorado and maintains visiting appointments at Stanford University and Luleå University of Technology.

    Further Reading

    • Authors’ Conference Paper

    “GNSS/GPS Robustness for UAS” by J. Stubbs and D. Akos in Proceedings of ITM 2016, the 2016 International Technical Meeting of The Institute of Navigation, Monterey, Calif., Jan. 25–28, 2016, pp. 485–493. 

    • Procedures and Standards for Aviation

    Integration of Civil Unmanned Aircraft Systems (UAS) in the National Airspace System (NAS) Roadmap, First Edition, Federal Aviation Administration, U.S. Department of Transportation, Washington, DC, 2013.

    Global Positioning System Wide Area Augmentation System (WAAS) Performance Standard, First Edition, Federal Aviation Administration, U.S. Department of Transportation, Washington, DC, 2008.

    • Radio-Frequency Interference and GNSS

    “Radio Frequency Devices” in Code of Federal Regulations, Title 47 (Telecommunication), Chapter I (Federal Communications Commission), Subchapter A (General), Part 15, U.S. National Archives and Records Administration, Washington, DC, 2016.

    “The Impact of RFI on GNSS Receivers” by F. Dovis in Expert Advice, GPS World, Vol. 26, No. 4, April 2015, pp. 50–51.

    “Interference Heads-Up: Receiver Techniques for Detecting and Characterizing RFI” by P.W. Ward in GPS World, Vol. 19, No. 6, June 2008, pp. 64–73.

    “Interference, Multipath, and Scintillation” by P.W. Ward, J.W. Betz and C.J. Hegarty, Chapter 6 in Understanding GPS: Principles and Applications, 2nd ed., E.D. Kaplan and C.J. Hegarty, Eds., Artech House, Boston and London, 2006.

    “Analytical Derivation of Maximum Tolerable In-Band Interference Levels for Aviation Applications of GNSS” by C.J. Hegarty in Navigation, Vol. 44, No. 1, Spring 1997, pp. 25–34, doi: 10.1002/j.2161-4296.1997.tb01936.x.

    “A Growing Concern: Radiofrequency Interference and GPS” by F. Butsch in GPS World, Vol. 13, No. 10, Oct. 2002, pp. 40–50.

    “Interference: Sources and Symptoms” by R. Johannessen in GPS World, Vol. 8, No. 11, Nov. 1997, pp. 44–48.

    • Vulnerability, Integrity and Robustness of GNSS

    “Robustness to Faults for a UAV: Integrated Navigation Systems Using Parallel Filtering” by T. Layh and D. Gebre-Egziabher in GPS World, Vol. 26, No. 5, May 2015, pp. 40-48.

    “GPS Integrity and Potential Impact on Aviation Safety” by W.Y. Ochieng, K. Sauer, D. Walsh, G. Brodin, S. Griffin and M. Denney in the Journal of Navigation, Vol. 56, No. 1, Jan. 2003, pp. 51–65, doi: 10.1017/S0373463302002096. 

    Vulnerability Assessment of the Transportation Infrastructure Relying on the Global Positioning System, Final Report, prepared by the John A. Volpe National Transportation Systems Center for the Office of the Assistant Secretary for Transportation Policy, U.S. Department of Transportation, August 2001.

    • Real-Time Kinematic Positioning for Unmanned Aircraft Systems

    “A Precise, Low-Cost RTK GNSS System for UAV Applications” by W. Stempfhuber and M. Buchholz in the Proceedings of UAV-g 2011, the 2011 Conference on Unmanned Aerial Vehicles in Geomatics, Zurich, Switzerland, Sept. 14–16, 2011, International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. XXXVIII 1/C22, pp. 289–293, 2011.

  • Innovation: Clarifying the ambiguities

    Innovation: Clarifying the ambiguities

    Examining the interoperability of precise point positioning products

    By Garrett Seepersad and Sunil Bisnath

    INNOVATION INSIGHTS with Richard Langley
    INNOVATION INSIGHTS with Richard Langley

    CARRIER PHASE. We’ve all heard the term and recognize it as a more precise observable for GNSS positioning, navigation and timing than code phase, more commonly called the pseudorange. The carrier-phase measurement is the phase of the received continuous radio-frequency sinusoidal waveform that “carries” the pseudorandom noise ranging codes and the navigation messages. The underlying carrier of a satellite signal can be recovered and its phase measured at regular intervals by the receiver once it locks onto the signal.

    As long as there is no interruption in the carrier tracking, the receiver can generate a continuous series of measurements of the cumulative phase or cycle count including fractional cycles. The initial value at signal lock-on is arbitrary. Ideally, it would equal the exact number of cycles (and fractional cycle) of the waveform between the antenna of the satellite and the antenna of the receiver.

    If that was the case, then we could simply multiply that cycle count by the wavelength of the carrier in meters, say, and we would have the initial geometric distance (or range) to the satellite. Then we could update this value as time progresses with the receiver’s measurements and have a continuous sequence of range values, which, when corrected for satellite and receiver clock errors and other effects, would allow the receiver’s position to be accurately determined. But because we don’t know the true initial cycle count, the carrier-phase measurements are ambiguous by a constant integer amount (when measured in cycles). This characteristic of the observable is referred to as the integer ambiguity.

    It was realized early in the development of GPS, that if the integer ambiguity of carrier-phase measurements could be resolved, we would have a very precise observable for positioning, navigation and timing, some two orders of magnitude more precise than the code-based pseudorange. Instead of measurement precisions of tens of centimeters, we could have precisions of tenths of millimeters.

    In the early 1980s using the few test GPS satellites in orbit at the time, surveyors and geodesists developed a series of clever techniques that allowed them to make use of carrier-phase measurements to determine the baseline between pairs of receivers by estimating combinations of the ambiguities as unknowns along with the receiver relative coordinates or, for short baseline work, use a calibration procedure before starting a survey.

    Now jump forward a few decades. While it is still common practice to double difference carrier-phase measurements between pairs of satellites and pairs of receivers to determine relative receiver coordinates, the technique of precise point positioning or PPP, which uses carrier-phase (and pseudorange) measurements from a single user receiver, is growing in popularity. But, the integer ambiguity problem is still with us and has to be addressed by the analysis software. The ambiguities are often estimated as real- rather than integer-valued quantities, in part because of the contribution of satellite hardware biases to the carrier-phase measurements.

    However, it is possible to resolve the ambiguities to integer values by using PPP ambiguity resolution products distributed by several research organizations. In this month’s column, we take a look at the interoperability of these products for increasing the reliability and precision of position solutions and reducing the time required for a solution to converge to a required level of accuracy.

    Ambiguity resolution in precise point positioning (hereafter, PPP-AR) requires that hardware delays within the GPS measurements be mitigated, which will then allow for resolution of the integer ambiguities within the carrier-phase measurements. Resolution of these ambiguities converts the carrier-phases into precise “range” measurements, with measurement noise at the centimeter-to-millimeter level compared to the meter-to-decimeter level of the C/A- and P(Y)-code pseudoranges. If the ambiguities could be isolated and estimated as integers, then that information could be exploited to accelerate PPP convergence to provide, for example, few-centimeter horizontal positioning accuracy within tens of minutes or even minutes from a cold start.

    Integer ambiguity resolution of measurements from a single receiver can be implemented by applying additional satellite products, where the fractional component — representing the satellite hardware delay — has been separated from the integer ambiguities in a network solution. One method of deriving such products is to estimate the satellite hardware delay by averaging the fractional parts of steady-state real-valued or floating-point (float) ambiguity estimates, and the other is to estimate the receiver clock offset in the pseudorange and carrier-phase measurements independently by fixing the undifferenced ambiguities to integers in advance.

    Similar positioning performances have been demonstrated among three approaches of different groups or agencies using the two methods: FCB (Fractional Cycle Bias), IRC (Integer Recovery Clock) and DC (Decoupled Clock). For the PPP user, the mathematical model is similar. The different PPP-AR products contain the same information and, as a result, should allow for one-to-one transformations, allowing interoperability of the PPP-AR products. The advantage of interoperability of the various products is to allow the PPP user to transform independently generated products to obtain multiple fixed solutions of comparable precision and accuracy, with no changes to the core PPP user software. An overview of the different providers and their products is presented in FIGURE 1.

    FIGURE 1. Public providers of PPP-AR products. (Source: Richard Langley)
    FIGURE 1. Public providers of PPP-AR products. (Source: Richard Langley)

    The ability to use different products would increase the reliability of a positioning solution in real-time processing, for example. If there was an outage in the generation of a particular PPP-AR product, a user could instantly switch streams to a different provider. The research presented in this article examines the PPP-AR products generated from the FCB and IRC models that have been transformed into the DC format and applied within a PPP user solution. The novelty of the research is the solution analysis using the transformed product. We examine the convergence time (time-to-first-fix and time to a pre-defined performance level), position precision (repeatability), position accuracy and solution outliers. The temporal and spatial behavior of these estimated terms is examined for the different products applied to understand the unmodeled effects responsible for incorrect solution fixes.

    The Role of PPP-AR Products

    The standard GPS pseudorange ( Photo:and Photo: ) and carrier-phase (Photo:) observation equations are given by

    Photo:(1)

    where i denotes the frequency-dependent GPS measurements for frequencies L1 or L2, s represents the tracked satellite, r represents the receiver, P2-EQ  is the geometric range between the satellite s and the user position, T is the tropospheric delay, I-EQ is the first order slant ionospheric delay, γi is the frequency dependent coefficient, dts is the satellite clock and D-EQ is the pseudorange hardware delay. N-EQ is the ambiguity term and D2-EQ is the carrier-phase hardware delay, both of which are expressed in cycles and scaled by the wavelength λi . The error sources can be grouped into two main components, the geometric parameters and the timing parameters. Included in the timing parameters are the clock offsets and the hardware delay terms. Understanding the role of the hardware delays is critical in isolating the integer ambiguities.

    The following equations illustrate the effects of not mitigating the hardware delay. The set of equations was simplified by combining the clock and hardware delay parameters. Processing the carrier-phase measurements with the pseudoranges (code measurements) ensures that the pseudoranges provide a reference for the carrier-phase measurements and for the clock parameters. An implication of this is the manifestation of the hardware delay present in both the estimated clock parameters and the ambiguities.

    EQ2-Inn Source: Richard Langley(2)

    By not mitigating the hardware delay terms (D-EQ andD2-EQ), they are absorbed within the estimated ambiguity terms, rendering the integer nature of the ambiguity term inaccessible. The user observation equations do not contain sufficient information to solve for an integer-ambiguity-resolved user position. Ambiguity resolution would only become possible if information about the satellite hardware delays were provided to the user. The receiver hardware delay can be removed by single differencing (between satellites).

    In the following section, we present an overview of the different public providers of products that enable PPP-AR, their products and how they are applied to the PPP user equations.

    Public PPP-AR Products

    Currently, there are three main public providers of products that enable PPP-AR. These are Scripps Institution of Oceanography, which provides regional real-time FCB products; Natural Resources Canada (NRCan), which provides post-processed and real-time DC products; and Centre National d’Etudes Spatiales (CNES), which provides post-processed and real-time IRC products.

    FCB Model. The initial application of ambiguity resolution to PPP was the Uncalibrated Phase Delay (UPD) model, now called the Fractional Cycle Bias (FCB) model. The FCB method estimates the hardware delay by averaging the fractional parts of the steady-state float ambiguity estimates to be removed from common satellite clock estimates. The FCB products consist of Photo: , as1-EQ and Photo:, where WN indicates the Melbourne-Wübbena (widelane ambiguity) combination and IF indicates the ionosphere-free linear combination.

    DC Model. The underlying concept of the decoupled clock model is that the carrier-phase and pseudorange (code) measurements are not synchronized with each other at an equivalent level of precision. The timing of the different observables must be considered separately if they are to be processed together rigorously. The decoupled clock model is a reformulation of the ionosphere-free carrier-phase and pseudorange observation equations. When combined with the narrowlane pseudorange and the widelane phase, ambiguity resolution is possible. The DC products transmitted to the user are otsif, dtsif-EQ and oswn.

    IRC Model. The integer recovery clocks estimate constant daily widelane pseudorange/carrier-phase hardware delays by averaging arc-dependent estimates. Using float-solution estimates of the range parameters, narrowlane ambiguity resolution is performed and the ionosphere-free satellite carrier-phase clocks are estimated. In 2014, the format of the IRC products was changed from Photo: ,dtsif-EQ and oswn to a state-space uncombined representation, such that the satellite hardware delay is provided for each observable (Photo:, Photo:) and satellite pseudorange clock (dtsif-EQ).

    Summary. The three publicly provided products to enable real-time PPP-AR are listed in TABLE 1 along with their primary characteristics. The table summarizes the various measurements used, different products transmitted and the varying data rate of the transmitted products.

    TABLE 1. Comparison of different publicly provided real-time products to enable PPP-AR.
    TABLE 1. Comparison of different publicly provided real-time products to enable PPP-AR.

    Product Transformation

    While the different strategies (FCB, FC, IRC) make different assumptions, there are fundamental similarities among them. The mathematical models for the PPP user are similar, as the different products contain the same information and as a result would allow for a one-to-one transformation. The following sections examine the transformation matrix used to transform the IRC and FCB products to the DC format (see Figure 2.)

    FIGURE 2. Transformation of FCB and IRC products to DC input format. Source: Richard Langley
    FIGURE 2. Transformation of FCB and IRC products to DC input format.

    FCB. The FCB products consist of dtsif-EQ, as1-EQand Photo:, which are estimated in the network solution using International GNSS Service (IGS) ultra-rapid orbit and clock products. The fundamental difference between the FCB and DC products is that as1-EQ is not determined in the DC method, but assimilated within the clock estimates. Also, Photo: is assumed constant over a 48-hour time period, whereas in the DC method oswn the is neither constrained nor smoothed. Here is the transformation matrix used to transform from FCB to the DC model:

    Photo:  (3)

    where z1 is the single-differenced L1 ambiguity and zw is the single-differenced widelane ambiguity.

    IRC. The original IRC products used a decoupled-like approach, where independent clocks (dtsif-EQ and otsif) were transmitted for the pseudorange and carrier-phase measurements and widelane satellite hardware delays (oswn) were estimated. A redefined model was presented in 2014, where a state-space approach was adopted such that one phase bias per phase observable ( OSI-EQ and DSI-EQ) was identified and broadcast. The primary benefit of such an approach is interoperability, allowing the network and user side to implement different ambiguity resolution methods. Here is the transformation matrix used to transform from IRC to the DC model:
    (4)

    where d12 represents I-EQ-4a Source: Richard Langley.

    Analysis of Transformed Products. In FIGURES 3 to 5, we present the FCB and IRC products transformed to the DC format. The presented format was selected because it represents the nature of the transmitted real-time DC products. The philosophy of the DC model refers to the satellite hardware delay as an unmodeled timing error and, as such, the satellite carrier-phase clocks in Figure 3 are in units of seconds and in Figures 4 and 5 are in units of nanoseconds. Nanoseconds were selected because of the magnitude of the relative satellite pseudorange and widelane clock error, as well as being more bandwidth efficient.

    FIGURE 3. Transformed FCB and IRC satellite carrier-phase clock correction on day-of-year 28 of 2015 for PRN 10. DC was included for comparison. Source: Richard Langley
    FIGURE 3. Transformed FCB and IRC satellite carrier-phase clock correction on day-of-year 28 of 2015 for PRN 10. DC was included for comparison.

    Figure 3 illustrates the FCB and IRC products transformed to the DC satellite carrier-phase clock. The satellite-clock corrections presented were not differenced with respect to a reference satellite, to illustrate their differences in an absolute nature. If the clocks are differenced, in a relative nature, they are equivalent. The data gaps in the FCB products are expected because of the regional nature of the products. Unlike the DC and IRC products, the FCB pseudorange clocks illustrate different trends such as those between hours 3 and 4. The noise illustrated in the IRC clock can be removed either by filtering or by differencing with respect to another satellite clock.

    In Figure 4, we present the relative satellite clock error ( dtsif-EQ −  otsif ) for the transformed FCB (upper subplot) and IRC (lower subplot) products. For the original DC product (middle subplot), a simple moving average filter was applied with a bin size of five minutes to reduce the noise and illustrate the underlying equipment delay. The relative satellite clock error represents the difference between the pseudorange and carrier-phase clocks. The distinct differences of the products are easily visible, such as the filtering present within FCB and IRC products in contrast to the DC. The underlying relative satellite clock error is also significantly different in contrast to the DC product, such that FCB and IRC have an average relative satellite clock error of -0.041 ± 0.101 nanoseconds and -0.645 ± 0.005 nanoseconds, respectively, whereas the DC has an average of 8.465 ± 1.546 nanoseconds.

    FIGURE 4. Transformed FCB and IRC products to code-phase relative clock correction on day-of-year 28 of 2015 for PRN 10. DC was included for comparison. Linear trend has been removed. Source: Richard Langley
    FIGURE 4. Transformed FCB and IRC products to code-phase relative clock correction on day-of-year 28 of 2015 for PRN 10. DC was included for comparison. Linear trend has been removed.

    Figure 5 shows the relative satellite widelane clock error for the transformed FCB (upper subplot) and IRC (lower subplot) products. For the original DC product (middle subplot), a simple moving average filter was applied with a bin size of five minutes, to reduce the noise and illustrate the underlying equipment delay. The relative satellite clock error represents the difference between the widelane clocks and phase clocks. Similar to the relative satellite clock error, the differences in the transformed relative satellite widelane clock error are noticeable. As expected, the transformed FCB has a constant widelane estimate of -0.24 nanoseconds, whereas the transformed IRC and DC have an average widelane estimate of 0.0589 ± 0.002 and 3.6704 ± 0.34 nanoseconds, respectively.

    FIGURE 5. Transformed FCB and IRC products to code-phase relative widelane clock correction on day-of-year 28 of 2015 for PRN 10. DC was included for comparison. Linear trend has been removed. Source: Richard Langley
    FIGURE 5. Transformed FCB and IRC products to code-phase relative widelane clock correction on day-of-year 28 of 2015 for PRN 10. DC was included for comparison. Linear trend has been removed.

    Performance of Transformed Products

    One of the metrics we can use to examine the performance of the transformed products is the quality of the solution in the position domain. The solutions were examined with respect to the time for convergence to a pre-defined threshold and position stability. We used five stations from the Scripps Orbit and Permanent Array Center (SOPAC) network for days 23 to 30 of 2015. These five stations were selected because of the regional nature of FCB products provided by SOPAC. We show the results for site Brand Basin (BRAN) on day-of-year 30 of 2015 as it reflects the performance of the whole dataset processed.

    In FIGURES 6 to 8, we show the varying convergence periods at the site BRAN on day-of-year 30 for the “float” and “fixed” solutions using the different PPP-AR products, where fixed means the ambiguity-resolved solution and float the unresolved solution. Figure 6 uses the decoupled clock products, and the fixed solution performs as expected. After a few minutes, the solution attains the correct ambiguity candidate, and a fixed state is maintained.

    FIGURE 6. Position errors for site BRAN located in Burbank, Calif., on day-of-year 30 of 2015 illustrating the difference between the float and fixed solutions using the DC products. Source: Richard Langley
    FIGURE 6. Position errors for site BRAN located in Burbank, Calif., on day-of-year 30 of 2015 illustrating the difference between the float and fixed solutions using the DC products.
    FIGURE 7. Position errors for site BRAN located in Burbank, Calif., for day-of-year 30 of 2015 illustrating the difference between the float and fixed solutions using the IRC products. Source: Richard Langley
    FIGURE 7. Position errors for site BRAN located in Burbank, Calif., for day-of-year 30 of 2015 illustrating the difference between the float and fixed solutions using the IRC products.
    FIGURE 8. Position errors for site BRAN located in Burbank, Calif., for day-of-year 30 of 2015 illustrating the difference between the float and fixed solutions using the FCB products. Source: Richard Langley
    FIGURE 8. Position errors for site BRAN located in Burbank, Calif., for day-of-year 30 of 2015 illustrating the difference between the float and fixed solutions using the FCB products.

    The performance of the fixed solution using the IRC products is depicted in Figure 7. Initial convergence is similar to the DC products in the northing and easting components where a fixed state is attained after a few epochs. In the up component, the solution quality deteriorates after 30 minutes. What is also easily visible is the solution sensitivity to changes in the satellite geometry. As the number of satellites changes, the fixed ambiguities change, causing datum shifts in the user solution.

    Similar trends were also observed when the transformed FCB products were used, with the results presented in Figure 8. The solution deterioration is most evident in the easting component, as the incorrect integer candidate is selected.

    Challenges of Interoperability

    Interoperability of the various PPP-AR products is a challenging task because of the different qualities of the publicly available products, limited literature documenting the conventions adopted within the network solution of the providers, and unclear definitions of the corrections.

    In TABLE 2, we summarize the various qualities of the products we used in the study, showing why it was challenging to perform a consistent comparison. IRC products were generated from a network of reference stations globally distributed and in real time. Similar to the IRC products, the DC products were generated from a global network of solutions, but post-processed, and the FCB products were based on a regional network of reference stations, but were available in real time. Post-processed orbits and clocks have an accuracy of ~2.5 centimeters and ~75 picoseconds, respectively, whereas the predicted half of ultra-rapid orbits and clocks have an accuracy of ~5 centimeters and ~3 nanoseconds, respectively. While it is evident in the existing literature that PPP-AR is possible in real time, the solution is rather sensitive to changes experienced by the PPP user solution, such as varying local conditions and satellite geometry. The sensitivity is illustrated in Figures 7 and 8 with solution jumps typically occurring when there is a change in the number of satellites.

    TABLE 2. Summary of the different quality of products provided by public providers to enable PPP-AR. Source: Richard Langley
    TABLE 2. Summary of the different quality of products provided by public providers to enable PPP-AR.

    The general assumption when PPP-AR products are estimated within a network is that the PPP user would follow similar conventions when using the products. Consequences of different conventions adopted may result in incorrect ambiguities being resolved. For example, if inconsistent satellite antenna conventions were adopted between the network and user, then when phase wind-up corrections are applied, fractional cycles would be introduced. The introduced fractional cycles would result in incorrect ambiguities being resolved. FIGURE 9 shows the orientation of the spacecraft body frame for GPS Block IIR/IIR-M satellites adopted in the IGS axis convention (subplot (a)) and those provided in the manufacturer specifications (subplot (b)). The difference between the manufacturer specifications and IGS axis convention is the orientation of the x- and y-axes.

    FIGURE 9. Orientation of the spacecraft body frame for GPS Block IIR/IIR-M satellites as (a) adopted within the International GNSS Service axis convention, and (b) those provided in the manufacturer specifications. Source: Richard Langley
    FIGURE 9. Orientation of the spacecraft body frame for GPS Block IIR/IIR-M satellites as (a) adopted within the International GNSS Service axis convention, and (b) those provided in the manufacturer specifications.

    Conclusions

    The mathematical model for the PPP user is similar for all PPP-AR products, as the different products contain the same information and, as a result, would allow for one-to-one transformations, allowing interoperability of the PPP-AR products. Interoperability of the various PPP-AR products would allow the PPP user to transform independently generated PPP-AR products to obtain multiple fixed solutions of comparable precision and accuracy. The ability to provide multiple solutions would increase the reliability of the solution such as in real-time processing: if there was an outage in the generation of the PPP-AR products, the user can instantly switch streams to a different provider.

    We looked at the PPP-AR products provided by three organizations and examined position solutions for a set of stations in the SOPAC network with respect to convergence time to the pre-defined threshold and position stability.

    Using the decoupled clock products, we found that the fixed solutions performed as expected. After a few minutes, a solution attains the correct ambiguity candidate and a fixed state is maintained. Unlike the fixed solutions using the decoupled clock products, instantaneous convergence was not attained in the horizontal and vertical components when the transformed IRC and FCB products were used. The ambiguity-resolved solutions were sensitive to changes in the satellite geometry. As the number of satellites change, the fixed ambiguities change, causing datum shifts in the user solution.

    The unstable solutions from both transformed products are attributed to the magnitude of the relative satellite code and widelane clock errors. Additional refinement of the transformation model is required as the satellite hardware delay has not been completely mitigated. Mismodeling of the hardware delay was absorbed by the ambiguity terms, causing incorrect fixed solutions.

    Future Research

    Future prospective research includes refinement of the proposed transformation models to include the mismodeled effects, thus providing the user with a more reliable solution. The functional model needs to be further examined to ensure that the corrections were applied consistently. Further analysis of the instability of the user solution is required, as solution jumps typically occur when there are changes in the number of satellites tracked. Also to be analyzed are the post-fit residuals, to examine the effects of mismodeling. The temporal and spatial behavior of the estimated terms will be examined for the different products used to understand the unmodeled effects that introduce incorrect solution fixes. We would also consider increasing the number of reference stations to further test the reliability of the transformed products under varying user conditions.

    Acknowledgments

    We acknowledge Paul Collins, Jianghui Geng and Denis Laurichesse for our valuable discussions and their suggestions. The research was funded by the Natural Sciences and Engineering Research Council of Canada. The results we have presented were derived from data and products provided by Natural Resources Canada, Scripps Institution of Oceanography, Centre National d’Etudes Spatiales and the International GNSS Service.

    This article is based on the paper “Examining the Interoperability of PPP-AR Products” presented at ION GNSS+ 2015, the 28th International Technical Meeting of The Satellite Division of the Institute of Navigation held in Tampa, Fla., Sept. 14–18, 2015.

    GARRETT SEEPERSAD is a Ph.D. candidate at York University, Toronto, Canada, in the Department of Earth and Space Science and Engineering. He completed his B.Sc. in geomatics at the University of the West Indies and his M.Sc. in geomatics engineering at York University. His area of research currently focuses on the development and testing of PPP functional, stochastic and error-mitigation models.

    SUNIL BISNATH is an associate professor in the Department of Earth and Space Science and Engineering at York University. His research interests include geodesy and precise GNSS positioning and navigation.

    Further Reading

    • PPP Ambiguity Resolution Techniques

    “Review and Principles of PPP-RTK Methods” by P.J.G. Teunissen and A. Khodabandeh in Journal of Geodesy, Vol. 89, No. 3, 2014, pp. 217–240, doi: 10.1007/s00190-014-0771-3.

    “A Novel Un-differenced PPP-RTK Concept” by B. Zhang, P.J.G. Teunissen and D. Odijk in Journal of Navigation, Vol. 64, Supplement S1, 2011, pp. S180–S191, doi: 10.1017/S0373463311000361.

    “Isolating and Estimating Undifferenced GPS Integer Ambiguities” by P. Collins in Proceedings of the 2008 National Technical Meeting of The Institute of Navigation, San Diego, Calif., January 28–30, 2008, pp. 720–732.

    “Resolution of GPS Carrier-Phase Ambiguities in Precise Point Positioning (PPP) with Daily Observations” by M. Ge, G. Gendt, M. Rothacher, C. Shi and J. Liu in Journal of Geodesy, Vol. 82, No. 7, 2008, pp. 389–399, doi: 10.1007/s00190-007-0187-4.

    “Integer Ambiguity Resolution on Undifferenced GPS Phase Measurements and Its Application to PPP” by D. Laurichesse and F. Mercier in Proceedings of ION GNSS 2007, the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation, Fort Worth, Texas, Sept. 25–28, 2007, pp. 839–848.

    • PPP-AR Transformation Models

    “Phase Biases for Ambiguity Resolution: From an Undifferenced to an Uncombined Formulation” by D. Laurichesse. An unpublished white paper, Oct. 2014.

    • Precise Point Positioning Algorithms

    Improved Convergence for GNSS Precise Point Positioning by S. Banville, Ph.D. dissertation, Department of Geodesy and Geomatics Engineering, Technical Report No. 294, University of New Brunswick, Fredericton, New Brunswick, Canada. Recipient of The Institute of Navigation 2014 Bradford W. Parkinson Award.

    “Precise Point Positioning: A Powerful Technique with a Promising Future” by S.B. Bisnath and Y. Gao in GPS World, Vol. 20, No. 4, April 2009, pp. 43–50.

  • Innovation: Null-steering antennas

    Innovation: Null-steering antennas

    Assessing the performance of multi-antenna interference-rejection techniques

    Several factors affect the levels of signal rejection using antenna arrays. Our authors describe experiments to assess the bounds the factors impose on its signal rejection capability.

    By James T. Curran, Michele Bavaro and Joaquim Fortuny-Guasch

    INNOVATION INSIGHTS with Richard Langley
    INNOVATION INSIGHTS with Richard Langley

    IT’S ALL PHYSICS. How things work, that is. Well, maybe a little chemistry too in some cases. But I might be a little biased in my opinion given that I’m an applied physicist by training. Radio? Satellite navigation? Yes, the principles of their operation are all governed by physics. Many physicists of my generation started out as radio tinkerers. I’ve recounted in this column before that I built my first radio (from a kit) when I was 14 (not counting the crystal radio that my father helped me to put together when I was 9). Built a few more during high school, got into radio astronomy as an undergraduate, and did a Ph.D. in the application of very long baseline (radio) interferometry to geodesy.

    The great American physicist Richard Feynman was also a radio tinkerer in his youth. He recounts in one of his autobiographical books how he used to fix radios. And because he would approach the task of repairing each non-functioning set by first contemplating why it wasn’t working, he got the reputation of fixing radios by thinking!

    One of Feynman’s special abilities was in explaining how things worked. In fact, he has been called “The Great Explainer.” He authored what is arguably the best physics textbooks ever produced: The Feynman Lectures on Physics. The three-volume set, developed from his Caltech lectures to undergraduates between 1961 and 1964, covers mechanics, radiation, electromagnetism, matter and quantum mechanics. Many students and practicing physicists have learned or re-learned aspects of physics from the famous “red books.” Many more will now thanks to Caltech, which recently put the Lectures on line for anyone to read (feynmanlectures.caltech.edu).

    In this month’s column, we are going to learn about the development of a microprocessor-controlled multi-element GNSS antenna array for interference rejection. While there are many textbooks that describe how multi-element antennas work, Feynman explains their operation in his Lectures from first principles — from the principles of physics.

    The phenomenon governing the behavior of antennas with multiple elements is called interference. If we combine two electromagnetic waves, they will interfere with each other with a result that depends on the phase difference of the waves. The waves might reinforce each other leading to a larger net amplitude, called constructive interference, or partially or fully null each other out, called destructive interference. When we apply this concept to the signals received by a pair of antennas making up an array, we find that the array has directionality and we can have a null in the reception pattern in the directions parallel to the antenna baseline and will be insensitive to signals arriving from those directions. And as Feynman describes in his Lectures, by adding more antennas to the array and “some cleverness in spacing and phasing our antennas,” we can have a fairly narrow pattern null in a chosen direction. In the case of a GNSS antenna array, that direction might be that of a jamming signal and so we can null out the jammer and maintain a positioning capability.

    Several factors affect the levels of signal rejection using antenna arrays. In this article, our authors describe these factors and the experiments they conducted with their microprocessor-controlled array to assess the bounds the factors impose on its signal rejection capability.

    Directional antennas offer a powerful means of achieving signal selectivity when various signal sources observed by a receiver are separated spatially. In the context of GNSS, which must accommodate a mobile receiver observing many moving transmitters, adaptive antennas — or controlled radiation pattern antennas—are an attractive option. The benefits of antenna arrays have been demonstrated both for signal rejection, such as interference and multipath mitigation or anti-spoofing; and for the purposes of gain enhancement, angle-of-arrival, or attitude estimation.

    A number of different factors can influence the achievable levels of signal rejection using antenna arrays. These factors include: the gain and phase stability of the analog radio-frequency (RF) and intermediate-frequency (IF) stages, the linearity of the active analog stages, and the fidelity of the signal-combining stages. Seeking to identify the bound imposed by each of these limiting factors, we have carefully examined the signal rejection capability of an antenna array in our work. The study considers a circular antenna array, consisting of seven passive dual-polarized (right-hand circularly polarized [RHCP] and left-hand circularly polarized [LHCP]) L1-L2 elements. Although signal rejection can be performed both in the analog and in the digital domain, this article focuses only on the analog combination of signals at RF, using a bank of controllable phase shifters and attenuators. We conducted broadcast experiments in a large-diameter anechoic chamber, housing a rotatable central pillar upon which the array is mounted, and two broadcast antennas mounted on movable sleds.

    The results presented here include a precise three-dimensional phase and gain calibration of the antenna array using a network analyzer to explore the properties of antenna elements when placed in close proximity on a common ground plane. Further results include an investigation of the nulling depth achievable by the array via the synchronous broadcast of two GNSS-like code-division multiple access (CDMA) signals from different broadcast antennas. We then extrapolated these results to infer the relative degradation in nulling capability when the receiver’s estimate of the amplitude and phase of the signal to be rejected is poor. Finally, a comparison of analog and digital element combining is explored, with emphasis on the rejection of strong jamming signals.

    This experiment sought to illustrate and quantify the unique benefits and limitations of each technique. In particular, we note that analog combining enjoys high linearity and can accommodate high interference power, but is typically restricted to the use of coarse phase and gain coefficients when combining elements. In contrast, digital combining can offer notably higher gain and phase resolution, but is limited by the dynamic range of the digitizer.

    Antenna Characterization

    The work reported in this article has focused on the use of a seven-element circular antenna array, consisting of dual-polarized (RHCP and LHCP), dual-frequency (L1 and L2) elements. The antenna elements are mounted on a single circular aluminum ground plane 2 millimeters thick and 50 centimeters in diameter, and placed in a hexagonal arrangement at a spacing of 12.5 centimeters, as depicted in FIGURE 1. Because the antennas are passive, and can be used both for transmission and for reception, characterization tests were performed in broadcast mode while the typical receive-mode operation of the array is performed using an in-line low-noise amplifier (LNA) after the antenna.

    The experiments described here were conducted in an anechoic chamber, hemispherical in shape with a diameter of 20 meters, as depicted in FIGURE 2. The array was mounted on a surveyor’s tripod and placed at a known position on a rotatable pillar at the center of the chamber. The chamber contains two sleds, Sled A and B, which can be precisely positioned along an arc through the zenith at positions between ±115° either side of the vertical. These antennas include 1.0 to 6.0 GHz vertically and horizontally polarized standard-gain horn antennas.

    Source: GPS world staff
    FIGURE 2. Antenna array and digitizing front end in the anechoic chamber during broadcast tests.

    Because the characteristics of the antenna array itself are central to the ultimate performance of beamforming or null-steering techniques, a thorough characterization of the gain and phase properties of each of the seven antenna elements was conducted.

    To do so, a network analyzer was used to observe the gain and phase response of the antenna under test from a range of observation angles. The array was operated in transmit mode, broadcasting a signal sourced from Port A of the network analyzer, which was received by an antenna mounted on one of the movable sleds, and fed to Port B of the network analyzer.

    The network analyzer was configured to broadcast a series of 201 equally spaced tones spanning 20 MHz centered at 1575.42 MHz at a power of -7 dBm from the antenna array.

    A mechanical RF multiplexer was used to implement a time-division multiplexing of this broadcast measurement signal across each of the seven elements, such that the series of tones were transmitted once per antenna element. By performing the scan for each antenna element, for a range of positions of Sled A, and repeating this for different rotations of the central pillar, a precise frequency response could be calculated for a large set of points across the entire upper hemisphere of the antenna. The scan was computed on signals received by both the horizontal and vertical elements on Sled A, such that both the RHCP and LHCP response could be computed. The vertical cuts of this gain pattern were measured with resolution of 2°, while the horizontal cuts were measured with a resolution of 5°.

    The average gain response, calculated across the 20-MHz band, for each of the seven elements is depicted in FIGURE 3. The elevation cut of the peripheral element is taken such that the -90° direction of the cut aligns with a radial line pointing away from the center of the array. The azimuth cuts are oriented such that the 0° direction aligns with a radial line extending from the center of element number 1 to the center of element number 2.

    Source: GPS world staff
    FIGURE 3. The measured gain pattern of the central element, number 1, (blue lines) and one of the peripheral elements, number 2, (red lines). The gain of the peripheral element is deflected inwards toward the center of the array because of the asymmetry of its positioning on the ground plane. (a) Elevation angle cut at an azimuth of 0°; (b) Azimuth cut at an elevation angle of 40°.

    It is interesting to note that the gain pattern exhibited by each element is sensitive to its position on the ground plane and its position relative to other elements. Because of the rotational symmetry of the array, the gain patterns of all of the peripheral elements are similar, differing only in orientation, each one exhibiting a deflection of the maximum gain towards the center of the array. The central element is circularly symmetric with a single lobe in the direction of the zenith, while gain of the peripheral elements is deflected inwards, having lower gain away from the center of the array and an increased gain for high elevation angles from the center of the array. The difference in gain pattern across elements is stark and should, perhaps, influence the choice of elements to be used when forming a beam or null in a given direction. One or other of the signals should be scaled to compensate for this gain difference.

    Measuring Signal Rejection

    Before exploring factors that influence signal rejection, this section details the figure of merit, which might quantify the achievable performance of the array. We examined the nulling performance of the system in terms of its rejection capability: assessed as the relative received power of the signal of interest, b(t), that is to be preserved, and an unwanted signal, a(t), which is to be rejected, before and after the nulling combination. If sj(t) denotes some signal as received at antenna j, then the combination of signals received at antennas j and k can be denoted by:

    Source: GPS world staff   (1)

    where κ and ϕ, respectively, represent a unitless scaling gain and a phase rotation in radians applied in the combination. When intending to form a beam in the direction of the source of s(t), then this phase might be chosen to bring sk(t) into alignment with sj(t), and the gain may be determined as a function of the signal-to-noise ratio at each antenna, or simply set to unity. In contrast, when it is intended to reject s(t) then eiϕ must be chosen to place sk(t) in antiphase with sj(t) and must be chosen to scale the amplitude of sk(t) to be exactly equal to that of sj(t).

    In this case, we consider the problem of placing a null in the direction of signal a(t) while preserving signal b(t). If the relative received power of a(t) and b(t) at antenna j is taken as a reference, then the rejection of a(t) with respect to b(t), denoted Ra,b , can be assessed by examining the change in relative power after the null has been placed:

    Source: GPS world staff    (2)

    where denotes the expected value of x. Note also that this convention implies that a value of Ra,b greater than unity corresponds to signal rejection.

    Analog Null Steering at RF

    This section explores some of the receiver-side factors that can limit nulling performance. The performance of an analog RF-combining circuit is examined, wherein the combining function was implemented using controllable analog attenuators and phase shifters.

    The received signal from each of two antennas, j and k, was fed to a custom RF circuit board hosting a controllable phase shifter and attenuator chips. The output of two of these boards was then combined using a passive power combiner, filtered by an analog RF filter, limiting the band to the range 1530–1620 MHz, and finally fed to a power detector, which produced a signal voltage that was proportional to the total observed power. The experimental setup is depicted in FIGURE 4. The attenuators and phase shifters were controlled digitally via a microcontroller board, which also sampled the output of the power detector.

    Source: GPS world staff
    FIGURE 5. A simplified example of the steering constellation of an analog gain and phase shifter, having 3-bit phase and gain control and a gain step-size of ~1 dB.

    The attenuators accept a 6-bit control, providing a dynamic range of 30 dB in steps of approximately 0.5 dB, while the phase shifters accept a 4-bit control traversing the unit circle in steps of 22.5°.

    A simplified example of the finite resolution achievable using such a phase and gain shifter is shown by the steering constellation depicted in FIGURE 5, taking the case of 3-bit gain and phase control and assuming a gain step size of 1 dB. Note that the gain is displayed on a logarithmic scale. Each of the circular markers represents a possible gain and phase coefficient for a received signal, which would be used to steer one signal, a, to be approximately equal in amplitude and in anti-phase with the second signal, b.

    Source: GPS world staff
    FIGURE 4. A custom-built programmable analog phase shifter and attenuator pair used for the analog null-steering configuration.

    The residual misalignment between the signals stems from the finite constellation of steering points and results in a reduced nulling performance, whereby a portion of the interference signal remains. The relative magnitude of the remaining interference signal is maximum when the true relative phase and amplitude of the signals a and b lies equidistant from the four nearest steering vectors. This is depicted in Figure 5, where the cross marker lies equidistant from the four vertices located at the corners of {0°,45°} and {7,8} dB. Note that as the gain is depicted on a logarithmic scale, the relative error is equal for points centered in any of the quadrants.

    To investigate the performance of the system, we broadcast a continuous-wave interference toward the array, while the signal from one antenna was manipulated by all possible gain and phase combinations, keeping the signal from the second antenna at a fixed zero phase shift and –15 dB attenuation. For each of the 1,024 possible gain and phase combinations, the power detector was sampled and logged. A trace of the measured signal rejection as a function of the gain and phase is depicted in FIGURE 6, wherein a sharp peak is observable at approximately {–15 dB, 210°}, corresponding to the point at which the unwanted signal is most rejected — in this particular case, to a level of approximately 29 dB.

    Source: GPS world staff
    FIGURE 6. The measured interference rejection for a broadcast jamming scenario, where a brute-force search through all possible combinations of phase shift and attenuation was conducted. In this case, the maximum rejection happens to occur at an attenuation of 16.5 dB and a phase shift of 225°.

    Estimating the Achievable Rejection Level. In this particular experiment, because all 1,024 possible gain and phase combinations were examined in a brute-force search, the signal rejection was not limited by inaccuracies in the estimation of the steering variables κ and ϕ. Rather, it was limited by how accurately the steering variables can be applied. A residual error exists between the phase and gain that would perfectly align and null the signal and the nearest values of phase and gain that the circuit can produce. This error is a function of the distribution of the true steering parameter and the resolution with which it is rendered. In this case, as the range and angle to the unwanted signal source is arbitrary and the distance between antenna elements is comparable to the carrier wavelength, then it is reasonable, perhaps, to assume that the residual error in the steering parameters is zero mean and uniform over the discrete control steps. To model this effect, similar to the previous section, the combining function, inclusive of these errors, can be expressed as:

    Source: GPS world staff   (3)

    where U denotes a uniform distribution, δϕ denotes the step size of the phase shifter control and δA denotes the attenuator step size. Note that as κ is in units of amplitude and δA represents the discrete steps in power gain, which corresponds to discrete steps of Eq-4a  in amplitude, then the residual error will be distributed over a region extending Eq-4b in either direction. In this case, if a B-bit phase shifter is used, then:

    Source: GPS world staff  .  (4)

    From this model, the minimum expected rejection level can be estimated as a function of the phase and attenuator resolution. Considering first the rejection expression given by Equation (2), we note that the variation of the power signal of interest, b(t), is a function only of the relative angles between each of a(t) and b(t) and the antenna array. When the signals are well separated, a gain of 3 dB is observed on b(t), and when a(t) and b(t) are located nearby or in exact opposite directions, then the rejection of a(t) will also reject b(t). As this power variation is a function of geometry and not of the particular nulling technique, for simplicity it is assumed that b(t) experiences no power variation. What remains is the relative power variation of a(t) with respect to and δϕ.

    To find the minimum expected rejection level, we must examine the following metric:

    Source: GPS world staff  (5)

    Source: GPS world staff  (6)

    where the two variables, eκ and eϕ, respectively represent the residual errors in amplitude and phase between the perfect steering vector, and that which can be attained by the combiner. Examining Equations (3) and (6), it is clear that the minimum rejection will be achieved when the residual phase error is equal to eϕ = 1/2δϕ and the amplitude mismatch is given by eκ = Eq-4b. Substituting these values yields the minimum expected rejection, as given in Equation (7):

    Source: GPS world staff.(7)

    Determination of the average expected rejection level requires the averaging of Equation (6) over the distributions of the two error variables, eκ and eϕ. As these errors are assumed to be uniform in this particular case, this reduces to the following:

    Source: GPS world staff(8)

    which, after some manipulation, admits the closed form expression of Equation (9):

    Source: GPS world staff.
    (9)

    Inserting the specifications of the experimental setup used here, we find that the minimum rejection that can be expected is equal to approximately 14 dB with an average value equal to 18.8 dB. Further exploring this result, it is possible to predict the minimum performance that can be achieved given some arbitrary, but finite, resolution in gain and phase rotation. A portion of the surface defined by Equation (9) is presented in FIGURE 7. One useful application of this result is that it may be used by a designer to ensure that the resolution in gain and in phase are commensurate. This can be inferred by examining the gradient of the surface, noting that optimal choices of gain and phase step size will lie along the line of steepest gradient of this surface. A flattening of the surface in one dimension indicates that the performance is limited by the other dimension. For example, it can be seen that an increase in phase resolution beyond 6 bits yields no improvement in rejection when the gain step size is greater than 0.5 dB.

    Source: GPS world staff
    FIGURE 7. Minimum achievable rejection of analog nulling-combiner as a function of phase-shifter resolution (bits) and attenuator step size (dB).

    Conclusion

    Early results from this study suggest that the achievable signal rejection using a controlled radiation pattern GNSS antenna, under ideal conditions, is in excess of 70 dB, and is primarily limited by the accuracy with which the angle of incidence of the interference can be estimated. Accounting for typical estimation errors, the nominal rejection levels of the order of 20 to 40 dB can be expected. However, it is observed that other aspects limit the signal rejection performance. In a practical receiver, these factors stem from component selection for the signal-combining circuitry.

    For analog combining schemes, this is the resolution of the controlled attenuators and phase shifters used. The results here attempt to characterize the relationship between the minimum expected performance and the component properties. Results suggest that the choice of analog combining components should be chosen such that the phase and gain resolution are commensurate and such that resolution in one parameter is not rendered useless by a lack of resolution in the other. These results may form useful guidelines when designing analog RF null-steering antennas.

    Acknowledgments

    This article is based, in part, on the paper “Analog and Digital Nulling Techniques for Multi-Element Antennas in GNSS Receivers” presented at ION GNSS+ 2015, the 28th International Technical Meeting of the Satellite Division of The Institute of Navigation held in Tampa, Fla., Sept. 14–18, 2015.

    Manufacturers

    The equipment used in our study included an Agilent, now Keysight Technologies E8361A PNA network analyzer, Antcom Corporation 2DG1215A-MNS-4 GPS L1/L2 antennas, an Arduino LLC (www.arduino.cc) Arduino Uno microcontroller, a MACOM MAPS-010143 4-bit digital phase shifter, a Skyworks Solutions  SKY12347-362LF 6-bit digital attenuator and a Tallysman Wireless TW127 in-line amplifier.

    Further Reading

    • Authors’ Conference Paper

    “Analog and Digital Nulling Techniques for Multi-Element Antennas in 
GNSS receivers” by J.T. Curran, M. Bavaro and J. Fortuny in Proceedings of ION GNSS+ 2015, the 28th International Technical Meeting of the Satellite Division of The 
Institute of Navigation, Tampa, Fla., Sept. 14–18, 2015, pp. 3249–3261.

    • Adaptive GNSS Antennas for Interference Suppression

    “Advances in the Theory and Implementation of GNSS Antenna Array Receivers” by P. Arribas, C. Closas, M. Fernández-Prades, M. Cuntz, M. Meurer and A. Konovaltsev, Chapter 9 in Microwave and Millimeter Wave Circuits and Systems: 
Emerging Design, Technologies, and Applications, edited by A. Georgiadis, H. Rogier, L. Roselli and P. Arcioni and published by Wiley, 2012, pp. 227–273.

    “Mitigation of Continuous and Pulsed Radio Interference with GNSS Antenna Arrays” by A. Konovaltsev, D.S. De Lorenzo, A. Hornbostel and P. Enge in Proceedings of ION GNSS 2008, the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation, Savannah, Ga., Sept. 16–19, 2008, pp. 2786–2795.

    “Navigation Accuracy and Interference Rejection for an 
Adaptive GPS Antenna Array” by D.S. De Lorenzo, J. Rife, P. Enge and D.M. Akos in Proceedings of ION GNSS 2006, the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation, Fort Worth, Texas, Sept. 26–29, 2006, pp. 763–773.

    “A Novel Interference Suppression Scheme for Global Navigation Satellite Systems Using Antenna Array” by M.G. Amin and W. Sun in IEEE Journal on Selected Areas in Communications, Vol. 23, No. 5, May 2005, pp. 999–1012, doi: 10.1109/JSAC.2005.845404.

    “Wideband Cancellation of Interference in a GPS Receive Array” by R.L. Fante and J. Vaccaro in IEEE Transactions on Aerospace and Electronic Systems, Vol. 36, No. 2, April 2000, pp. 549–564, doi: 10.1109/7.845241.

    • GNSS Antennas

    “GNSS Antennas: An Introduction to Bandwidth, Gain Pattern, Polarization, and All That” by G.J.K. Moernaut and D. Orban in GPS World, Vol. 20, No. 2, February 2009, pp. 42–48.

    “A Primer on GPS Antennas” by R.B. Langley in GPS World, Vol. 9, No. 7, July 1998, pp. 50–54.

    JAMES T. CURRAN received a B.E. in electrical and electronic engineering in 2006 and a Ph.D. in telecommunications in 2010 from the Department of Electrical Engineering, University College Cork, Ireland. He worked as a senior research engineer with the Position, Location and Navigation group at the University of Calgary between 2011 and 2013 and is currently a grant holder at the Joint Research Center (JRC) of the European Commission (EC), Ispra, Italy. His main research interests are signal processing, information theory, cryptography and software-defined radios (SDRs) for GNSS.

    MICHELE BAVARO received his master’s degree in computer science in 2003 from the University of Pisa, Italy. Shortly afterwards, he started his work on SDR technologies applied to navigation. First in Italy, then in The Netherlands and in the United Kingdom, he worked on several projects directly involved with the design, manufacture, integration, and test of GNSS equipment and supporting customers in the development of their applications. Today he is appointed as a grant holder at the EC JRC.

    JOAQUIM FORTUNY-GUASCH received the engineering degree in telecommunications from the Technical University of Catalonia, Barcelona, Spain, in 1988, and the Dr.- Ing. degree in electrical engineering from the Universität Karlsruhe, Germany, in 2001. Since 1993, he has been working for the EC JRC as a senior scientific officer. He is the head of the European Microwave Signature Laboratory and leads the JRC research group on GNSS and wireless communications systems.

  • Innovation: Guidance for road and track

    Innovation: Guidance for road and track

    Real-time single-frequency precise point positioning for cars and trains

    By Peter de Bakker and Christian Tiberius

    INNOVATION INSIGHTS with Richard Langley
    INNOVATION INSIGHTS
    with Richard Langley

    “IT’S GETTING BETTER ALL THE TIME.” This refrain from the Beatle’s song could well describe precise point positioning or PPP. PPP is a positioning technique that relies on GNSS carrier-phase measurements (in addition to code or pseudorange measurements) from a user’s receiver along with satellite orbit and clock data much more precise (and accurate) than that included in broadcast satellite navigation messages to achieve accuracies down to the centimeter level. It also requires a more sophisticated model of the measurements compared to that used in most consumer GNSS equipment and even some professional devices, including accounting for residual tropospheric propagation delay, carrier-phase windup, and even solid Earth tides.

    PPP has been around for more than a decade and ongoing research has gradually improved its capabilities. Until recently, it has been used primarily with dual-frequency GPS observables. However, the technique is not restricted to GPS. It works equally well with observables from other constellations including GLONASS, Galileo and BeiDou. As long as precise orbit and clock products are available (typically from the International GNSS Service or its participating analysis centers), then PPP positioning solutions are possible. And, single-frequency PPP is also possible. The primary advantage of dual-frequency PPP is that the ionospheric propagation delay is almost completely removed by linearly combining the measurements on the two frequencies, taking advantage of the dispersive nature of signal propagation through the ionosphere. But, if good predictions of the ionospheric delay at, say, the L1 GPS frequency are available, then it is possible to do single-frequency PPP. While not as accurate as dual-frequency PPP, the technique is considerably more accurate than typical pseudorange point positioning (the so-called Standard Positioning Service).

    PPP is also traditionally a post-processing technique. That is, data is collected but it is not processed until some later convenient time when the necessary precise products are available. Such an approach is useful for many applications but clearly not for navigation, which requires real-time positioning. But in the past few years, a number of commercial and non-commercial entities have started streaming real-time satellite orbit and clock corrections over the Internet and various radio links, making real-time PPP a reality.      

    In this month’s Innovation column, we bring together, perhaps for the first time, single-frequency and real-time PPP. Our authors describe a series of experiments they have conducted on roadways and a railway achieving sub-meter horizontal positioning at a 95 percent confidence interval. Such accuracies may already be sufficient for freeway lane and railway track guidance. But we might expect even better accuracies in the future. After all, PPP is getting better all the time.

    The single-frequency precise point positioning (SF-PPP) method, developed at Delft University of Technology, was previously demonstrated to provide lane-level position accuracy on a freeway in post-processing mode. Important applications of SF-PPP are lane-level traffic state estimation and lane-level specific driver advice for next-generation car navigation. For a functional system, as well as for advanced experiments in this field, the computed positions have to be available in real time. Therefore, a new real-time implementation of the SF-PPP method was developed as part of the Dutch Dynamic Lane Guidance project. In this article, we outline aspects of the real-time implementation, and we present experimental results from this new implementation collected on a busy freeway in the Netherlands and in a parking lot, as well as results from a railway experiment.

    In these experiments, a test vehicle was equipped with a low-end, automotive-type single-frequency receiver with a patch antenna to collect raw GPS observations. A 3G mobile communications link was used to obtain data-correction streams over the Internet using the Ntrip protocol. The SF-PPP processing was performed on a laptop computer onboard the vehicle, in real time. Various forms of ground-truth positions were used to assess the real-time SF-PPP positioning accuracy. For some of our tests, the vehicle was also equipped with high-end GPS antennas and receivers to provide ground truth. The position solutions obtained with the SF-PPP algorithm have been compared to (post-processed) network-RTK solutions using the Netherlands Positioning Service (NETPOS). Additional validation was performed by means of a 5-centimeter-accuracy road-infrastructure map from Rijkswaterstaat, the Dutch Ministry of Infrastructure and the Environment, and by a centimeter-level a priori ground survey.

    The new real-time SF-PPP software was tested successfully with performance comparable to our previous post-processing software, and meeting the required accuracy for freeway lane identification. Statistics on the performance are provided, as well as their dependence on a number of external parameters including the number of available satellites.

    Precise corrections from both the German Aerospace Center (Deutsches Zentrum für Luft- und Raumfahrt or DLR) and the International GNSS Service (IGS) were used. Delays in the correction streams vary between providers and can increase further in the event of a time-out of the mobile link. The influence of these delays is considered, and an optimal approach for dealing with outages is discussed.

    PPP Model and Corrections

    The GNSS positioning model is non-linear. The observations are non-linear functions of the unknown parameters plus noise.

    To solve for the unknown parameters (including the receiver position coordinates), through least squares estimation, the model must be linearized around an approximate solution.

    In our SF-PPP model, the primary observations are, from each satellite, the pseudorange measurement and the carrier-phase measurement. The unknown parameters are the receiver position vector and the receiver clock offset, both of which are involved in the linearization, and also the ambiguity, associated with the carrier-phase measurement, for which the model is already linear.

    In the context of PPP, it is important to note that in addition to the linearization around the initial approximate values, the computed observations contain a number of a priori model values for parameters which are not estimated, including:

    • The precise satellite position and clock offset (including the relativistic effect): The GPS satellite positions and clock offsets are computed from the broadcast products (navigation message) and corrected with real-time data streams via Ntrip. The correction streams of DLR and IGS were used at different times as detailed in Table 1. In post-processing older files, the satellite orbits and clocks are taken from sp3 files, but to keep the processing as close as possible to the real-time functionality, these are first converted to corrections to the broadcast products.
    • The (neutral) troposphere delay: The troposphere delay is modeled with the a priori Saastamoinen model using the Ifadis mapping function and parameters from the 1976 U.S. Standard Atmosphere.
    • The ionosphere delay and satellite differential code bias: The ionosphere delay is computed a priori using the one-day predicted Global Ionosphere Maps (GIMs) from the Center for Orbit Determination in Europe (CODE), together with the corresponding differential code biases.
    • The carrier-phase observations are corrected for the phase wind-up at the receiver and satellite. The user orientation is estimated from the vehicle velocity vector.
    TABLE 1. Four SF-PPP field tests.
    TABLE 1. Four SF-PPP field tests.

    Besides the primary observations, the ambiguity estimate from the previous epoch can be added to the current epoch as an additional observation per satellite, because it is assumed to be constant in the absence of a cycle slip.

    Observations from different epochs are assumed to be uncorrelated, and consequently the ambiguity estimates from previous epochs are uncorrelated to the current observations. Observations to different satellites are also assumed to be uncorrelated.

    The carrier-phase ambiguities are the only parameters propagated from a previous epoch to the current epoch. The receiver position coordinates (and receiver clock offset) are estimated each epoch anew — no vehicle dynamics model is involved.   

    The computed positions are finally corrected for solid Earth tides with an efficient numerical model. Computed positions result in the International Terrestrial Reference Frame (ITRF) 2008 at the epoch of the observations.

    In parallel with the positioning filter, statistical hypothesis testing is used to detect errors in the observations or propagated ambiguities (such as those caused by excessive multipath or a cycle slip), based on the detection, identification and adaptation (DIA) procedure. First, an overall model test is run at each epoch to test the validity of the model and observations. If the test is rejected, data snooping is applied to determine which observation is most likely to have caused the problem. If one of the pseudorange measurements is identified, it is removed from the model. If either a carrier-phase measurement or ambiguity is identified, the ambiguity for that satellite is reset; that is, the propagated ambiguity is removed.

    Experiments

    Four field tests that we have carried out are considered here.

    • In October 2012, more than 100 laps were driven over a 5-kilometer stretch of the A13 freeway between Delft and Rotterdam. The data collected were reprocessed to validate the new real-time software implementation (but obviously carried out in post-processing mode).
    • The first real-time tests were performed in December 2014 and later in May 2015 on the same stretch of the A13 freeway.
    • In May 2015, a third dataset was collected on a recently constructed and nicely outlined parking lot in Delft.
    • In July 2015, a train carriage was equipped with a GPS receiver and data were collected on a train trip from the center of The Netherlands to the far southern part — a distance of more than 200 kilometers.

    Details of the four field tests are collected in Table 1.

    Ground Truth

    In our earlier experiments, the ground truth for the vehicle positions was computed with measurements from high-end equipment onboard the same vehicle. Both the antenna of the SF-PPP receiver and the high-end antennas were rigidly connected to a wooden beam on the roof rack of the van (positions of the two high-end antennas at both ends of the beam were obtained through network RTK GPS). As our results from this experiment show, the performance, and especially the precision, is very good, but a moderate bias of 17 centimeters in the cross-track direction was observed (see FIGURE 1 and TABLE 2). The suspect cause of this bias was the antenna location, close to the side of the vehicle and not attached to the metal roof itself.

    FIGURE 1. 2D histogram of SF-PPP position errors (with respect to the network RTK GPS solution) in horizontal directions for the 2012 test on the A13 freeway, expressed in local east and north directions (left), and in cross-track and along-track directions (right). The color indicates the number of samples in each bin.
    FIGURE 1. 2D histogram of SF-PPP position errors (with respect to the network RTK GPS solution) in horizontal directions for the 2012 test on the A13 freeway, expressed in local east and north directions (left), and in cross-track and along-track directions (right). The color indicates the number of samples in each bin.
    TABLE 2. Statistics of the position errors in each direction, for the 100 laps on the A13 freeway.
    TABLE 2. Statistics of the position errors in each direction, for the 100 laps on the A13 freeway.

    Therefore, during more recent experiments, the test vehicle was only equipped with a patch antenna for the low-end, automotive-type GPS receiver, and attached directly to the roof of the car, in the middle of the centerline of the vehicle. In this case, the metal roof acts as a ground plane for the antenna, improving the gain and not acting as a source of multipath. However, this setup also has complications for the accuracy assessment. Thus, instead of computing accurate ground truth from the measurements from high-end equipment directly near the test receiver, a number of other ways were used to determine the ground truth.

    During the first real-time test on the A13 freeway, a 5-centimeter accurate road infrastructure map from Rijkswaterstaat was used as previously mentioned. This comparison was done both visually and numerically.

    For our next experiment, we selected a recently constructed parking lot with a simple, neat rectangular layout. By surveying the corners of the rectangle and using the repetitive pattern, a schematic drawing of the parking lot was made, and used to evaluate the positioning performance in a visual manner. The car was first driven over the lined-up parking spaces in a lengthwise manner, circling round at each end of the parking lot, and changing lanes once each lap at the same point. Then the car was driven along the edges of the rows of parking spaces to and fro over the parking lot.

    SF-PPP positions were obtained live in the vehicle while driving. The raw (single-frequency) observations of this experiment were also post-processed with the RTKLib software package using the nearby permanent DLF1 station at the TU Delft GNSS observatory on a very short baseline (less than 1 kilometer). The ambiguity-fixed results could then be used to also numerically assess the SF-PPP positioning performance.

    For the test on the train, again the network RTK GPS solution provided the ground truth positions. Two antennas were mounted along the centerline of the carriage at a fixed offset from each other: a patch antenna for the single-frequency  receiver and a geodetic antenna for the ground truth. With this known offset, and the direction of motion, the ground truth position for the single-frequency receiver was obtained.

    The ground-truth positions, either in the European Terrestrial Reference System (ETRS) 89 (from NETPOS or our own survey) or in the local national reference frame Rijksdriehoeksmeting (National Triangulation System) / Normaal Amsterdams Peil (Amsterdam Ordnance Datum) or RD/NAP, have been transformed into ITRF2008, to allow for comparison with the SF-PPP positions.

    Computational Performance, Data Rates

    The real-time software was used under the 64-bit Windows 8.1 operating system on a moderately fast laptop with i5-4200U CPU running at 1.60 GHz. The software consists of uncompiled Matlab R2014b scripts and functions using timer objects to repeatedly read in new observations, corrections and ephemerides, and to update the position computation. The software can run with data arriving at about 20 Hz in the current state on this platform, but was used with 5-Hz data because of limitations of the receiver to provide raw data and to prevent any overrun. It should be noted that only a few obvious potential computational bottlenecks were targeted; the software was not optimized for efficiency.

    The RT SF-PPP implementation relies on a 3G mobile Internet connection for a number of data products. The ionosphere map, which is a predicted product (24 hours ahead), comes as a 200-kilobyte file (and 5 kilobytes for the associated differential code biases), which covers the globe and is valid for 24 hours. The file contains 13 maps at 2-hour intervals, between which interpolation in time is required.

    Spatial interpolation is also required for the ionosphere pierce point of each satellite signal, between the grid points in the map (at intervals of 5 degrees in longitude and 2.5 degrees in latitude). The satellite orbit/position corrections (every 60 seconds) and satellite clock corrections (every 10 seconds) are retrieved over the Internet using the Ntrip protocol by means of the Bundesamt für Kartographie und Geodäsie (BKG) Ntrip Client (BNC), which passes these on to Matlab.

    The data-rate used by this correction stream is about 1 kilobit per second. The corrections are applied to the broadcast ephemerides (in quasi-Keplerian-element form), which are therefore also required. These satellite ephemerides can be extracted by the GPS receiver itself (from the GPS navigation message), but in our implementation are also collected via Ntrip for convenience only, with a bandwidth consumption of 6 kilobits per second. Note that, much like the software implementation itself, the data stream has not been optimized for any particular bandwidth limitation. For instance, orbit and clock corrections are needed only for those satellites in view, and hence transmitting the data for all satellites of the constellation is not needed.

    Results

    In this section, we present the results of our tests, followed in the next section with a discussion of important common factors affecting accuracy and continuity of RT SF-PPP.

    Road-Test A13 Freeway (100 Laps). Under different conditions, we collected a large amount of data with a van, driving repeatedly the same 5-kilometer stretch of road on the A13 freeway from Rotterdam to Delft. The test amounted to almost a full day of driving.

    2D histograms of the results are shown in Figure 1 with corresponding statistics in TABLE 2. Note a small bias in the cross-track direction. The total number of position solutions was 2.0  × 105.

    Road-Test A13 Freeway (Real Time). The results of the real-time freeway road test are shown in FIGURE 2. The different lanes used by the vehicle are clearly visible in the figure. The number of GPS satellites is indicated by the color bar. Shown is the Delft-Zuid / TU Delft exit of the A13 freeway, roughly a 300 × 300 meter area, taken from the Digitaal Topografisch Bestand (DTB) of Rijkswaterstaat. Note that only the cross-track performance can be assessed in this manner, but fortunately this is exactly the performance aspect that is most interesting for the target application of lane identification. Note also that if the vehicle was not driving exactly in the middle of the lane, which to some extent is unavoidable, this effect cannot be separated from the positioning errors.

    FIGURE 2. SF-PPP solution displayed on a 5-centimeter accurate road infrastructure map, on Dec. 18, 2014.
    FIGURE 2. SF-PPP solution displayed on a 5-centimeter accurate road infrastructure map, on Dec. 18, 2014.

    The 95-percent error southbound and northbound is 0.65 meters and 0.58 meters respectively, in the cross-track direction.

    Road-Test Parking Lot. FIGURE 3 shows an aerial photograph (left) and schematic drawing (right) of the 3M company parking lot in Delft showing measured positions and driven tracks. The lines in red and yellow represent the measured tracks while driving the same loop over the parking lot again and again (more than 60 times in total), and the purple lines show the track while driving around and following the parking space boundaries with the left front wheel of the test vehicle (4 laps). These lines show both the SF-PPP position error and the driver error. The white parking spaces are each 2 meters wide.

    FIGURE 3. Aerial photograph, from Google Earth, (left) and schematic drawing (right) of the parking lot in Delft showing measured positions and driven tracks.
    FIGURE 3. Aerial photograph, from Google Earth, (left) and schematic drawing (right) of the parking lot in Delft showing measured positions and driven tracks.

    The position errors in local north, east and up directions for part of the first dynamic session, of about 4.5 laps, of the 3M parking lot experiment (lane change 1) are shown in the upper panel of FIGURE 4. We see a clear periodic signal as well as a bias in each direction. The driving direction gives an approximation of the heading (shown in the bottom panel), which confirms that the periodic signal coincides with the driven laps.

    FIGURE 4. Position errors (top) in local north, east and up directions and heading (bottom) for part of the first dynamic session, about 4.5 laps, of the 3M parking lot experiment (lane change 1).
    FIGURE 4. Position errors (top) in local north, east and up directions and heading (bottom) for part of the first dynamic session, about 4.5 laps, of the 3M parking lot experiment (lane change 1).

    The figure shows that the errors in the position solution are on the order of 0.2 meters, and consist of a bias in each of the three directions and a periodic signal with a period equal to the lap-time (confirmed by the driving direction of the vehicle). Since the bias does not depend on the orientation of the vehicle, and given the slow variation over time, the most likely cause is a residual ionosphere error or errors in the satellite products. The repeating pattern, on the other hand, is most probably related to multipath or near-field effects related to the vehicle antenna.

    Rail-Test Amersfoort to Simpelveld. The train carriage with the GPS antennas installed was pulled by a 1955-built diesel-electric locomotive. A trip of more than 200 kilometers was made, over the main Intercity Network of Nederlandse Spoorwegen (NS) / ProRail (Dutch Railways). Only the last 20 kilometers were on a local line to a historic railway station.

    The overhead power line (about 1 meter above the GPS antennas) and portals seem to have no impact on the SF-PPP positioning performance. An example of the positioning accuracy is shown in FIGURE 5. The figure shows position error scatter for an almost 20-kilometer stretch of nearly straight east-west track through rural and forest areas (Weert to Roermond). The time span of the data is 10 minutes, and the data rate was 5 Hz. SF-PPP positions were compared with NETPOS network RTK GPS solutions. Generally, eight satellites were received and used in the SF-PPP solution. The corresponding error statistics are presented in TABLE 3.

    FIGURE 5. Position error scatter for an almost 20-kilometer stretch of nearly straight east-west track through rural and forest areas (Weert to Roermond); 10 minutes of data at 5 Hz.
    FIGURE 5. Position error scatter for an almost 20-kilometer stretch of nearly straight east-west track through rural and forest areas (Weert to Roermond); 10 minutes of data at 5 Hz.
    TABLE 3. Statistics of the position errors, over 2994 epochs, in along- and cross-track directions, for the position scatter shown in Figure 5.
    TABLE 3. Statistics of the position errors, over 2994 epochs, in along- and cross-track directions, for the position scatter shown in Figure 5.

    A heavy steel-construction bridge along the route at the River Lek near Culemborg, 15 kilometers south of Utrecht, was found to degrade positioning performance considerably. The heavy steel construction of the bridge hampers reception of GPS satellite signals. The positioning performance on the bridge is shown in FIGURE 6. The computed SF-PPP trajectory overlaid on a Google Earth aerial photograph is shown on the left.

    FIGURE 6. Positioning performance on the Lek Bridge. Left: measured trajectory overlaid on a Google Earth aerial photograph. The number of satellites available is indicated by the color bar. Right top: SF-PPP positions in local east-north directions. Right bottom: Absolute cross-track offset of position solution with respect to a straight line, as a function of time.
    FIGURE 6. Positioning performance on the Lek Bridge. Left: measured trajectory overlaid on a Google Earth aerial photograph. The number of satellites available is indicated by the color bar. Right top: SF-PPP positions in local east-north directions. Right bottom: Absolute cross-track offset of position solution with respect to a straight line, as a function of time.

    From the positions, one can clearly see the train driving straight on the right-hand track (going south) on the ramp onto the bridge, and on the ramp down from the bridge. However, on the bridge itself, position solutions show considerably larger variations of up to 8 meters. The image shows a 250-meter stretch of the track. Also, the number of satellites available, and used in the position solution, drops considerably (indicated by the color bar) while the train is on the bridge. On the right of the figure at the top, the SF-PPP positions in local east-north coordinates are shown along with a straight line between the first and last epochs, representing the assumed straight track. The plot at bottom right shows the absolute cross-track offset of the position solutions with respect to the straight line, as a function of time, over 250 5-Hz epochs.

    Analysis

    Two factors significantly affect the performance of our tests: the number of satellites available and the continuity and latency of the corrections.

    Number of Satellites. As can be expected, the SF-PPP position accuracy depends to a large extent on the number of satellites used to compute the solution. For the third test, the road-test in the 3M parking lot, the three-dimensional position error (SF-PPP versus RTK GPS) is shown as a boxplot in FIGURE 7 in which various accuracy measures are plotted as a function of the number of satellites for the second and longest dynamic part of the test (lane change 2), consisting of about 12,000 epochs of data. During this session, the available number of satellites varied between 10 and 12. This number was reduced artificially by increasing the elevation mask angle to 15 and to 30 degrees. The red lines show the medians, the boxes show the 25th and 75th percentiles, the dashed lines cover all data points not considered outliers, and outliers are plotted with red plus signs. The graph shows a clear improvement going from six to seven or more satellites.

    FIGURE 7. Boxplot of 3D position error vs. the number of satellites for the second and longest dynamic part of the 3M parking lot test (lane change 2).
    FIGURE 7. Boxplot of 3D position error vs. the number of satellites for the second and longest dynamic part of the 3M parking lot test (lane change 2).

    PPP Correction-Stream Outages. To determine the optimal approach to an interruption in the correction data stream, we studied the variation of the corrections over time. Suppose we lose reception of the correction stream at epoch 0, and we keep using the last-received corrections (simply hold onto them). Then the change in values can be interpreted as the additional error introduced in the positioning algorithm by the outage on the mobile link. The effect is not catastrophic. Only after about 200 seconds do the additional satellite clock errors grow to the decimeter level. The position errors remain even smaller.

    However, one might wonder whether this can be improved further by performing a linear extrapolation of the corrections, for example, using a number of previous epochs. We looked at what would happen in this case if 5 minutes of previous data are used. For the clock errors, there is no real benefit — the errors only grow larger. But the position errors do remain smaller during the first 5 minutes of extrapolation. After that time, the errors are larger than those without the linear extrapolation (just holding onto the last corrections). The effect of increasing the order of the polynomial extrapolation was also considered. The polynomials of different order outperform each other at different extrapolation times, and also the number of previous epochs used for the polynomial estimation impacts this. Further optimization to reduce the satellite position errors might well be possible, but may be of marginal value, since, the extrapolated clock error is dominant and polynomial extrapolation does not improve this. Simply using the most recent corrections is thus a straightforward and acceptable approach.

    Conclusions

    In this article, we outlined a real-time implementation of single-frequency GPS precise point positioning. With a fairly low-cost GPS receiver and reception of a modest correction data stream, it is possible to achieve sub-meter horizontal positioning accuracy, in real-time, live in the vehicle (95-percent error of better than 1 meter). Actual results were shown from four field tests: two tests using a vehicle on a freeway, a vehicle test in a parking lot, and one test on a train.

    The number of satellites used in the position solution has a big effect on the positioning performance; seven or more satellites yields a good position accuracy. And up to 5 minutes outage of the satellite position and clock corrections does not seem to pose a serious threat to SF-PPP positioning performance.

    Acknowledgments

    The Dynamic Lane Guidance project under which the first road test was carried out was funded by the Ministry of Infrastructure and Environment, the Province of Noord-Brabant and the Eindhoven Regional Government in the context of Brabant in-car III. This project was carried out in close cooperation with colleagues in the Transport and Planning Department at TU Delft.

    We acknowledge the provision of the Real-Time Clock Estimation (RETICLE) satellite clock products by André Hauschild at DLR for several of our field tests. We are also grateful for the use of the IGS Real-Time Service. Also, we acknowledge the provision of the NETPOS network RTK GPS service as ground truth by Lennard Huisman of Kadaster, the Dutch Land Registry and Mapping Agency. Colleague Hans van der Marel analyzed the NETPOS RTK-GPS solution of the train test. Colleagues of the TU Delft Railway Engineering Department offered the opportunity to carry out the test on the train trip from Amersfoort to Simpelveld.

    Manufacturers

    The vehicle receivers used for the tests were u-blox AG TIM LP and 7P modules in evaluation kits fed by a Tri-M Technologies Inc. Big Brother SM-66 or Taoglas Dominator AA.161 antenna. A Trimble Navigation R7 receiver with a Zephyr Geodetic antenna was used to establish ground truth for some tests. 

    PETER DE BAKKER is a researcher in the Faculty of Civil Engineering and Geosciences at Delft University of Technology (TU Delft). He recently finished his Ph.D. dissertation on user algorithms for GNSS precise point positioning, and is working on localization for automotive applications, including autonomous vehicles.

    CHRISTIAN TIBERIUS is an associate professor in the Faculty of Civil Engineering and Geosciences at TU Delft. He has been involved in GNSS positioning and navigation research since 1991, currently with an emphasis on data quality control, satellite-based augmentation and precise point positioning.

    Further Reading

    • Earlier Work on Single-Frequency Precise Point Positioning

    “Lane Identification with Real Time Single Frequency Precise Point Positioning: A Kinematic Trial” by R.J.P. Van Bree, P.J. Buist, C.C.J.M. Tiberius, B. van Arem and V.L. Knoop in Proceedings of ION GNSS 2011, the 24th International Technical Meeting of the Satellite Division of The Institute of Navigation Portland, Ore., Sept. 19–23, 2011, pp. 314–323.

    “Real Time Satellite Clocks in Single Frequency Precise Point Positioning” by R.J.P. Van Bree, C.C.J.M. Tiberius and A. Hauschild in Proceedings of ION GNSS 2009, the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation, Savannah, Ga., Sept. 22–25, 2009, pp. 2400–2414.

    “Single-frequency Precise Point Positioning with Optimal Filtering” by A.Q. Le and C. C. J. M. Tiberius in GPS Solutions, Vol. 11, No. 1, 2007, pp. 61–69, doi: 10.1007/s10291-006-0033-9.

    • Single- vs. Dual-Frequency Precise Point Positioning

    “GNSS Solutions: Single- versus Dual-Frequency Precise Point Positioning” by H. van der Marel and P.F. de Bakker with M. Petovello in Inside GNSS, Vol. 7, No. 4, July/Aug. 2012, pp. 30–35.

    • Precise Point Positioning: Overviews and Issues

    Improved Convergence for GNSS Precise Point Positioning by S. Banville, Ph.D. dissertation, Department of Geodesy and Geomatics Engineering, Technical Report No. 294, University of New Brunswick, Fredericton, New Brunswick, Canada. Recipient of The Institute of Navigation 2014 Bradford W. Parkinson Award.

    “Precise Point Positioning: A Powerful Technique with a Promising Future” by S.B. Bisnath and Y. Gao in GPS World, Vol. 20, No. 4, April 2009, pp. 43–50.

    • Real-Time Data Streaming

    “Ntrip – Networked Transport of RTCM via Internet Protocol” by the GNSS Data Center of the Bundesamt für Kartographie und Geodäsie (BKG), the German Federal Agency for Cartography and Geodesy.

    “Coming Soon: The International GNSS Real-Time Service” by M. Caissy, L. Argrotis, G. Weber, M. Hernandez-Pajares and U. Hugentobler in GPS World, Vol. 23, No. 6, June 2012, pp. 52–58.

    • Miscellaneous

    “Digitaal Topografisch Bestand” (in Dutch) by Rijkswaterstaat, the Dutch Ministry of Infrastructure and the Environment.

    “Development of the Low-cost RTK-GPS Receiver with an Open Source Program Package RTKLIB” by T. Takasu and A. Yasuda in Proceedings of the International Symposium on GPS/GNSS, Jeju, Korea, November 4–6, 2009.

    “Variations of Box Plots” by R. McGill, J.W. Tukey and W.A. Larsen in The American Statistician, Vol. 32, No. 1, Feb. 1978, pp. 12–16, doi: 10.2307/2683468.

  • Innovation: Enhanced Loran

    Innovation: Enhanced Loran

    A Wide-Area Multi-Application PNT Resiliency Solution

    By Stephen Bartlett, Gerard Offermans and Charles Schue

    INNOVATION INSIGHTS with Richard Langley
    INNOVATION INSIGHTS with Richard Langley

    WHERE HAVE ALL THE SYSTEMS GONE, long time passing?

    Radionavigation systems, that is (and apologies to Pete Seeger). If we look at the 1990 Federal Radionavigation Plan (FRP), published by the U.S. Departments of Transportation and Defense, as I did in this column in March 1992, we see that there were 10 radionavigation systems in use by different user segments: Loran-C, Omega, very high frequency (VHF) Omnidirectional Range/Distance Measuring Equipment, Tactical Air Navigation, the Instrument Landing System, the Microwave Landing System, Transit, aviation radiobeacons, marine radiobeacons and GPS.

    The latest FRP, issued in 2014, includes only seven or six and a half when you consider that marine radiobeacons were mostly phased out in the intervening years. Systems were shut down because with the advent of GPS, they were considered to be redundant. While there were attendant cost savings, the closure of the various systems has resulted in a dangerous virtual sole dependence on GPS for navigation without any backup.

    Transit, was the first to go. It consisted of a constellation of six or seven active satellites in circular, polar orbits at altitudes of roughly 1,100 kilometers. The satellites transmitted signals on 150 and 400 MHz, and receivers measured the integrated Doppler frequency shift of the received signals. Transit was terminated at the end of 1996.

    Transit was followed by the Omega hyperbolic navigation system. Omega consisted of eight stations around the globe transmitting time-shared carrier-wave signals on four frequencies between 10.2 and 13.6 kHz. The Omega system was closed down in September 1997.

    The marine radiobeacons have been mostly shut down in recent years, although aeronautical beacons continue to operate. Radiobeacons are nondirectional transmitters that operate in the low- and medium-frequency bands. Some marine radiobeacons became Differential GPS stations and subsequently part of the Nationwide DGPS network. That network is being scaled back to provide only coastal and Great Lakes coverage.

    And that brings us to Loran-C. Like Omega, it was also a hyperbolic navigation system. A receiver measured the difference in times of arrival of pulses transmitted at 100 kHz by a chain of three to five synchronized stations separated by hundreds of kilometers. At one time, the operation of Loran-C was the responsibility of the U.S. Coast Guard. Together with a number of host nations, the Coast Guard operated 17 chains of stations around the world, including one jointly operated with Russia. These stations provided coverage of the coastal areas of North America and the U.S. interior, northern Europe, the Mediterranean Sea, the Far East and the Hawaiian Islands. Additionally, several other countries operated Loran-C stations. Although moves were already underway to update the Loran technology, the Obama administration decided to terminate Loran-C in the U.S., considering it to be an unnecessary antiquated system. The Coast Guard terminated the transmission of all U.S. Loran-C signals in February 2010 and began dismantling stations.

    So, is there no longer a viable non-GNSS alternative or backup system for GPS navigation? While there are other possibilities for time transfer, one of GPS’s other applications, there is no widely available substitute navigation system. Currently. However, as we will see in this month’s column, a new version of Loran — Enhanced Loran or eLoran — has been developed and is being tested on the U.S. east coast. Not your father’s Loran, eLoran seems to be the perfect solution for PNT resiliency.

    Telecommunications, energy, finance and transportation are just four among the many critical infrastructure / key resource sectors that have come to rely solely on GPS for positioning, navigation and timing (PNT). In fact, the U.S. Department of Homeland Security (DHS) has determined that 11 of the 16 critical infrastructure sectors in the U.S. are critically dependent on GPS for timing. While we can start to imagine what a day without GPS might be like, we’d really rather not — it would be somewhat depressing and really quite dangerous. We would rather imagine a day when there is a wide-area complementary solution available that protects and augments GPS. In this article, we will delve into such a solution: Enhanced Loran, or eLoran for short. We will explain how it works, debunk some myths, speculate on how it could be used in the U.S. (and abroad), highlight the state of current technology and discuss the state of the possible. We will also summarize the state of eLoran in the world and where things might go from here.

    What Is eLoran?

    eLoran is the latest in the longstanding and proven series of low-frequency, LOng-RAnge Navigation (LORAN) systems, one that takes full advantage of 21st-century technology. It meets the accuracy, availability, integrity and continuity performance requirements for maritime harbor entrance and approach maneuvers, aviation non-precision instrument approaches, land-mobile vehicle navigation and location-based services. It’s a precise source of time (phase) and frequency. Additionally, eLoran provides user bearing (azimuth) and has built-in integrity. In full disclosure, however, eLoran is only a 2D positioning solution unless integrated with a simple altimeter.

    eLoran is a low-frequency radionavigation system that operates in the frequency band of 90 to 110 kHz. eLoran is built on internationally standardized Loran-C, and provides a high-power PNT service for use by all modes of transport and in other applications. eLoran is an independent dissimilar complement to GNSS. It allows GNSS users to retain the safety, security and economic benefits of GNSS even when their satellite services are disrupted.

    eLoran uses pulsed signals at a center frequency of 100 kHz. The pulses are designed to allow receivers to distinguish between the groundwave and skywave components in the received composite signal. This way, the eLoran signals can be used over very long ranges without fading or uncertainty in the time-of-arrival (TOA) measurement related to skywaves.

    Although eLoran is based upon Loran-C, it has key differences:

    • All transmissions are synchronized to UTC (like GPS)
    • Time-of-transmission control
    • The ability to use differential corrections (similar to DGPS)
    • Receivers use “all-in-view” signals
    • Includes one or more Loran data channels that provide: Low-rate data messaging, added integrity, differential corrections (dLoran and/or DGPS) and other communications including navigation messages.

    An eLoran receiver measures the TOA of the eLoran signal:

    TOA = TOR – TOT = PF + SF + ASF + ∆Rx

    where TOR is time of reception, TOT is time of transmission, PF is the primary factor (propagation delay through air), SF is the secondary factor (propagation delay over sea), ASF is the additional secondary factor (propagation delay over terrain) and ∆Rx is the delay due to receiver electronics and cables.

    The primary and secondary factors are well-defined delays and can be calculated as a function of distance. The additional secondary factor delay is mostly unknown at the time of installation. Fortunately, the ASFs remain very stable over time. Any fine changes in ASF over time may be compensated for by one or more differential eLoran reference station sites providing corrections over the Loran data channel.

    When eLoran is used for positioning, a minimum of three eLoran transmitting sites are needed to calculate a two-dimensional position fix and time. Time (phase) and frequency can be derived from a single transmitting site as well. With three sites, timing can be derived while a receiver is in motion. An integrated eLoran/GPS receiver can take advantage of combinations of eLoran and GPS transmissions to develop a PNT solution. Any additional measurements provide a means to improve the solution’s accuracy (using weighted least squares) or to protect the solution’s integrity (by receiver-autonomous integrity monitoring).

    To achieve the highest accuracy levels, the user receiver corrects its TOA measurements with the published ASF values for the area and differential eLoran corrections received through the Loran data channel. ASF maps for specific geographic areas are distributed to users in a receiver-independent data format that is currently being standardized by the Radio Technical Committee for Maritime Services’ (RTCM’s) Special Committee (SC) 127 on eLoran. The ASF map data would be published by the service provider responsible for aids to navigation.

    As described before, the measured ASF values remain stable over long periods of time. Any small changes in the published ASFs due to changes in propagation path characteristics or transmitter-related delays will be compensated for by differential corrections. For this, a differential eLoran reference station site is deployed within 20 to 30 miles (32 to 48 kilometers) of the area of interest. The reference station compares its measured ASFs against the published values and broadcasts corrections to the users through the Loran data channel. Figure 1 shows the principle of differential eLoran positioning in a maritime environment and is representative of its use in other modalities as well.

    Figure 1. Overview of a representative eLoran system.
    Figure 1. Overview of a representative eLoran system.

    eLoran meets the application requirements shown in Table 1. While unaided, Loran-C does not meet the requirements for a multi-modal, redundant PNT system, specifically the position accuracy requirement. The U.S. first developed eLoran to reduce the positioning error and to enable the system to meet modal performance requirements.

    Table 1. eLoran system performance requirements.
    Table 1. eLoran system performance requirements.

    eLoran Applications

    We are staunch advocates of GPS and believe it should be fully funded, kept technically advanced, protected, toughened and augmented. When GPS is available and trustworthy, it should be used. However, no technology is failsafe, and prudent users should not rely on a sole source for their PNT needs. GPS has been called “a single point of failure” for much of the U.S. economy and critical infrastructure. Applications and requirements vary widely from wireless network communications of ± 1.5 microseconds, to maritime harbor entrance and approach requirements of ± 20 meters, to phasor measurement unit requirements in the electric power grid of ± 500 nanoseconds.

    It is important to recognize the challenge of providing assured PNT while also taking advantage of the efficiencies gained by implementing a common solution across all sectors, industries and users. Point solutions can provide complementary PNT for specific individual or modal needs, and any resilient PNT ecosystem includes multiple levels of redundancy.

    Some key application areas in which eLoran can provide complementary PNT are telecommunications, energy, finance and transportation. We believe these will be some of the first sectors to adopt and exploit eLoran as a component of their critical infrastructure protection and possibly as a co-primary PNT solution alongside GPS.

    Telecommunications Sector. A March 2014 letter from the Alliance for Telecommunications Industry Solutions (ATIS) to the National Security Telecommunications Advisory Committee contained an attached document, Recommended Updates to Telecom Vulnerability to Loss of GPS Signals Documentation, that outlined three areas of concern that ATIS has identified relating to the exposure of commercial communications systems to a loss of the GPS signal. Included in the documentation was the statement: “With the Loran systems decommissioned, GPS is currently the only technology that can meet synchronization requirements for E911 as there is no other widely available access to UTC time of day in the United States.” eLoran’s Loran data channel provides the UTC time-of-day information that the telecommunications industry seeks, as well as providing complementary timing (phase) and/or frequency solutions that would mitigate ATIS’s concerns about: (1) the size of the area and duration effects of a GPS outage, (2) the effects of spoofing, (3) the inability of oven-controlled crystal oscillators (OCXOs) to maintain phase alignment for 24 hours at 1.5 microseconds, and (4) the phase performance of OCXOs in varying temperature environments.

    The European Telecommunications Standards Institute Primary Reference Clock mask is one tool used by the telecommunications industry to determine the quality of timing signals in telecommunication applications. Figure 2 shows that eLoran is able to meet maximum time interval error (a measurement of wander or time stability) requirements, often outperforming GPS. Testing was performed independently in a cooperative effort between the United Kingdom National Physical Laboratory and Chronos Technology Ltd., UrsaNav’s reseller in England.

    Figure 2. Maximum time interval error plot of eLoran and GPS.
    Figure 2. Maximum time interval error plot of eLoran and GPS.

    Energy Sector. At present, GPS is the only time source for phasor measurement unit (PMU) (also known as synchrophasor) and frequency data recorder (FDR) sensors used to collect data that measures the state of an electrical system and manages power quality. PMUs/FDRs are a necessary component of the movement to a smart-grid approach to improve energy efficiency on the electrical grid and in businesses and homes. PMUs and FDRs cease to work if the GPS signal is lost or unstable. In 2013, UrsaNav began working with the University of Tennessee at Knoxville (UTK) to demonstrate the capability of eLoran, alongside GPS, to provide the necessary timing accuracy for UTK’s high-precision FDRs to collect synchrophasor data from the U.S. power grid. The required accuracy of the timing reference source is ± 500 nanoseconds, needed by each device performing synchrophasor measurements.

    The laboratory setup in Bedford, Mass., used side-by-side FDRs: one using a GPS receiver and one using an eLoran receiver. Other than replacing the GPS receiver with an eLoran receiver in one of the FDRs, no other changes were made. The eLoran signals were being transmitted from a former U.S. Coast Guard (USCG) Loran Support Unit in Wildwood, N.J., more than 300 miles (483 kilometers) from our Bedford laboratory.

    “Raw” eLoran was used for the test, that is, with no differential corrections nor continuous receiver antenna calibration. Figure 3 shows the resultant frequency and phase angle comparisons between GPS and eLoran. Green is eLoran; black is GPS. Frequency comparisons are on the left, top and bottom. Phase angle comparisons are on the right, top and bottom. The bottom left graph is a blow-up of the area encircled in red in the top left graph. The bottom right graph is a blow-up of the area encircled in red in the top right graph. In both cases, eLoran performs on par with GPS.

    Figure 3. Frequency data recorder outputs from GPS and eLoran.
    Figure 3. Frequency data recorder outputs from GPS and eLoran.

    Financial Sector. A European Securities and Markets Authority (ESMA) report, dated May 22, 2014, indicates that the majority of trading venues are already coordinated with GPS time, and further states that the deployment of these systems might be costly and technically challenging. ESMA’s view is that each trading venue and market participant should rely on an atomic clock to issue timestamps. An eLoran timing alternative would be less costly, less technically challenging, and, when used in concert with other solutions (such as GPS, atomic clocks or Network Time Protocol / Precision Time Protocol) would also provide trusted time. eLoran would provide absolute time over very wide areas, thereby allowing dispersed markets and users to take advantage of this synchronized time solution. Additionally, eLoran can often provide time indoors, using a magnetic field (H-field) antenna, thereby precluding the permits and expense required for a rooftop antenna installation. ESMA has asked for industry comment on its proposed requirement to synchronize clocks to the microsecond level, and invited industry responses to its preliminary view that business clocks be accurate at least up to the microsecond level.

    Transportation Sector – Aviation. PNT use in air traffic management is illustrative. In accord with U.S. Federal Aviation Administration (FAA) planning, a principal surveillance source in the U.S. national air space (NAS) by 2020 will be Automatic Dependent Surveillance-Broadcast (ADS-B), where the required positional accuracy of aircraft relies on GPS position. Moreover, the independent validation and backup of GPS-derived positions relies on accurate time-of-arrival measurements at a network of 650 radio stations in the NAS that currently use GPS-disciplined clocks with accuracy down to 30 nanoseconds. These radio stations are critical infrastructure of the Surveillance and Broadcast Services (SBS) system, which provides ADS-B surveillance to FAA air traffic management (ATM).

    The FAA recognizes the need for a backup to surveillance and navigation in the event of local, regional and wide-scale GPS outages, and is examining both near-term and long-term strategies for continuity of operations during those outages. Because of the long lead times for ATM technology insertion, near-term mitigation strategies out to at least 10 years are constrained by existing ATM ground infrastructure and current avionics capabilities. Long-term solutions are not so constrained, and may be based on new signals in space, new ground infrastructure and new avionics capabilities.

    Surveillance. Beginning in 2020, ADS-B will be a principal surveillance technology. In recognition of the need for a backup if GPS fails, the FAA is planning to maintain a mix of beacon-interrogation radar and wide-area multilateration (WAM) in the near term. The long-term strategy is still very much in the evolutionary stage.

    Navigation. Near-term strategies involve a mix of approaches based upon existing infrastructure and the current capability of avionics. A leading approach, referred to as DME/DME/IRU, uses two-way ranging to multiple Distance Measuring Equipment (DME) facilities augmented by the avionics inertial reference unit (IRU). This approach is practical and applicable more to air carrier aircraft than regional jets or general aviation. Other approaches rely to some extent on the use of very high frequency Omni-Directional Range (VOR) facilities. As with surveillance, the long-term strategy is very much evolutionary.

    It is instructive to note that near-term solutions rely on existing radar, DME and VOR infrastructure because it is in place and is compatible with existing avionics. In the long-term view, new technologies with less costly infrastructure are likely to be more cost-effective, especially if they provide benefits beyond ATM applications. eLoran is such a technology.

    Transportation Sector – Maritime. There is an increasing awareness in the maritime world that no single system can provide PNT resiliently under all circumstances. At this moment, GPS (with augmentations) is used on most commercial vessels, and in many cases integrated into systems we did not expect would need or use GPS-derived position or time. Even though the introduction of GLONASS, Galileo, BeiDou and other GNSS systems will provide some resilience, the underlying (satellite) technology remains the same, only providing relatively weak signals from space at mostly the same or close-by frequencies for compatibility and inter-operability.

    The International Maritime Organization (IMO) recognizes the need for multiple PNT systems on board maritime vessels. The organization developed the e-Navigation concept to increase maritime safety and security via means of electronic navigation, which calls for at least two independent dissimilar sources of positioning and time in a navigation system to make it robust and fail safe. As a follow on, IMO’s Navigation, Communications and Search and Rescue Committee is considering performance standards for multi-system shipborne navigation receivers, which includes placeholders for satellite, augmentation and terrestrial systems.

    The most viable terrestrial system providing PNT services that meet IMO’s requirements is eLoran. With three eLoran transmitters in good geometry, eLoran can provide sub-10 meter (95 percent probability level) horizontal positioning accuracy and UTC synchronization within 50 nanoseconds, sufficient to be the co-primary PNT solution with GNSS. The General Lighthouse Authorities of the United Kingdom and Ireland (GLAs) have installed UrsaNav’s differential eLoran reference stations to provide the world’s first initial operational capability (IOC) eLoran system.

    Together with Loran transmitters in England, France, Germany, Norway and Denmark, the differential eLoran reference stations provide better than 10-meter positioning accuracy at seven ports and port approaches along the English and Scottish east coast. IOC was achieved at the end of 2014, with full operational capability planned for 2018. Other nations have either begun, or are exploring, similar projects.

    Figure 4 shows the accuracy of an eLoran position at the differential reference station on the Humber River in England. Figure 5 shows the position accuracy while on board a vessel transiting outbound on the river from Humber to the North Sea.

    Figure 4. Zero-baseline accuracy at Humber reference station.
    Figure 4. Zero-baseline accuracy at Humber reference station.
    Figure 5. Onboard, en route accuracy on the Humber River.
    Figure 5. Onboard, en route accuracy on the Humber River.

    Current State of eLoran Technology

    eLoran technology has been available since the mid-1990s and is still available today. In fact, the state-of-the-art of eLoran continues to advance along with other 21st-century technology. eLoran system technology can be broken down into a few simple components: transmitting site, control and monitor site, differential reference station site and user equipment.

    Modern transmitting site equipment consists of a high-power, modular, fully redundant, hot-swappable and software configurable transmitter, and sophisticated timing and control equipment. Standard transmitter configurations are available in power ranges from 125 kilowatts to 1.5 megawatts. The timing and control equipment includes a variety of external timing inputs to a remote time scale, and a local time scale consisting of three ensembled cesium-based primary reference standards. The local time scale is not directly coupled to the remote time scale. Having a robust local time scale while still monitoring many types of external time sources provides a unique ability to provide proof-of-position and proof-of-time. Modern eLoran transmitting site equipment is smaller, lighter, requires less input power, and generates significantly less waste heat than previously used Loran-C equipment.

    The core technology at a differential eLoran reference station site consists of three differential eLoran reference station or integrity monitors (RSIMs) configurable as reference station (RS) or integrity monitor (IM) or hot standby (RS or IM). The site includes electric field (E-field) antennas for each of the three RSIMs.

    Modern eLoran receivers are really software-defined radios, and are backward compatible with Loran-C and forward compatible, through firmware or software changes. ASF tables are included in the receivers, and can be updated via the Loran data channel. eLoran receivers can be standalone or integrated with GNSS, inertial navigation systems, chip-scale atomic clocks, barometric altimeters, sensors for signals-of-opportunity, and so on. Basically, any technology that can be integrated with GPS can also be integrated with eLoran.

    Figure 6 shows a resilient PNT receiver that includes GPS, DGPS, eLoran and a dual-band (100/300 kHz) E-field antenna. The left-hand antenna, shown installed on the P&O Ferries’ Pride of Hull, is the resilient PNT antenna. The right-hand antenna is a standard GPS antenna.

    Figure 6. Resilient PNT receiver and dual-band antenna.
    Figure 6. Resilient PNT receiver and dual-band antenna.

    World View of eLoran

    Nine nations are operating Loran-C or eLoran stations, including Russia and China. It is our understanding that the Republic of Korea, India and the Kingdom of Saudi Arabia are pursuing the installation of eLoran technology or upgrading their Loran-C technology to eLoran.

    The modernization and upgrade of the U.S. Loran-C system to eLoran was a congressionally mandated program jointly executed by the FAA and USCG from 1997 to 2009, and funded at $160 million. During this time, eLoran was successfully tested and demonstrated in all modes: aviation, maritime, land-mobile, location-based, and timing and frequency. Further, eLoran has been successfully in operation in the U.K. for several years. Every national and international government, industry and academic report has concluded that GNSS is vulnerable and that eLoran is the best complementary solution to help negate those vulnerabilities.

    The U.S. terminated its Loran-C service, and thereby its nascent eLoran program, in 2010. Canada followed suit and terminated its Loran-C service as well. Shortly thereafter, DHS/USCG began dismantling or demolishing the modernized infrastructure. However, in December 2014, Congress directed that DHS/USCG preserve the existing, unused U.S. Loran-C infrastructure, unless the Secretary of Homeland Security certifies it is not needed for a system to complement GPS.

    In March 2015, U.S. House of Representatives Resolution (H.R.) 1678, a bill that would require establishment of a strong, difficult-to-disrupt terrestrial system to complement GPS, and to serve as another source of PNT when GPS isn’t available, was referred to the Committee on Armed Services. The bill seeks to amend the language that provided for the establishment and management of GPS in Title 10, the section of law that deals with the armed services. We understand that other members of Congress have expressed interest and will be co-sponsoring the bipartisan bill. H.R. 1678 was introduced by Congressman John Garamendi (Democrat, Calif.) with Congressman Duncan Hunter (Republican, Calif.), Congressman Frank LoBiondo (Republican, N.J.) and Congressman Peter DeFazio (Democrat, Ore.) as the initial co-sponsors. In August, the bill was referred to the Subcommittee on Strategic Forces.

    Additionally, in May 2015, the DHS and USCG entered into a cooperative research and development agreement with UrsaNav and Exelis (now part of Harris Corp.) to research, evaluate and document at least one alternative to GPS as a means of providing PNT information in the form of eLoran.

    It is our understanding that the U.S. Congress is still considerably concerned about the lack of a complementary PNT solution to safeguard U.S. critical infrastructure and key resource sectors, and to protect our economy in the event of a GPS outage. Congress continues to press the administration for a resolution, in the form of a continental U.S. eLoran system, before our nation is placed at further risk.

    Acknowledgments

    The authors wish to acknowledge the assistance of Dr. Ron Bruno, Harris Corp., and Dr. Paul Williams and Chris Hargreaves, GLAs.

    Manufacturers

    UrsaNav provided the eLoran receiver and Symmetricom, now Microsemi, provided the GPS receiver for the timing tests shown in Figure 2.

    STEVE BARTLETT is vice president of operations at UrsaNav, Inc., North Billerica, Mass.

    GERARD OFFERMANS is senior research scientist at UrsaNav engaged in various R&D project work and product development.

    CHARLES SCHUE is co-owner and president of UrsaNav.

     

    FURTHER READING

    • eLoran

    “Can eLoran Deliver Resilient PNT?” by N. Ward, C. Hargreaves, P. Williams and M. Bransby in Proceedings of The Institute of Navigation 2015 Pacific PNT Meeting, Honolulu, Hawaii, April 20–23, 2015, pp. 1051–1054.

    “eLoran Initial Operational Capability in the United Kingdom – First Results” by G. Offermans, E. Johannessen, S. Bartlett, C. Schue, A. Grebnev, M. Bransby, P. Williams and C. Hargreaves in Proceedings of the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, Calif., January 26–28, 2015, pp. 27–39.

    “Implementing a Wide Area High Accuracy UTC Service via eLoran” by G. Offermans, E. Johannessen and C. Schue in Proceedings of the 46th Annual Precise Time and Time Interval Systems and Applications Meeting, Boston, Mass., December 2014, pp. 124–133.

    • Loran-C

    “GPS + LORAN-C: Performance Analysis of an Integrated Tracking System” by J. Carroll in GPS World, Vol. 17, No. 7, July 2006, pp. 40–47.

    • Alliance for Telecommunications Industry Solutions

    Letter to National Security Telecommunications Advisory Committee dated March 11, 2014, with attached document, Recommended Updates to Telecom Vulnerability to Loss of GPS Signals Documentation.

    • European Telecommunications Standards Institute

    Transmission and Multiplexing (TM); Generic Requirements for Synchronization Networks, EN 300 462-1-1, European Telecommunications Standards Institute, Sophia Antipolis, France, 1998.

    • European Securities and Markets Authority

    MiFID/MIFIR Discussion Paper, ESMA/2014/548, European Securities and Markets Authority, Paris, France, May 22, 2014.

    • U.S. Legislation

    H.R. 1678: National Positioning, Navigation, and Timing Resilience and Security Act of 2015, House of Representatives bill in the United States. Congress, Washington, D.C.

    • Federal Radionavigation Plan

    2014 Federal Radionavigation Plan (F, DOT-VNTSC-OST-R-15-01, U.S. Department of Defense, Department of Homeland Security and Department of Transportation, Washington, D.C., available from the National Technical Information Service, Springfield, Virginia, 2015.

    “The Federal Radionavigation Plan” by R.B. Langley in GPS World, Vol. 3, No. 3, March 1992, pp. 50–53.

    1990 Federal Radionavigation Plan, DOT-VNTSC-RSPA-90-3 and DOD-4650.4, U.S. Department of Transportation and U.S. Department of Defense, Washington, D.C., available from the National Technical Information Service, Springfield, Virginia, 1990.

  • Innovation: Faster, Higher, Stronger

    Innovation: Faster, Higher, Stronger

    Proposed GNSS Navigation Messages for Improved Performance

    By Wentao Zhang and Yang Gao

    INNOVATION INSIGHTS by Richard Langley
    INNOVATION INSIGHTS by Richard Langley

    TIME-TO-FIRST-FIX, commonly known by the initialism TTFF, is the elapsed time between the powering on or starting up of a GNSS receiver and when it successfully computes either a two-dimensional (height constrained) or three-dimensional position fix and sets its clock to the correct time. A three-dimensional fix requires simultaneous receiver measurements on the signals from a minimum of four satellites along with the satellites’ positions (ephemerides) and the offsets between the individual satellite clocks and the GNSS system time.

    TTFF depends crucially on the availability and timeliness of the satellite ephemerides and clock information when a receiver starts up and, accordingly, there are three types of start-up with correspondingly different TTFF.

    A cold start (sometimes also called a factory start) occurs when the receiver has no knowledge of its current position, time or the positions of the satellites and their clock offsets. The receiver must do a blind search of the sky trying different possible Doppler frequency shifts and pseudorange delays for all the satellites in the constellation. Once satellites are found and tracked, the ephemerides and clock information must be collected. This is repeated in each satellite’s navigation message every 30 seconds. In addition, the information on the offset between GNSS system time and UTC must be collected along with the ionospheric delay correction parameters and the almanac (an approximate ephemeris for all active satellites in the constellation) to be used for faster subsequent signal acquisition. This data is only transmitted once in the 12.5-minute-long navigation message. Therefore, the TTFF for a cold start can take up to 12.5 minutes and even longer especially if the GNSS signals are hard to acquire such as in obstructed environments.

    A warm start, or what we might call normal operation, occurs when the receiver has some a priori information on its position, the time and the approximate locations of the satellites. Typically, this means knowing the receiver position to within a few hundred kilometers, time to within 10 minutes or so, and a reasonably fresh almanac. Armed with that information, a receiver knows which satellites should be visible to it and can quickly acquire and track satellite signals and obtain the satellite ephemeris and clock information. Since that information is repeated every 30 seconds, TTFF for a warm start can be 30 seconds or less.

    A hot start occurs when a receiver is powered on after being off and stationary for a short interval and it therefore has a very good estimate of its position and the current time and valid satellite ephemeris and clock data. TTFF for a hot start, therefore, is typically only a few seconds. This mode of receiver operation would also apply to scenarios where all signals are temporarily lost in road or rail tunnels or where a number of signals are momentarily blocked by obstructions causing a break in position fixing.

    Fast first fixes were traditionally only possible when a receiver had a clear view of the sky and could readily acquire the navigation messages. Pseudorange measurements can be made, however, even if satellite signals are somewhat attenuated in strength to the point that navigation messages cannot be acquired. Position fixing in this case would be possible if the receiver could obtain the navigation information from elsewhere. Over the past decade or so, assisted GNSS techniques have been developed to provide frequently refreshed navigation information over cellular telephone networks, for example. But would there be a way to achieve fast first fixes autonomously without reliance on these assisted techniques? Not with the signals presently being transmitted by either the mature or nascent constellations, it seems, but in this month’s column, we look at proposed changes to the way navigation messages are formulated that could result in a future satellite navigation system providing faster fixes effectively giving receivers higher sensitivity and stronger performance.

    “Innovation” is a regular feature that discusses advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering, University of New Brunswick. He welcomes comments and topic ideas. Email him at lang @ unb.ca.

    Despite some differences in their structures, different GNSS broadcast navigation (NAV) messages usually consist of two parts: immediate (primarily ephemeris) and non-immediate (primarily almanac) data. The immediate data is repeated at a much shorter interval than the non-immediate data, and expires much sooner than the non-immediate data. Taking GPS as an example, the civilian navigation (CNAV) messages consist of five subframes with each lasting six seconds, as depicted in FIGURE 1. The first three subframes provide the ephemeris, with the content repeated every 30 seconds and updated every two hours, while the last two subframes provide the almanac for each satellite in 25 pages, with the content updated nominally every six days (according to the GPS Interface Specifications document), but updates are actually daily.

    FIGURE 1. Frame structure of GPS CNAV messages.
    FIGURE 1. Frame structure of GPS CNAV messages.

    Depending on the accuracy of receiver time and the availability of previously collected ephemerides (the immediate data) when powered on, GNSS user equipment (UE) might experience cold, warm or hot starts, among which the warm start is the most common case. In the widely accepted definition for warm start, no valid ephemeris is available, but the receiver time is roughly known at startup.

    As depicted in FIGURE 2, the position fix sequence by a standalone GNSS UE normally consists of signal acquisition, tracking, bit synchronization, frame synchronization, ephemeris downloading, measurements taking and position computation. In performing a regular warm start, signal acquisition usually takes only a few hundred milliseconds for a GPS device in open-sky environments. However, under weak signal conditions, signal acquisition might take much longer (say a few tens of seconds). Once the signal is acquired, the tracking loop is activated, and immediately after the signal is pulled in the process of data-bit synchronization is started. This process takes a few hundred milliseconds to several seconds depending on signal strength and algorithm efficiency. In a stable tracking status, the navigation bits are collected sequentially one by one. Collecting a complete copy of a GPS ephemeris takes about 18 seconds in open-sky environments but may take minutes or even forever in weak signal environments due to an increased bit error rate (BER). As soon as the ephemeris downloading from three to four satellites is completed and the measurements are made, the user position fix usually can be obtained immediately. Therefore, in weak signal environments, the obstacles to fast time-to-first-fix (TTFF) are primarily signal acquisition and ephemeris downloading, and in open-sky environments the obstacle mainly lies in the time needed for ephemeris downloading.

    FIGURE 2. Typical sequence of position fix process in standalone GPS user equipment (Msr=measurements).
    FIGURE 2. Typical sequence of position fix process in standalone GPS user equipment (Msr=measurements).

    For a GNSS UE in an open-sky environment on the Earth’s surface, the minimum received signal level for GPS L1 is around -130 dBm according to the interface specifications. For other GNSS signals, the nominal received signal levels are approximately the same.

    However, in some extreme cases, such as urban canyon, foliage and indoor environments, the signals finally arriving at a receiver’s antenna could be heavily attenuated by 30 dB or even more. Working under such conditions requires GNSS UE to have high-sensitivity capability.

    When the GNSS signal strength drops to a certain level, it causes immediate difficulties in the GNSS receiver tracking loop and for ephemeris downloading. Firstly, the parameters of the tracking loop, designed for normal signal strengths, are no longer optimum for either obtaining enough gain for signal detection or for maintaining signal tracking. Secondly, BER increases with decreasing signal strength. When the signal carrier-to-noise-density ratio drops below 27 dB-Hz, even if signal tracking is maintained, the increased BER would make it difficult for successful decoding of NAV messages.

    Sensitivity improvements for a GNSS receiver can involve contributions from the antenna, the RF front end and baseband signal processing. In the signal processing, to obtain adequate processing gain in signal-to-noise ratio for signal detection, combined coherent and non-coherent integrations are needed. An approximate relationship for calculating such processing gain is given in Equation (1). Considering that non-coherent integration is subject to squaring loss, for a fixed total integration period (TI), increasing the coherent period (Tc) is more efficient for achieving higher processing gain. However, without knowing the navigation bits, the coherent integration is limited within a 1-bit period or 20 milliseconds for GPS signals.

    Eq-3  (1)

    To improve sensitivity to -160 dBm, coherent integration over multiple bits is desired. Therefore, valid navigation bits as well as the bit boundaries are needed for data wipe-off. For this purpose, previously collected navigation bits can be directly used if they are still valid or fresh navigation messages from different sources, including ephemeris and almanac, can be used to recover the navigation bits.

    GNSS Assistance Technologies

    The existing efforts for improving TTFF and sensitivity for GNSS UE include developing assistance systems and implementing new algorithms for UE. The concept of AGPS goes back to the late 1990s when lots of patents were filed and then granted in early 2000s. Seeing the challenges of TTFF and sensitivity for standalone GPS devices, the general idea from the patents is to provide assistance information to GNSS UE, such as time, rough location, a list of visible satellites, the Doppler shift of each satellite, ephemerides and so on, in a way to speed up each stage in the process of a position fix (Figure 2). With a series of AGPS specifications embodied in the 3GPP and Open Mobile Alliance standards since 2001, AGPS-enabled products have become quite popular in the GNSS marketplace.

    The assistance data definitely brings enhanced performance in TTFF and sensitivity for GNSS UE, but it is a challenge when network connectivity is not available. A technology often referred to as ephemeris extension (EE) was introduced by Global Locate and SiRF, which enables fast TTFF and high sensitivity for GNSS UE even without network connectivity. According to the descriptions of the long-term orbit used by Broadcom and InstantFix used by CSR, both are based on orbit determination theory and provide alternative ephemerides with a validity period extending to a few days, rather than two hours for the regular GPS ephemerides. As of today, a variety of EE products are available from many companies and research institutes, and EE has become a standard feature for GNSS products in the market place.

    Limitations of Existing GNSS Assistance Technologies

    In spite of the benefits to TTFF and improved sensitivity, the assisted GNSS (AGNSS) and EE technologies have obvious limitations, as detailed in TABLE 1. Building and maintaining the AGNSS infrastructure require significant efforts and continuous cost. Any AGNSS-capable UE, unlike standalone GNSS UE, are tied to good signals from the subscriber cellular phone networks to get assistance data on time, which substantially limit their areas of operation. The EE technologies consist of server-based and client-based modes. Client-based EE is good for standalone UE, but the accuracy is subject to the validity of the embedded Earth orientation parameters (EOPs), and the quantity and quality of the local data collection. Server-based EE is able to provide better accuracy, but it also needs support from the global infrastructure for data collection and is subject to network connectivity. Table 1 clearly indicates that AGNSS and EE can only be beneficial under certain prerequisite conditions, such as with network connectivity and data availability. In other words, even with the above-described technologies, fast TTFF and high sensitivity may still not be obtainable when those prerequisite conditions are not met, which is not uncommon in practical use.

    TABLE 1. Comparison of assisted GNSS (AGNSS) and extended ephemeris in improving time-to-fist-fix (TTFF) and sensitivity.
    TABLE 1. Comparison of assisted GNSS (AGNSS) and extended ephemeris in improving time-to-fist-fix (TTFF) and sensitivity.

    Suggested New GNSS NAV Messages

    The fundamental cause of the problem related to TTFF and sensitivity, in our view, lies in the congenital weakness of the design of the existing GNSS NAV messages. Taking GPS as an example, the contents of GPS subframes 1–3 are updated every two hours, although the ephemeris is valid for up to four hours. It is challenging for standalone GPS UE working in weak signal environments to catch up with such frequent ephemeris updates. Working properly during the past two hours does not mean that the UE can work properly in the next two hours if ephemerides are not downloaded in time. The NAV messages received two hours ago cannot be used for data aiding in the subsequent two hours to improve tracking sensitivity. For startups under normal signal conditions, the UE, if missing the start of subframe 1, have to wait 30 seconds to get to the next subframe 1 to download a complete copy of the ephemeris. Successful startups four hours ago also do not help much to reduce the TTFF in the subsequent startups, as time is needed again for ephemeris downloading.

    For other GNSSs, some specifications of their NAV messages are listed in TABLE 3. According to these specification, the downloading of Galileo ephemerides takes at least 30 seconds, and if the start of the first ephemeris page is missed, it will take at least 50 seconds to get a complete copy. So, from this perspective, the Galileo TTFF for standalone devices is expected to be longer than that for GPS. As to BeiDou, given the high degree of similarity between BeiDou D1 and GPS CNAV messages, it is expected that for standalone BeiDou UE, TTFF is also similar to standalone GPS UE. For GLONASS, the downloading takes just about10 seconds, and it will take about 30 seconds to get a complete copy of the ephemeris if the start of the first ephemeris string is missed. Therefore, in this regard, the GLONASS TTFF for standalone devices is expected to be the fastest among the GNSSs. It is worth noting that the GLONASS ephemeris, unlike that of other GNSSs, comprises Cartesian coordinates, velocity components and solar/lunar gravitational accelerations at the reference time, with the content valid over about 0.5 hours. Upon receiving the ephemeris, the UE is to calculate the satellite orbit by numerically integrating the motion equations that include the second zonal geopotential coefficients through a fourth-order Runge-Kutta method. Since the designed NAV messages for GPS, GLONASS, BeiDou and Galileo are all valid for only short periods (see Table 3), they are all subject to the aforementioned limitations.

    TABLE 3. Comparison of the NAV messages for GPS/GLO/BD(D1)/GAL(F/NAV)/New GNSS.
    TABLE 3. Comparison of the NAV messages for GPS/GLO/BD(D1)/GAL(F/NAV)/New GNSS.

    The common weaknesses in the NAV messages of GPS, GLONASS, BeiDou and Galileo described above can be overcome and fast TTFF and high sensitivity can be facilitated through the design of new NAV messages, when the following guidelines are followed:

    • Update interval, as short as possible
    • Repeat interval, as high as possible
    • Length of ephemeris content, as short as possible
    • Ephemeris life expectancy, as long as possible

    Let’s take a closer look at the GPS CNAV messages in terms of the above four guidelines. In the GPS CNAV messages, the primary content includes:

    • Satellite clock
    • Satellite ephemeris
    • Ionosphere information
    • UTC parameters
    • Almanac

    Two types of atomic clocks, rubidium and cesium, with stabilities of 10-12 to 10-13 are used on the GPS satellites. Given such stabilities, it is possible to have the clock parameters updated at an interval much longer than two hours, without introducing significant errors in the pseudorange observations. For the Keplerian parameters in the GPS ephemerides, they are derived from the fitting of four-hour orbit curves. The orbit, represented by the Keplerian parameters plus perturbation corrections, gives the overall best fitting of the whole orbit segment. If fitting over a longer orbit curve, it would be harder for the fitted orbit to agree well with each small portion of the original orbit. A set of Keplerian orbital parameters can be a good approximation of a short orbit segment (say four hours), but can hardly be the case over a long period (say 24 hours). Frequent updating of the ephemeris content is therefore indispensable in order to guarantee the orbit accuracy using this approach. As a result, there is not much room for extending the ephemeris update interval or equivalently to lower the update frequency.

    GPS CNAV messages include ionosphere information using the Klobuchar model, UTC parameters for relating GPS Time to UTC, and the almanac providing the rough orbits for all GPS satellites in service. According to the GPS Interface Specifications, all these messages will be updated at least once every six days, but they are typically updated on a daily basis.

    Based on the above analysis, it can be concluded that, in GPS CNAV messages, the only part that changes frequently is the ephemeris (primarily the Keplerian parameters). To facilitate fast TTFF and high sensitivity, we should reduce the update frequency of the GPS CNAV message. For that, the key is to find a way to minimize the update frequency of the ephemerides.

    Taking a close look at the satellite orbit may help us find a hint. For a satellite in space, given the initial conditions (position, r, velocity, r-dot, and so on) in Equation (2) at time t0 , the succeeding orbit, r(t), can be obtained by integrating the accelerations, r-twodots, in Equation (3), as illustrated in Equation (4).

    Eq-2  (2)

    Eq-3  (3)

    Eq-4  (4)

    To ensure the accuracy of the derived orbit, r(t), the forces exerted on the satellites that result in the acceleration, r-twodots(t), should be well modeled. The forces are both gravitational and non-gravitational.

    Standard gravitational force models embedded in UE can be independently used for years without introducing significant accuracy loss. As to the force of solar radiation, it is related to the reflectivity and attitude of the solar panels of the satellite, which can also be well modeled by some slow-varying and satellite-dependent parameters. If a set of such solar radiation parameter(s) along with some satellite initial conditions (position and velocity) can be provided with a certain period (say one day), the satellite orbit can be derived in the UE through some embedded force models.

    By now, we have found what we are looking for — namely, the solar radiation parameter(s) together with the satellite initial condition at a reference time, which can be the ideal content for our new ephemeris that can deliver a long orbit even if updated at a low frequency.

    Consider that, at any epoch, the satellite position and velocity expressed in Cartesian form (r, r-twodots) can also be identically expressed in Keplerian form through the set of standard elements as is currently done with GPS.

    The initial condition expressed in Keplerian form may give a better idea of what the orbit looks like and may have advantages for message encoding and sanity checks when it is adopted as the ephemeris content.

    The above fundamental analysis leads us to propose the new GNSS NAV messages provided in TABLE 2, which comply with the previously mentioned guidelines and therefore should be able to inherently facilitate fast TTFF and provide UE with high sensitivity.

    Note that the EOP data in the above table, used for relating coordinates in an Earth-centered Earth-fixed (ECEF) frame and those in an Earth-centered inertial (ECI) frame, are slowly varying parameters. The update interval for each part of the new NAV messages in Table 2 is one day, but for the almanac part, the update interval can be possibly extended to a few days similar to that currently used for GPS. In the ephemeris part, the proposed messages contain the six basic Keplerian elements and one solar radiation parameter for a selected reference time (t0). Once the ephemeris is downloaded, the six Keplerian elements can be immediately transformed to Cartesian position, r(t0), and velocity, r-dot(t0), in the ECEF frame, and further converted to the initial condition in the ECI frame to derive the entire orbit through Equation (4).

    TABLE 2. Proposed content of new GNSS navigation messages.
    TABLE 2. Proposed content of new GNSS navigation messages.

    Compared to the current GPS ephemeris, Table 2 contains many fewer parameters, so it is possible to have the new GNSS ephemeris and clock data packed in only two subframes, assuming that the data rate, word structure and subframe length are the same as for GPS CNAV messages. For the remaining parts listed in Table 2, they can be packed into multiple pages of 2 subframes in a similar way as the pages of subframes 4 and 5 in GPS CNAV messages. Therefore, we have the frame structure of the proposed new GNSS NAV messages as depicted in FIGURE 3. Considering that the contents of the first two subframes play a primary role in TTFF, the pages of subframes 3 and 4 are not further discussed here.

    FIGURE 3. Frame structure of the new GNSS NAV messages.
    FIGURE 3. Frame structure of the new GNSS NAV messages.

    Advantages of the New NAV Messages

    The content of the new NAV messages have been proposed in the last section, but the detailed format design is beyond the scope of this article. In TABLE 3, a comparison of the new NAV messages to the current GPS, GLONASS (GLO), BeiDou (BD) and Galileo (GAL) messages is presented. For the convenience of comparisons, the same data rate (50 bits per second [bps]) and the same length of subframe (6 seconds) as for the GPS CNAV messages have been used for the new GNSS NAV messages.

    Compared to other GNSS NAV messages, the new NAV messages have a smaller size, but the contained ephemeris has a longer life and, as a whole, the new NAV messages just need to be updated once every 24 hours. To help understand the advantages of the new NAV messages, we have made several comparisons.

    Standalone UE, New GNSS vs. GPS. For any new GNSS that deploys the new NAV messages, the UE just need to download the ephemeris from the satellites once in a whole day, whereas current GPS UE need to do it 12 times. In each downloading, it takes about 18 seconds for current GPS UE compared to about 12 seconds for the new GNSS UE. So there is no doubt that, from the TTFF perspective, the new NAV messages have incomparable advantages over the current GPS ones. Once a complete copy of the new NAV messages is downloaded, it can be used for data aiding in tracking loops for the rest of the whole day, even without network connections in weak signal environments. However, for current standalone GPS UE, they have to be in a strong signal environment to acquire fresh NAV messages every two hours. Otherwise there could be no position fix available in the next two hours due to the stale NAV bits and expired ephemerides. So, from a sensitivity point of view, a GNSS with the new NAV messages (referred to as new GNSS below) will also have incomparable advantages over GPS.

    Assisted UE, New GNSS vs. GPS. There are three purposes for assistance information for mobile devices: 1) to expedite signal acquisition; 2) to save time in ephemeris downloading; and 3) to have navigation bits for data aiding in the tracking loops. For assisted GPS UE and assisted GNSS UE with the new NAV messages, there is not much difference in the first aspect, as the assistance data, such as a satellite vehicle list, Doppler frequency, code phase, location and time, are common to both. For the second and third purposes, the assistance data sent from the assisting network to the UE are only needed once per day using the new NAV messages because they are updated only once per day. For assisted GPS UE, the assistance data are needed once every 2 hours, which means that GPS UE need frequent network connectivity and more network bandwidth for data transportation. In addition, as the size of a GPS frame is larger than the frame of the proposed new NAV messages, the time delay in transporting the assistance data will be longer in a GPS assistance network.

    New GNSS, Standalone vs. Assisted. When the new GNSS NAV messages are deployed, as the messages are only needed to be downloaded once a day, the assisted UE mostly show advantage in sensitivity and the required time for signal acquisition. Since signal acquisition is difficult only when the signal becomes weaker than a certain level, the performance of standalone and assisted new GNSS UE is expected to be comparable under normal signal conditions. Under weak signal conditions, as long as the NAV messages are received once a day, the performance in tracking sensitivities for both standalone and assisted UE is also expected to be comparable.

    Feasibility Considerations

    Since the proposed update interval for the new NAV messages is 24 hours, a period much longer than that currently used by all constellations, some immediate concerns may arise, such as:

    • Is the orbit/clock derived from the ephemeris good enough for 24 hours?
    • Is the calculation load for deriving satellite orbits affordable for a UE?

    The advancement in orbit determination and EE technologies can help relieve the worry on the first concern. For the JPL predicted orbit and clock states, it is claimed that the user range error (URE) of around one meter for one day and URE of less than 10 meters for seven-day predictions can be obtained.

    For a future GNSS that deploys the proposed new NAV messages, an orbital determination center (ODC) on the ground should be able to provide orbit predictions better than or at least comparable to those already obtained. Every 24 hours, as the intermediate results of the orbit predictions are obtained in the ODC, the new ephemeris data can be extracted and packed as one part of the new NAV messages. Once uploaded to the satellites and broadcast to GNSS UE on the ground, they can be used in deriving satellite orbits. The accuracies of the orbits/clock finally derived by GNSS UE will be subject to the accuracy of ephemeris, clock coefficients, EOPs and force models embedded in UE.

    The EOP data, describing the irregularities of the Earth’s rotation, are needed for coordinate transformations between ECEF and ECI, so the up-to-date EOP data carried in the new NAV messages ensures no accuracy loss in such transformations. For the force models embedded in GNSS UE, accuracy is not a problem as long as they are the same as that used by the ODC.

    As to the satellite clock, it is desired that, even if the clock coefficients are updated once per day, the accuracy of the predicted clock is still sufficient for navigation. For the current spaceborne clocks on GPS satellites, they are primarily rubidium atomic clocks with stability not better than about 10-13. The advancement of atomic clock technologies is fast, especially in recent years, and the era of rubidium, cesium and hydrogen maser clocks is evolving to ytterbium and even optical atomic clocks. As of today, atomic clocks as stable as 10-18 have been operated in laboratory settings. A project called the Space Optical Clock aims to put a lattice optical clock with a stability of 10-16 on the International Space Station by 2020. So it is foreseeable that new GNSSs should be able to deploy atomic clocks with stability several orders better than those currently deployed. At the stability of 10-16, the clock will only introduce millimeter-level errors in ranging in a 24-hour period. With such a stable satellite clock, there should be no accuracy concerns with clock data being updated once per day.

    Once the broadcast ephemeris is received by a UE, numerical integration can be started to derive the satellite orbit. During the numerical integration, the calculation load is primarily dependent on the following factors: 1) the length of numerical integration; 2) the numerical integration step size; 3) the order of the integrator; and 4) the complexity of local force models. Regarding the run-time necessary for orbital numerical integration on an embedded system, some published results indicate that a three-day prediction (numerical integration) takes only around 0.6 seconds on a 600-MHz processor with floating point unit. So a 12-hour integration would take only about 0.1 seconds on the same platform. As of 2014, for the popular high-end smartphones on the market, the speed of embedded processors ranges from 1.2 to 2.5 GHz with dual- or quad-cores. Considering the drastically growing computation power of mobile processors and the potential of further algorithm optimizations in orbital integration, the calculation load of numerical integration for a 12-hour interval is not at all an issue on a mobile device today, much less in the future.

    The GPS system designers four decades ago might not have realized that GPS would become so popular in the 21st century. Fast TTFF and high sensitivity have become standard requirements. The growing power of the application processors has also been beyond the imagination of people 40 years ago. So in their design, fast TTFF and high sensitivity might not have been given too much attention. The GPS modernization program is an attempt to meet the growing expectation on the system performance in the applications for today and the near future. In view of this, there is no reason not to give special considerations to inherently support fast TTFF and high-sensitivity applications when investigating and designing a new GNSS. Certainly, such efforts can be found both in recently launched GPS (Block IIF) and Galileo satellites, such as the pilot channels, but navigation under weak signal conditions for future standalone GPS and Galileo devices is still susceptible to the frequent change of NAV messages (see Table 3).

    Conclusions

    In this article, we have analyzed the benefits and limitations of the existing technologies (AGNSS and EE) widely adopted to improve TTFF and sensitivity performance, and pointed out the weakness in current GNSSs. Instead of seeking solutions in the user terminal, this article proposes to deploy new NAV messages on future GNSSs, with the contents updated once a day, to inherently facilitate fast TTFF and high sensitivity in the standalone GNSS UE. A future GNSS that uses such new NAV messages will have significant advantages for both standalone and assisted UE.

    Acknowledgment

    This article is based, in part, on the paper “New GNSS Navigation Messages for Inherent Fast TTFF and High Sensitivity” presented at the 2015 Pacific PNT Meeting of The Institute of Navigation, held in Honolulu, Hawaii, April 20–23, 2015.

    WENTAO ZHANG is a Ph.D. student in the Department of Geomatics Engineering at the University of Calgary. His research interest lies in different location technologies, and he is focusing his research on potential new GNSS navigation messages in an attempt to inherently improve time-to-first-fix and receiver sensitivity.

    YANG GAO is a professor in the Department of Geomatics Engineering at the University of Calgary. His research expertise includes both theoretical aspects and practical applications of satellite-based positioning and navigation systems. His research focuses on high-precision GNSS positioning and multi-sensor integrated navigation systems.

    FURTHER READING

    • Authors’ Conference Paper

    “New GNSS Navigation Messages for Inherent Fast TTFF and High Sensitivity” by W. Zhang and Y. Gao in Proceedings of The Institute of Navigation 2015 Pacific PNT Meeting, Honolulu, Hawaii, April 20–23, 2015, pp. 131–141.

    • Assisted GNSS

    A-GPS: Assisted GPS, GNSS, and SBAS by F. van Diggelen, published by Artech House, Boston and London, 2009.

    “First AGPS–Now BGPS: Instantaneous Precise Positioning Anywhere” by I. Petrovski, H. Hojo and T. Tsujii in GPS World, Vol. 19, No. 11, Nov. 2008, pp. 42–48.

    “Assistance When There’s No Assistance — Long-Term Orbit Technology for Cell Phones, PDAs” by D. Lundgren and F. van Diggelen in GPS World, Vol. 16, No. 10, Oct. 2005, pp. 32–36.

    “Assisted GPS: Using Cellular Telephone Networks for GPS Anywhere” by R. Bryant in GPS World, Vol. 16, No. 5, May 2005, pp. 40–45.

    “Assisted GPS: A Low-Infrastructure Approach” by J. LaMance, J. DeSalas and J. Järvinen in GPS World, Vo. 13, No. 3, March 2002, pp. 46–51.

    • Satellite Orbits

    Satellite Orbits: Models, Methods and Applications by O. Montenbruck and E. Gill, published by Springer-Verlag, Berlin and Heidelberg, 2000.

    “The Orbits of GPS Satellites” by R.B. Langley in GPS World, Vol. 2, No. 3, March 1991, pp. 50–53.

    • Predicted Orbits and Clocks

    Predicted GNSS Ephemeris, Rx Networks Inc., Vancouver, Canada.

    Multiple GNSS Assistance Services for u-blox GNSS Receivers: User Guide, UBX-13004360 – R02, u-blox AG, Thalwil, Switzerland, March 2015.

    “Predicted Orbit & Clock States,” Global Differential GPS System, Jet Propulsion Laboratory, Pasadena, Calif., Nov. 14, 2013.

    “SiRF InstantFix II Technology” by W. Zhang, V. Venkatasubramanian, H. Liu, M. Phatak and S. Han in Proceedings of ION GNSS 2008, the 21st International Technical Meeting of the Satellite Division of The Institute of Navigation, Savannah, Ga., Sept. 16–19, 2008, pp. 1840–1847.

    Long Term Orbits (LTO™), Technical Brief, Broadcom Corp., Irvine, Calif., 2007.

    • Assisted GNSS Standards

    Enabler Release Definition for Secure User Plane Location (SUPL), Candidate Version 3.0, OMA-ERELD-SUPL-V3_0-20140916-C, Open Mobile Alliance Ltd., San Diego, Calif., September 2014.

    “GNSS Test Standards for Cellular Location: Multi-Constellations Working in a Dense Urban Future” by P. Anderson, E. Anyaegbu and R. Catmur in GPS World, Vol. 24, No. 5, May 2013, pp. 27–37.

    Universal Mobile Telecommunications System (UMTS); LTE; Universal Terrestrial Radio Access (UTRA) and Evolved UTRA (E-UTRA) and Evolved Packet Core (EPC); User Equipment (UE) conformance specification for UE positioning; Part 1: Conformance test specification (3GPP TS 37.571-1 version 9.0.0 Release 9), European Telecommunications Standards Institute, Sophia Antipolis, France, 2012.

    • GNSS Interface Control Documents

    BeiDou Navigation Satellite System Signal in Space Interface Control Document, Open Service Signal, Version 2.0, China Satellite Navigation Office, Dec. 2013.

    Navstar GPS Space Segment / Navigation User Interfaces, Interface Specification, IS-GPS-200 Revision H, Global Positioning Systems Directorate, Systems Engineering and Integration, Los Angles, Calif., Sept. 2013.

    European GNSS (Galileo) Open Service Signal in Space Interface Control Document, Ref : OS SIS ICD, Issue 1.1, European Union, September 2010.

    GLONASS Interface Control Document, Navigation Radiosignal in Bands L1, L2, Edition 5.1, Russian Institute of Space Device Engineering, Moscow, 2008.

  • Innovation: Getting There by Tuning In

    Innovation: Getting There by Tuning In

    Using HD Radio Signals for Navigation

    By Ananta Vidyarthi, H. Howard Fan and Stewart DeVilbiss

    INNOVATION INSIGHTS by Richard Langley
    INNOVATION INSIGHTS by Richard Langley

    THE YEAR WAS 1906. On Christmas Eve of that year, Canadian inventor Reginald Fessenden carried out the first amplitude modulation (AM) radio broadcast of voice and music. He used a high-speed alternator capable of rotating at up to 20,000 revolutions per minute (rpm). Connected to an antenna circuit, it generated a continuous wave with a radio frequency equal to the product of the rotation speed and the number of magnetic rotor poles it had. With 360 poles, radio waves of up to about 100 kHz could be generated. However, Fessenden typically used a speed of 10,000 rpm to produce 60 kHz signals. By inserting a water-cooled microphone in the high-power antenna circuit, he amplitude-modulated the transmitted signal. On that Christmas Eve, he played phonograph records, spoke and played the violin with radio operators being amazed at what they heard.

    Fessenden had earlier worked with spark-gap transmitters, as these were standard at the time for the transmission of Morse code, or telegraphy, the wireless communication method already in use. But they couldn’t generate a continuous wave and couldn’t produce satisfactory AM signals. But as telegraphy was the chief means of communication, they remained in use for many years along with high-powered alternators and the Poulsen arc transmitter, which could also generate continuous waves.

    Although other experimental AM broadcasts were carried out using alternators or arc transmitters, voice transmissions — and in particular sound broadcasting — didn’t take off until the invention of amplifying vacuum tubes. Just before World War I, it was found that they could be used in an oscillator circuit to produce continuous waves, which could be easily modulated to make an AM transmitter. Such transmitters could be used for point-to-point communications but also for broadcasting, and a number of experimental broadcasting stations were established in Europe and North America during and just after the war. Tubes were also instrumental for improvements in receiver technology. “Where there was one licensed station in America in 1920, there were nearly 600 stations just five years later, and the number of radio receivers went from thousands of crystal sets to millions of vacuum-tube circuits.” — from The Science of Radio by Paul J. Nahin, one of my favorite writers on electronics and mathematics.

    AM radio broadcasting used frequencies in the long-wave, medium-wave and short-wave frequency bands, and still does. But AM signals often have low audio quality due to bandwidth limitations imposed by regulators and interference from other stations, atmospheric disturbances and electrical noise. So, over the past decade or so, many broadcasters have abandoned long-wave and medium-wave frequencies and moved to the frequency modulation or FM broadcast band with its superior signal capability.

    However, this migration pattern might be slowed or stopped if digital broadcasting were to be fully embraced on the AM broadcast bands. A digital technique developed by the iBiquity Digital Corporation is gradually being adopted by broadcasters in the United States and elsewhere. The technique provides FM-quality sound in the medium-wave band by supplementing existing AM signals or replacing them altogether. It can also supply data about the transmitting station and its broadcast. Some 240 AM radio stations in the U.S. already use the technology. (It can also be used in the FM band to provide CD-like quality.)

    But these digital signals in the AM broadcast band might serve an additional purpose beyond improving the listening experience. In this month’s column, our authors tell us about some extensive simulation work they have carried out to demonstrate the feasibility of using digital radio signals for navigation. In the future, you may be able to turn on your radio and tune in to get to where you’re going.

    “Innovation” is a regular feature that discusses advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering, University of New Brunswick. He welcomes comments and topic ideas. Email him at lang @ unb.ca.

    It is well known that the GPS signals are weak and are therefore subject to interference and blockage due to obstruction. Signals of opportunity (SOO), on the other hand, which are designed for other purposes such as communication, may also be used for navigation and have relatively greater signal power than GPS. They are plentiful and relatively more resistant to blockage and jamming compared to GPS. Many authors have presented methods and algorithms utilizing SOO such as AM and FM broadcast signals, TV broadcast signals and 3G/4G wireless communication signals (see Further Reading for examples). These signals are robust and have very good received power levels compared with GPS, and are capable of penetrating through buildings. In addition, these signals are readily available and there is no need for any additional installation of transmitting devices or infrastructure.

    In this article, we present the results of a study using AM HD Radio, digital radio in the 540–1700 kHz band of the frequency spectrum, with known transmitter locations, to locate and track receiver locations that are otherwise unknown. HD Radio, originally meaning hybrid-digital radio, is a trademarked term for iBiquity Digital Corporation’s digital radio technology. Unlike analog AM radio signals, digital radio signals are well structured and more immune to co-channel interference, and hence could be better adapted for navigation. In addition, with the proliferation of software-defined radios (SDRs), digital AM radio may eventually replace analog AM radio.

    The challenges of navigation using digital radio signals include narrow signal bandwidths, long symbol durations and lack of synchronization among transmitters. Therefore, digital radio signals are not an ideal choice for accurate position estimation, similar to many other SOO that aren’t designed for navigation. Nevertheless, in this work, we have designed algorithms to overcome such difficulties to obtain a good level of location accuracy, making it a feasible alternative for SOO navigation.

    Signal Format of Digital AM Radio

    Digital AM signals have a well-defined structure called in-band-on-channel (IBOC) that can be exploited for localization purpose. It employs sophisticated digital radio waveforms, which can deliver compact-disc-like sound quality, free of interference and noise, to radio listeners. It uses the existing AM and FM analog broadcasting bands and channel schemes to transmit digital signals. The IBOC digital radio transmitter system encodes analog audio into binary form for transmission.

    The design provided by IBOC AM radio has two service modes with two new waveform types: hybrid (denoted by MA1) and all-digital (denoted by MA3). The hybrid waveform retains the analog AM signal, while the all-digital waveform completely replaces the analog AM signal. In the hybrid service mode, the bandwidth of the analog audio signal waveform can be 5 kHz or 8 kHz. The digital signal is transmitted on both sides of the analog host signal in the primary and secondary sidebands. It is also transmitted on the tertiary sidebands, which are 20 dB beneath the analog signal as shown in FIGURE 1.

    FIGURE 1. Logical channels and sidebands on the frequency spectrum; hybrid mode with 5-kHz analog signal bandwidth. (After iBiquity.)
    FIGURE 1. Logical channels and sidebands on the frequency spectrum; hybrid mode with 5-kHz analog signal bandwidth. (After iBiquity.)

    For the 8-kHz configuration, the secondary sidebands are also beneath the analog host signal. The greatest system enhancements are realized with the all-digital system, as shown in FIGURE 2. In this system, the analog signal is replaced with the all-digital primary sidebands whose power is increased relative to the hybrid system levels. Secondary and tertiary sideband powers are also increased to the level of the hybrid waveform. Reference subcarriers are also provided to convey system control information. The end result is a higher power digital signal with an overall bandwidth reduction.

    FIGURE 2. Logical channels and sidebands on the frequency spectrum; all-digital mode. (After iBiquity.)
    FIGURE 2. Logical channels and sidebands on the frequency spectrum; all-digital mode. (After iBiquity.)

    Digital radio offers distinct advantages over analog, including mitigation of transmission artifacts and improved audio quality. These changes provide a more robust digital signal that is less susceptible to adjacent channel interference, thereby reducing the noise in the system. An overview of the AM digital system for both the service modes, MA1 and MA3, is given in the following paragraphs. However, in the simulation study we carried out, we used the all-digital AM (MA3) mode. The all-digital AM system has a smaller bandwidth than the hybrid signal. If reasonable localization results can be obtained with it, then we can predict that better localization results may be obtained with the hybrid signal.

    IBOC uses an orthogonal frequency-division multiplexing (OFDM) waveform for signal modulation. Each OFDM subcarrier channel has a spacing of 181.7 Hz. The hybrid MA1 service mode comprises 163 subchannels indexed from -81 to 81 over a total bandwidth of 29.4 kHz as shown in Figure 1. The all-digital MA3 service mode has only 105 subchannels indexed from -52 to 52 over a total bandwidth of 18.9 kHz as shown in Figure 2. Therefore, when compared to the all-digital mode, hybrid mode contains more training symbols per OFDM symbol duration. The training symbols are important since these symbols are known and will be used to perform correlation to estimate the signal time of arrival. We predict that since the hybrid mode contains more training symbols than the all-digital mode, detection accuracy will be higher for the hybrid mode. Hence, choosing the all-digital MA3 service mode for the localization will be more challenging, and this is another reason for our decision to use MA3. Demonstrating the capability of the all-digital MA3 service mode for localization would imply that the hybrid mode could be used for the same, with at least the same or better performance.

    Interleaving in time and frequency is used to mitigate the effects of burst errors. The interleaver output is according to a structured matrix (not shown here). Each interleaver matrix consists of information associated with a specific portion of the transmitted spectrum, and consists of eight interleaver blocks, with each block of size of 32 × 25. Hence, each block has 800 symbols to be filled, out of which 50 are known training symbols. Since this work entirely relies on training symbols, understanding interleaving is important so we know exactly where the training symbols are in a signal data stream. From the interleaving matrix, the positions of all training symbols are given, which have a periodic appearance of every 16 rows.

    The OFDM subcarrier mapping transforms interleaver output into scaled 16 quadrature amplitude modulation (QAM) and 64 QAM and binary phase-shift keying (BPSK) symbols and then maps them to specific OFDM subcarriers. The inputs to OFDM subcarrier mapping are according to the interleaver matrices, which map respective symbols to the primary, secondary, tertiary, Primary IBOC Data Service (PIDS) and reference subcarriers. One row of each active interleaver matrix and one bit of the system control vector are mapped into each OFDM symbol (every Ts seconds) to produce one output vector X, where Ts = 5.805 × 10-3 seconds.

    OFDM signal generation takes the complex frequency domain OFDM symbol X as generated above and outputs a time-domain representation of the digital signal. Let Xn be the vector X for the nth OFDM symbol, and Xn[k] be the kth element of Xn, which is the complex scaled constellation points for the subcarrier mapping for the nth symbol, where k = 0, 1,…, L-1 is the subcarrier index in the frequency-domain input to the signal generation for transmission. The input vector X is transformed into a shaped time-domain baseband pulse yn(t) defining the nth OFDM symbol as

    Inn-E1

    where n = 0, 1, …, ∞, Inn-E2.  Note that n indexes consecutive OFDM symbols, L = 105 is the maximum number of OFDM subcarriers, Ts and ∆f are the OFDM symbol period and OFDM subcarrier spacing, respectively, and W(t) is the time-domain pulse shaping function.

    Time of Arrival Acquisition

    Since the training symbols are known, a local copy can be generated at a receiver to correlate with the received digital AM signal to measure signal time of arrival (TOA). Measuring TOA accurately from a correlation peak is crucial, since any error in TOA measurement directly affects localization accuracy. The relatively narrow bandwidths and hence long symbol durations of the digital AM radio signals pose a challenge as they give rise to potentially large timing errors, thereby greater localization errors. To improve the location accuracy, strong digital AM signal levels are used to our advantage so methods such as curve fitting and time averaging can be performed. Moreover, unlike the structures of the civil GPS signals, which are all known, only the training symbols and their positions in the digital AM signals are known. Other data in the digital AM signals are random and cannot be used for correlation. Therefore, using long correlation vectors will help in detecting peaks as there will be more training symbols.

    Sampling. Correlation is performed, of course, after sampling. So we first discuss how to choose an appropriate sampling frequency. After correlation, if we detect the peak and record it as TOA only at the corresponding sampling instant, a maximum distance error of c/2fs can occur between two adjacent samples, where c is the speed of light and fs is the sampling frequency. At the Nyquist sampling frequency, say 40 kHz, this error could be as large as 3,750 meters. Sampling at a frequency much higher than the Nyquist can help to improve accuracy, but this improvement diminishes as the sampling frequency increases beyond a certain value, because the narrow signal bandwidth makes the peak of its correlation function rounded, so detection of the actual peak becomes less accurate. In our simulations, we found that this point of diminishing returns is at about fs = 10 MHz, at which the error between two adjacent samples is 15 meters, much better than that at the Nyquist sampling rate. This high sampling rate is easily doable with today’s digital technologies. However, this 15-meter error is the ranging error between one transmitter and one receiver. Five or more transmitters have to be considered for the location algorithm presented in a later section. Then, the ranging error of 15 meters may magnify to the order of a few kilometers as location errors. Clearly, there is a need to detect TOA of a correlation peak between two adjacent samples; that is, we need interpolation to achieve a smaller TOA error.

    Interpolation. To calculate the TOA between two adjacent samples, we interpolate by curve fitting the correlation data and estimate the TOA by solving polynomial functions. It was observed that the correlation peak is asymmetric, so the correlation curve is shaped differently to the left and right of the peak value. This is illustrated in FIGURE 3. Therefore, we need to fit two different curves on each side of the correlation peak. By a trial-and-error process, we determined that a quadratic polynomial is sufficient to fit the correlation values close to the peak. Therefore two simple quadratic functions are fitted for the correlation data points to the left and right of the peak.

    FIGURE 3. Asymmetric correlation peak denoting different slopes on either side.
    FIGURE 3. Asymmetric correlation peak denoting different slopes on either side.

    FIGURE 4 shows curve fitting for the correlation of a received signal and a local signal sampled at 10 MHz. The maximum time error due to sampling is Tsamp/2, which equals 5 ×10-8 seconds. This translates into a distance error of 15 meters and localization error of a few kilometers as mentioned before. From Figure 4, it is seen that the intersection point, which is taken as the measured TOA, is much closer to the actual TOA resulting in a much smaller distance error.

    FIGURE 4. Enlarged views of Figure 3 near the peak.
    FIGURE 4. Enlarged views of Figure 3 near the peak.

    Based on the HD Radio documentation, a normal signal-to-noise ratio (SNR) is calculated to be 52 dB. However, in case of adverse channel conditions, lower SNR levels of 30 dB and 10 dB have also been considered. Our simulations show that, with additive white Gaussian noise, the TOA estimation errors are affected by SNR very little above 10 dB, and are improved by an order of magnitude compared with no curve fitting. To make sure the TOA estimation error for the 10 dB SNR case can be used for the purpose of localization, we carried out a Monte Carlo simulation. Twenty-one different random signals were simulated, and the TOA measurement errors after curve fitting were recorded at different delays. The ensemble average of these TOA estimation errors was within 2 ×10-9 seconds. These results confirm that a 10 dB SNR signal can be very well used for localization. Thus, we used an SNR of 10 dB for all the simulations discussed later in this article.

    Differential Time-Difference of Arrival

    Once all the TOAs from different transmitters are obtained, they are sent to a processing station, which could be one of the receivers. Due to lack of synchronization in digital AM radio transmitters as well as unknown clock offsets in digital AM radio receivers, the obtained TOAs are not aligned, so they cannot be directly used for location determination. A technique called differential time-difference of arrival (dTDOA), which is similar to GPS double differencing and was published by the authors elsewhere (see Further Reading), is employed here to overcome this problem.

    Consider the case where there are two transmitters, A and B, and two receivers, C and D, as shown in FIGURE 5.

    FIGURE 5. Principle of differential time-difference of arrival (dTDOA).
    FIGURE 5. Principle of differential time-difference of arrival (dTDOA).

    When transmitter A is transmitting, its signal is received at different time instances by receivers C and D due to different propagation delays. The internal clock of each receiver records the correlation peak with respect to its local time at the corresponding receivers. TOAs of the signal from transmitter A at both receivers C and D are recorded as Inn-TAC and Inn-TAD, which also contain the unknown transmitter A clock time offset. Differencing these two TOAs Inn-TAC-TAD , the unknown transmitter A clock time offset is cancelled. But this TDOA is unsynchronized, so it cannot be used for location determination. Then we find the similar unsynchronized TDOA from transmitter B, Inn-TBC-TBD. To eliminate the unknown receiver clock offsets we difference the two TDOAs, resulting in a dTDOA:

    Inn-E3

    Thus, by using a minimum of two transmitters and two receivers, a dTDOA cancels receiver clock offsets and transmitter clock offsets, thus avoiding the need of precise clock synchronization. The number of independent dTDOA equations required to solve for the locations of n receivers is given by (m-1)(n-1) where m is the number of transmitters, and n is the number of receivers. For two receivers, there are four unknowns in a two-dimensional positioning plane, so we need a minimum of five transmitters to obtain four independent equations to solve for four unknown location parameters. If one of the receivers is permanently stationary with a known location such as in differential GPS, then we only need three transmitters to solve for two unknown horizontal location parameters, or four transmitters for three unknown location parameters in 3-D .

    The above dTDOA equations, when expressed in terms of receiver locations, are non-linear. The non-linear over-determined or exact system of equations can be solved using iterative procedures, such as non-linear least squares or the Levenberg-Marquardt (LM) technique. In the simulations we ran, we found that the LM method was more robust than the Gauss-Newton method because it was capable of converging to the solution in the global minimum even if the initial guess was relatively far away. But a reasonable initial estimate of the solution can help with faster convergence. If the initial estimate is too far away, the solution often converges to a local minimum instead of the global minimum.

    Therefore, a good initial estimate of the solution is crucial. An approximate initial estimate can be calculated in several ways. For example we can solve linearized equations based on the non-linear dTDOA equations. Or we can use a simple table lookup if we have some a priori knowledge of roughly where the receivers are located.

    Once the initial locations are found, the next step is to track the locations of the receivers when they are moving. A Kalman filter should be used for tracking. A Kalman filter can also incorporate the non-linear dTDOA equations with TOA measurement as input for close coupling between localization and tracking. Or, for simplicity, short of using a Kalman filter, the previous locations can be fed into the LM method to find the next locations. The LM method for this kind of tracking has faster convergence than for repeated initialization, so the next locations can be calculated quickly.

    Time Averaging. Due to error in tracking, the computed locations are not exact but are usually around the actual location. Time averaging is then used to further improve tracking performance. Time averaging can also be used to smooth the TOA measurements or the locations computed from dTDOA equations as input to a Kalman filter.

    Repeated use of the LM method, as shown in FIGURE 6, for estimating a stationary receiver’s coordinates always forms an error ellipsoid because of the noise and computation error. The estimated points are depicted by black points in Figure 6. The small yellow circle in the middle corresponds to the actual location. By simulation, it was found that averaging all the possible estimated locations produced a location much closer to the actual location, as depicted by the red cross in Figure 6. Obviously the more points to average — that is, the larger the time-averaging window — the more accurate the averaged location will be. In general, such time averaging can improve location and tracking performance by an order of magnitude.

    FIGURE 6. Image depicting time averaging of a stationary receiver’s location.
    FIGURE 6. Image depicting time averaging of a stationary receiver’s location.

    For a moving receiver, there is a trade off in choosing the time-averaging window. The larger the time-averaging window, the better the averaged location accuracy, but the larger the resulting time delay in the averaged location. This time delay is also affected by how frequently we update the tracked locations. Receiver velocity and the Doppler effect also affect the choice of the time-averaging window.

    Simulation Results

    We performed a comprehensive computer simulation study. The primary aim of this simulation study was to prove that the accuracy of digital AM signals for navigation can be improved using the methods introduced in the previous sections, despite the narrow bandwidth of the signals, thereby making digital AM a viable choice for navigation. A number of factors will affect the performance of navigation using digital AM signals including the sampling frequency, SNR, time-averaging window and location update frequency. In this simulation study, these factors have been taken into consideration.

    To simulate a realistic environment, we chose the city of Chicago, where there are many digital AM transmitters providing good coverage to the city. We chose the six best transmitters in Chicago based on the power of the signal and location. The working range of the receivers is large enough to perform a detailed study of all the navigation techniques. The locations of the radio station transmitters are shown in FIGURE 7. All figure axes are in kilometers. Colored dots are transmitter locations; colored circles are their ranges. Green tracks are the chosen routes for a fast-moving receiver. Short brown tracks are those of the other receiver, somewhere in the same zone and traveling slowly.

    FIGURE 7. Transmitter locations and two different routes considered for simulation with two receivers. (Map courtesy of Google.)
    FIGURE 7. Transmitter locations and two different routes considered for simulation with two receivers. (Map courtesy of Google.)

    We simulated two receivers moving along the chosen green and brown routes, but we will only show the navigation results of the faster moving receiver along the green routes. A minimum of five transmitters is needed. The entire simulation was done in Matlab. The time-domain digital AM received signals were modeled according to the specifications described previously. Delays corresponding to transmitter and receiver locations were calculated and simulated into the signals received at the two receivers. An SNR of 10 dB was used for all received signals. Along Route 1 (upper left corner of Figure 7), five transmitter signals can be received, whereas along Route 2 (center right in Figure 7), six transmitter signals are received. Simulation conditions and results for these two routes are given in TABLES 1 and 2.

    TABLE 1. Simulation parameters and results of Route 1 (five-transmitter zone).
    TABLE 1. Simulation parameters and results of Route 1 (five-transmitter zone).
    TABLE 2. Simulation parameters and results of Route 2 (six-transmitter zone).
    TABLE 2. Simulation parameters and results of Route 2 (six-transmitter zone).

    In addition, the tracking results for the fast-moving receiver are laid on top of photo maps of the routes, and are shown in FIGURES 8 and 9. The worst-case situation happens when, for example, transition of zones or handover of transmitters happen, for which no specific additional measures were taken in the simulations as shown in Figure 8.

    FIGURE 8. Worst-case result for five-transmitter tracking. (Photo map courtesy of Google.)
    FIGURE 8. Worst-case result for five-transmitter tracking. (Photo map courtesy of Google.)

    However, the typical tracking result in Figure 9 happens most of the time. Clearly, the more transmitters that can be used, the better the accuracy results. Use of more than two receivers or use of a stationary receiver with a known location can reduce this demand on the number of transmitters.

    FIGURE 9. Typical six-transmitter tracking result. (Photo map courtesy of Google.)
    FIGURE 9. Typical six-transmitter tracking result. (Photo map courtesy of Google.)

    The fast sampling frequency, the curve fitting and the time-averaging window are the most important factors affecting the accuracy of this work, and are easily adjustable. In our simulations we used a time-averaging window of 1 second. We expect that the accuracy would further improve as the time-averaging window is increased, but this would result in increased latency. The velocity of the receiver is one limiting factor in choosing the time-averaging window. For a receiver traveling at a maximum speed of 145 kilometers per hour, a time-averaging window of 1 second corresponds to 20.14 meters of tracking lag. Any greater tracking lag may become intolerable. In general, our simulations show that curve fitting alone and time averaging alone each improved localization accuracy by an order of magnitude. When curve fitting and time averaging were combined, the localization accuracy was improved by two orders of magnitude. If a Kalman filter were used for tracking, we would expect further accuracy improvement.

    Other challenges that deserve further study to make this concept a mature technology include multipath propagation and its mitigation, incorporation of estimating digital AM carrier phase, and incorporation of a Kalman filter for tracking. Further increased location accuracy is expected by incorporation of these techniques.

    Acknowledgment

    This article is based, in part, on the paper “A Navigation Solution Using HD Radio Signals” presented at the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, Calif., Jan. 26–28, 2015.

    ANANTA VIDYARTHI graduated from Anna University, India, in 2009 with a B. Tech. degree in electronics and communication engineering. She came to the University of Cincinnati in the fall of 2009 and earned her M.S. degree in 2012 in electrical engineering. Currently, she is working with Cummins Inc. in Columbus, Ind.

    H. HOWARD FAN graduated from the University of Illinois in Urbana-Champaign with a Ph.D. in electrical engineering in 1985. He has been on the faculty of the University of Cincinnati since then, where he is a professor of electrical engineering and computing systems. His research interests are in digital signal processing, system identification, signal processing for communications, interference mitigation, direction finding, and navigation and location.

    STEWART DEVILBISS graduated from Ohio State University with a Ph.D. in electrical engineering in 1994. Since 2007 he has served as the technical advisor for the Navigation and Communication Branch at the Sensors Directorate of the Air Force Research Laboratory, headquartered at Wright-Patterson Air Force Base, Ohio. His primary research interest is in technologies to improve navigation robustness and accuracy.

    FURTHER READING

    • Authors’ Conference Paper

    “Navigation Solution Using HD Radio Signals” by A. Vidyarthi and H.H. Fan in Proceedings of ION ITM 2015, the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, Calif., Jan. 26–28, 2015, pp. 285–292.

    • HD Radio

    The IBOC Handbook: Understanding HD Radio Technology by D.P. Maxson. Published by Focal Press, Burlington, Mass., 2013.

    HD Radio Air Interface Design Description – Layer 1 AM, Doc. No. SY_IDD_1012s, Revision E. Published by iBiquity Digital Corporation, Columbia, Md., March 22, 2005.

    HD Radio AM Transmission System Specifications, Doc. No SY_SSS_1082s, Revision F. Published by iBiquity Digital Corporation, Columbia, Md., Aug. 24, 2011.

    • Differential Time-Difference of Arrival

    “Asynchronous Differential TDOA for Non-GPS Navigation Using Signals of Opportunity” by C. Yan and H.H. Fan in Proceedings of ICASSP 2008, the IEEE 2008 International Conference on Acoustics, Speech and Signal Processing, Las Vegas, Nev., March 31–April 4, 2008, pp. 5312–5315, doi: 10.1109/ICASSP.2008.4518859.

    • Positioning Using Analog AM Signals of Opportunity

    “Opportunistic Navigation: Finding Your Way with AM Signals of Opportunity” by J. McEllroy, J.F. Raquet and M.A. Temple in GPS World, Vol. 18, No. 7, July 2007, pp. 44–49.

    “Phase Measurements Using Direct Conversion AM Radio Navigation” by A. Dinh, R. Mason, R. Palmer and K. Runtz in Proceedings of WESCANEX 97, the IEEE 1997 Conference on Communications, Power and Computing, 22–23 May 1997, pp. 280–285, doi: 10.1109/WESCAN.1997.627154.

    • Positioning Using TV Signals of Opportunity

    “Cooperative position location with signals of opportunity” by C. Yang, T. Nguyen, D. Venable, M. White and R. Siegel in Proceedings of NAECON 2009, the IEEE 2009 National Aerospace and Electronics Conference, Dayton, Ohio, July 21–23, 2009, pp. 18–25, doi: 10.1109/NAECON.2009.5426658.

    “Prime Time Positioning: Using Broadcast TV Signals to Fill GPS Acquisition Gaps” by M. Martone and J. Metzler in GPS World, Vol. 16, No. 9, Sept. 2005, pp. 52–60.

    “A New Positioning System Using Television Synchronization Signals” by M. Rabinowitz and J. J. Spilker, Jr. in IEEE Transactions on Broadcasting, Vol. 51, No. 1, March 2005, pp. 51–61, doi: 10.1109/TBC.2004.837876.

    • Positioning Using 3G Cellar Signals of Opportunity

    “A Signals of Opportunity Based Cooperative Navigation Network” by M.A. Enright and C.N. Kurby in Proceedings of NAECON 2009, the IEEE 2009 National Aerospace and Electronics Conference, Dayton, Ohio, July 21–23, 2009, pp. 213–218, doi: 10.1109/NAECON.2009.5426626.

  • Innovation: Seeing the Light

    Innovation: Seeing the Light

    A Vision-Aided Integrity Monitor for Precision Relative Navigation Systems

    By Sean M. Calhoun, John Raquet and Gilbert L. Peterson

    INNOVATION INSIGHTS by Richard Langley
    INNOVATION INSIGHTS by Richard Langley

    TO MEET THE ACCURACY,  availability, continuity and integrity requirements for many navigation applications, multiple-sensor systems are commonly used. For example, a GPS receiver might be combined with an inertial measurement unit, electronic compass and an altimeter to permit enhanced navigation accuracy, availability and continuity in obstructed or otherwise difficult environments. The use of arrays of sensors can also help to ensure that systems used in safety-critical navigation applications provide safe information by maintaining a high level of integrity.

    An important group of devices that can be used in multi-sensor systems is one whose processes are based on light. These optical or vision-based devices include laser rangefinders and digital cameras. We could even consider our eyes to be in this group. In common with many other animals, we have built-in visual sensors to get around in our daily lives. Together with our memories, we use our eyes to get safely from one place to another. Ancient mariners tended to sail close to shore so that they could use visual cues for navigation. Later on, they learned how to use the light from celestial objects to navigate in the open ocean. And these days, while we could use the so-called “Mark 1 Eyeball” to continuously monitor the performance of a navigation system, this is often impractical, impossible or unwise.

    In this month’s column, we’ll take a look at the development of a generalized vision-aided integrity monitor for precision relative navigation applications. The work is based on the concept of using a single-camera vision system, such as a visible-light or infrared electro-optical sensor, to monitor the occurrence of unacceptably large and potentially unsafe relative navigation errors. A vision-aided integrity monitor of this type could be extremely valuable in augmenting existing precision relative navigation systems, such as GPS, for many different safety-critical aerospace applications such as formation flying, aerial refueling, rendezvous/docking systems, and even precision landing.

    It is particularly appropriate that such vision-aided systems be discussed at the present time since 2015 is the International Year of Light and Light-based Technologies, or IYL 2015. This United Nations initiative aims to raise awareness of the achievements of light science and its applications, and its importance to humankind. As mentioned on the IYL 2015 website, “[l]ight plays a vital role in our daily lives and is an imperative cross-cutting discipline of science in the 21st century. It has revolutionized medicine, opened up international communication via the Internet, and continues to be central to linking cultural, economic and political aspects of the global society.”

    2015 is also an important anniversary year for several notable developments in our understanding of light. It is the 1,000th anniversary of the work of the Arabic scholar Ibn Al-Haytham, which culminated in his Book of Optics. A Latin translation significantly influenced a number of scholars in medieval and renaissance Europe including Leonardo da Vinci, Galileo Galilei, and Johannes Kepler. 2015 is also the 200th anniversary of Augustin-Jean Fresnel’s proposal that light behaves as a wave and the 150th anniversary of the publication of James Clerk Maxwell’s paper describing electromagnetic wave propagation as we discussed in “Insights” this past March. And we should also mention that 2015 is the 100th anniversary of the publication of Albert Einstein’s general theory of relativity, which includes a description of the propagation of light and other electromagnetic waves in the presence of a gravitational field.  And where would GPS and the other global navigation satellite systems and their augmentations be without the understanding that general relativity provides? Nowhere.

    “Innovation” is a regular feature that discusses advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering, University of New Brunswick. He welcomes comments and topic ideas. Email him at lang @ unb.ca.

    Recently, there has been an increased recognition of GNSS limitations in terms of robustness, availability and interference. As a result of this recognition, there has been renewed interest in developing non-GNSS-based navigation systems to augment system capability. This has become particularly important with the trend toward autonomous systems, where required navigation performance (RNP) metrics, such as accuracy, integrity, continuity and availability become operational drivers. Because of this trend, there is renewed interest in gaining navigational diversity using imaging or vision-aided navigation approaches. Early research with vision systems used 3-D terrain databases and imaging systems to provide periodic position updates in collaboration with onboard inertial navigation systems (INS), much like radar systems did prior to the wide proliferation of GNSS.

    For precision relative navigation applications such as formation flying, aerial refueling, rendezvous and docking systems and even precision landing, there is a significant body of research for the use of vision navigation systems. For example, a vision-based relative navigation solution for aerial refueling with the use of an a priori 3-D tanker model has been developed. Results from flight tests showed that image-rendering relative navigation is a viable precision navigation technique for close formation flight, specifically aerial refueling, and  demonstrated 95% relative navigation accuracies on the order of 35 centimeters within the operational envelope.

    As the body of vision-aided navigation research continues to grow, consideration of other RNP metrics is required. Ensuring that systems are providing safe information and maintaining a high level of integrity is paramount when considering safety-critical navigation applications, but is largely neglected in current vision-navigation research.

    The concept of integrity, particularly for navigation systems, refers to the level of trust that can be placed in a navigation system in terms of detecting gross errors and divergences. Many navigation applications have adopted the use of protection levels, which are real-time navigation system outputs that bound the navigation errors to the required probability of integrity risk. For the case of vertical navigation, the vertical navigation system error (NSE) is bounded by the real-time vertical protection level (VPL), and as the long as the VPL is below the vertical alert limit (VAL), the system can continue its operation. Loss of integrity is defined by the case when the NSE > VAL without an alert or, in other words, when NSE > VAL and VPL ≤ VAL.

    One of the richest sources of information for how integrity can be handled for precision relative navigation systems can be found with the Local Area Augmentation System (LAAS), which focused on providing integrity under fault-free and single ground reference receiver failure conditions. LAAS employs several quality monitors such as receiver autonomous integrity monitoring (RAIM).

    Much of the vision-aided navigation research to date has focused more on system and algorithmic robustness, rather than quantitative and verifiable integrity, particularly for feature-based processing. One approach has introduced the concept of regional bounding for feature correspondence between time-sequenced image frames, including some feature-unique criteria that can provide some protection from feature correspondence errors. Although this approach does yield some robustness for the algorithms, no quantitative integrity characterization was developed. Another approach introduced a truly quantitative integrity monitor for failures in the mapping of features to pixels, particularly in the presence of a bias. This approach predicts the largest possible position error in the presence of one such bias due to feature mismatch using a GPS RAIM-type approach. The current state of research addressing integrity for vision navigation, using an image-rendering or template-matching approach, is even less mature. In fact, we have not identified any previous integrity-specific work for image-rendering vision navigation.

    The research presented in this article generalizes the concept of integrity in terms of operating and alerting regions. Applications that use navigation systems generally have objective operating regions that require a certain navigation performance, whether this be around a glide-slope, a formation flight position or even a flight-path clearance. Navigation integrity becomes critical because large divergences from these operating regions, without an alert, can become safety risks. The alert limit is simply the instantiation of this concept. It is the threshold or measure of how much undetected divergence from the operating region can be tolerated without inducing unacceptably large safety risks.

    The remaining sections of this article will describe the development of a rigorous and quantitative vision-aided integrity monitor for precision relative navigation systems. First, an introduction to relative navigation using image rendering will be covered in order to describe the fundamental vision navigation approach. This will be followed by a detailed derivation of the proposed vision-aided integrity monitor and simulation based performance results.

    Using Image Rendering

    The basis of our research is that vision-aided techniques, specifically image rendering, can be used to construct a high-performance integrity monitor for precision relative navigation systems. Image rendering approaches and/or template matching have been used extensively in vision applications such as machine vision, medical image registration, object detection and pose estimation, and recently as a precision navigation system for applications such as aerial refueling and formation flight. The general concept of image-rendering precision relative navigation was evaluated for an automated aerial refueling application, using the approach illustrated in Figure 1. The image rendering approach is based on comparing image sensors with rendered imagery from high-fidelity models, to estimate a relative location based on the best image correspondence.

    FIGURE 1. Image rendering relative navigation approach.
    FIGURE 1. Image rendering relative navigation approach.

    The image correspondence process is the most critical aspect of the image-rendering or template-matching navigation approach, but the focus of our research is not to make claims of optimality or performance-difference judgments between these image correspondence techniques, but rather show feasibility in the overall vision-aided integrity approach using some of these techniques. Most image correspondence approaches transform the images into feature space, such as scale-invariant feature transform, silhouette, edges and corners, to name a few, and then compute a distance metric between the feature sets, such as Minkowski or Mahalanobis distance, to determine the degree of matching.

    Once the actual sensor image is converted to feature space, rendered images are generated based on the relative navigation state estimate using the model, converted to feature space, and compared to the sensor features. This process is repeated across the navigation state space, computing an image correspondence value for each state estimate. The selected navigation state estimate is based on the “best” image correspondence value across the state space.

    An example result of this process is presented in FIGURE 2, which shows correspondence values for an edge-based image-correspondence process. In this case, the minimum correspondence value represents the best estimate of the relative navigation state. These image correspondence values between the sensor image (IS) and the rendered reference images (IR) will form the basis for the integrity monitor detection rule.

    FIGURE 2. GRD-based image correspondence illustration as a function of 2-D relative navigation state.
    FIGURE 2. GRD-based image correspondence illustration as a function of 2-D relative navigation state.

    Vision-Aided Integrity Monitor Development

    As indicated in the preceding sections, our research is based on defining a vision-aided integrity monitor in terms of detecting when the system navigation state (x) is within a specified operating region (XOR) versus being within the alert region state space (XAR). The integrity monitor can yield four distinct conditions: rejection (PR), misdetection (PMD), detection (PD) and false-alarm (PFA). The performance of this type of binary (H0/H1) detection scheme can be characterized using just two of these metrics, the detection and false-alarm rates, which will be the two primary performance metrics for this research. PD is the primary metric measuring navigation integrity, describing the probability that the monitor successfully detects the condition when x ∈ XAR.

    Bayesian, Minimax and Neyman-Pearson are a few of the detection schemes available to solve this type of binary detection problem. These detection schemes rely on the knowledge of the underlying statistics of the H0 and H1 condition, often characterized in terms of the probability density functions (PDFs). The main difference between these approaches is the resulting detection rule value (δ). Once δ has been established, the resulting theoretical performances of the detectors are computed by integrating the underlying PDFs of the H0 and H1 conditions, pH0 and pH1 respectively. The probability of detection (PD) is computed as

    Inn-eq1(1)

    The integrity performance of the monitor can also be described in terms of integrity risk or probability of missed detection

    (PMD), which is computed as

    Inn-eq2(2)

    Similarly, the probability of false-alarm (PFA) is computed as

    Inn-eq3(3)

    This is represented graphically in FIGURE 3.

    FIGURE 3. Graphical illustration of detection performance.
    FIGURE 3. Graphical illustration of detection performance.

    The PDFs represent the statistical distributions of image correspondence values for the respective H0/H1 condition. The general detection rule premise is such that for a given sensor image, the underlying PDF for the “best” image correspondence with the rendered reference set is sufficiently distinct when the sensor image is in an H0 condition versus H1. The characteristics of the H0/H1 PDFs that dictate the monitor performance are dependent on many factors, including the fidelity and accuracy of the world model, the general observability of the image rendering process and the image correspondence approach for the specific application. For our research, we used two image correspondence techniques to evaluate the overall integrity monitor approach.

    The first image correspondence technique evaluated is a simple binary silhouette (SIL). In this approach, both the sensor image IS(x) and reference image set IR(x-character) are converted to a silhouette using pre-defined thresholds to first convert the red-green-blue (RGB) images to gray scale and then subsequently to a binary image. An image correspondence function computes the percentage of overlap between the silhouettes.

    The resulting image correspondence is based on the ratio of the cardinality of these sets. The navigation state estimate (x-character) that yields the maximum image correspondence value from the set of rendered reference images or template database is considered the most likely for that particular image sensor (IS).

    The second image correspondence utilizes edge features for the image correspondence process. Under this approach, magnitude of gradient (GRD) processing is used, in which the sensor image and the rendered reference images are preprocessed through a Prewitt filter to determine changes in image intensities between adjacent pixels. This process computes the components of the gradient. The gradient magnitude is computed by root-sum-squaring the x-y components and normalized, resulting in an edge detection. A Gaussian blur filter is then applied to the output of the edge detection.

    The application of the Gaussian blurring compensates for the spatial discrepancies between the discrete reference set or template database and the sensor image. Finally, the resulting feature images, including both the reference image (IR_GRD) and the sensor image (IS_GRD), are processed through a sum-squared-difference (SSD) image correspondence.

    The resulting PDFs are based on the best image correspondence with the RE reference set, which is the minimum for the GRD processing.

    These image correspondences build the basis of the detection metric, utilizing both the sensor image (IS) and the rendered reference set (IR), which is spatially distributed across the operating region, illustrated by FIGURE 4. This illustrated example shows instances of both a H0 and H1 sensor image (blue and red, respectively). The underlying H0/H1 PDFs for establishing the detection threshold are determined by sampling sensor images from XOR and XAR and computing the image correspondence against IR. This can be done through a combination of high-fidelity simulation and/or test data. The overall performance of the integrity monitor will be dictated by these underlying distributions. The following sections show the results of this integrity monitor approach for an aerial refueling application.

    FIGURE 4. Simplified example of rendered reference set (IR) illustrating image correspondence process for integrity monitoring.
    FIGURE 4. Simplified example of rendered reference set (IR) illustrating image correspondence process for integrity monitoring.

    Simulation Evaluation

    To explore the performance of the proposed integrity monitor approach, an aerial refueling (AR) application was modeled within a simulation environment. The AR operation lends itself well to the construct of the proposed integrity monitor and is developed to show that the system (refueling aircraft) is in the refueling envelope (RE) and has not violated the alert limit, which in the AR case is the safety boundary (SB). In this operational case, H0 is defined as the condition when the integrity monitor determines the refueling aircraft is in the RE, and H1 as the case when the integrity monitor determines the refueling aircraft to be within the SB. A validity region is also defined in order to bound the problem, in which it is assumed that the refueling aircraft is always within, under both H0 and H1 conditions, as shown in FIGURE 5.

    FIGURE 5. Integrity regions of interest for an aerial refueling application and illustrated example of a rendered H0 image set for the refueling envelope used as the correspondence basis for the integrity detection metric.
    FIGURE 5. Integrity regions of interest for an aerial refueling application and illustrated example of a rendered H0 image set for the refueling envelope used as the correspondence basis for the integrity detection metric.

    To determine the underlying H0/H1 distributions, a set of reference images uniformly sampled from the RE was rendered using the associated tanker and camera models. This rendered image set was used as the common basis for performing the image correspondence with the actual sensor image.

    The baseline RE reference set used for this research was developed using 504 rendered images distributed in a spherically uniform manner across the entire RE volume. Then, two random sets of simulated sensor images were generated and drawn from both RE and SB regions. It is assumed that the refueling aircraft and corresponding sensor images are within the validity region in order to bound the simulation. This bounding assumption is an acceptable constraint, given that the system most likely had to pass several operational checks to ensure the refueling aircraft is in the general region of the RE as defined by the validity region. To get detailed statistical representation of the PDFs, particularly at the tails of the distribution, both RE and SB image sets included more than 100,000 simulated sensor images, representing true states of the refueling aircraft. The simulation environment for this analysis uses the same refueling tanker model for the sensor images and the RE reference set, which eliminates the effects of modeling errors. Additionally, variations in the attitude are currently not considered. The resulting PDFs for H0 (blue) and H1 (red) conditions are shown in FIGURE 6.

    FIGURE 6. Underlying image correspondence distribution for H0 (blue) and H1 (red) conditions.
    FIGURE 6. Underlying image correspondence distribution for H0 (blue) and H1 (red) conditions.

    Figure 6 shows generally good distinction between the H0 and H1 hypotheses — a necessary condition to achieve good detection performance. Several techniques were evaluated for determining the PDF including histogram, nearest neighbor and kernel with a Gaussian weighting function. These underlying H0 and H1 distributions will be used as the basis for designing the detection thresholds, based on the image correspondence of the sensor image with the RE reference set. These results assume uniform prior distributions across the RE and SB regions; however, it would be relatively straightforward to incorporate non-uniform prior information, based on a particular application, as available.

    Detection schemes are often characterized using receiver operating characteristics or ROC curves, which illustrate the detection-monitor trade-off between probability of detection and probability of false alarm. The predicted detection performance for this AR application is a function of these underlying H0/H1 PDFs, and this performance is captured in the ROC curves shown in FIGURE 7. The ROC curves show that 10-3 level integrity-monitor detection performance (PD) is realizable for both SIL and GRD image correspondence approaches, while still maintaining a reasonable probability of false alarm (PFA) of less than 0.05 (5%). The SIL approach demonstrates slightly better performance than GRD under the chosen image resolution and RE reference set density. Normally, theoretical ROC curves would extend through the whole range of values [0,1] for both PD and PFA; however, this assumes unbounded PDFs. Doing so would require an infinite number of simulation cases and is obviously not practical for a simulation evaluation to gain statistics necessary to extend the PDFs near the entire theoretical ranges. Overbounding of the PDF tails could be performed to extrapolate and extend the tails of H0/H1 PDFs to determine the integrity detection performance beyond the current ranges, but this was not performed as part of this research.

    FIGURE 7. Predicted integrity detection performance for both SIL and GRD image correspondence techniques.
    FIGURE 7. Predicted integrity detection performance for both SIL and GRD image correspondence techniques.

    In most applications, conditions exist that are outside of the nominally defined operational envelope, but yet are not significant enough deviations to be considered safety risks that require alerts and action. Such a case exists for the refueling operation under consideration in this research, where there exists a region outside the RE, but not in the SB, which we will refer to as the operational limit volume (OLV). The current definitions of H0 and H1 for the vision-aided integrity-monitor approaches developed above only consider conditions within the RE or the SB volume, and not within the OLV volume. OLV conditions were omitted since they technically aren’t considered a safety or integrity risk. However, it is possible under certain implementations and operational considerations that integrity monitoring coverage is desired under these OLV conditions.

    Using the same analysis process as the original evaluation, an updated simulation was performed, this time considering all points within the validity region, including the OLV points. To construct a detection scheme under this new paradigm, the OLV conditions must be either mapped to the existing H0 or H1 hypotheses, or a new hypothesis must be defined, possibly creating an M-ary hypothesis scenario. The approach taken for this research was to consider OLV conditions as a safety risk, which is a conservative approach, rather than defining any new hypotheses. The resulting image correspondence distributions are shown in FIGURE 8. Subplots (a) and (b) show the difference the OLV points have on the underlying PDF distributions. As expected, when the OLV points are excluded, the PDFs track the original distributions quite well. The impact of including sensor locations from the OLV is clear from these figures, yielding a much bigger overlap between the H0/H1 conditions.

    FIGURE 8. Simulation testing results assuming OLV states are a safety risk. The prediction represents expected performance without consideration of the OLV states. (a) SIL image correspondence PDFs,(b) GRD image correspondence PDFs, (c) SIL ROC curve, (d) GRD ROC curve.
    FIGURE 8. Simulation testing results assuming OLV states are a safety risk. The prediction represents expected performance without consideration of the OLV states. (a) SIL image correspondence PDFs,(b) GRD image correspondence PDFs, (c) SIL ROC curve, (d) GRD ROC curve.

    Much like the PDFs, the ROC curves align with the previous results quite well when the OLV conditions are omitted, but take a order of magnitude integrity performance hit when OLV is captured under the existing H0/H1 definition and detection thresholds. Even under this conservative assumption, the overall monitor performance still yields a 0.96 (96%) detection rate at a 0.05 (5%) false-alarm rate, as illustrated by the ROC curves shown in subplots (c) and (d) of Figure 8. It is likely that these results could be significantly improved by redefining the terms of the H0 and H1 conditions or defining an H2 condition specifically for the OLV region.

    Sensitivity Analysis

    In addition to the baseline integrity monitor results, various sensitivity studies were performed to evaluate the integrity monitor performance impacts of environmental and hardware considerations. These sensitivity evaluations focused on common vision-based considerations such as sensor distortions and lighting conditions, and monitor design choices such as pixel resolution and reference image density. The sensitivity aspects that were evaluated under this research included the number of reference images, the effects of image distortion, pixel resolution and lighting conditions.

    Reference Set Density. In addition to our standard reference set of 504 RE images, we conducted tests using 288 and 729 images. While a larger number of images improves integrity detection performance, processing speed is decreased. It is possible to trade off processing power for performance as necessary for a particular application and the associated integrity monitor performance requirements.

    Image Distortion. We applied radial and tangential distortions to the simulated sensor images (IS) such that they represented a 95% certainty of the residual error to represent an outer envelope case for this type of sensor. The impact on the H0/H1 PDFs is very minimal, and the results demonstrate a potential robustness to this common type of sensor effect.

    Pixel Resolution. We evaluated eight different pixel resolutions from 12 × 9 to 1280 × 1024 pixels per image. Our results showed a surprising robustness to pixel resolution, indicating only marginal performance impacts down to extremely limited pixel densities.

    Lighting Conditions. To explore the impact of lighting conditions, the simulated sensor images (IS) used as the basis for the sensitivity analysis were regenerated under a secondary lighting condition, intended to emulate a much brighter background environment, and processed against the original RE reference set. The results demonstrate that under these varying lighting conditions, the system again demonstrates a high level of robustness, particularly using the SIL image correspondence approach.

    Ratio Test Integrity Test

    The initial integrity monitor results discussed thus far only used reference images from the operational region, RE. However, it is also possible to use a reference image set created with rendered images from the alert region, SB, by including an additional image correspondence process between the sensor image and rendered SB reference set. This is done to create a ratio test statistic as the detection metric. We compute the ratio of the highest image correspondence between the RE and SB reference sets. This approach is very analogous to the use of ratio tests for GNSS carrier-phase integer fixing.

    The resulting ROC detection performance of the ratio threshold approach showed that, as with the single RE reference set, the SIL image correspondence approach yields the best H1 detection performance, resulting in the best integrity protection.

    The GRD ratio detection performance also yields improved performance and is comparable to the SIL image correspondence approach solely with RE reference set.

    Conclusions and Future Work

    In this article, we have discussed the feasibility of a vision-aided integrity monitor for precision relative navigation systems. The research posed the relative navigation integrity problem within the context of an aerial refueling application. Using image rendering, where an imaging sensor and high-fidelity 3-D model is used, we have shown that 10-3 to 10-5 level of integrity monitoring is attainable for aerial refueling and formation flight applications. Having this level of independent monitoring could provide significant relief to a GPS-based precision relative-navigation system from a system-safety and certification perspective. The research demonstrated the proposed integrity monitor was robust against several degrading imaging effects, including lens distortions, lighting conditions and reductions in pixel resolution. Although more work is required to validate the results of this research, which was based on simulated images, the results show high promise for this type of integrity monitor approach.

    Disclaimer

    The views expressed in this article are those of the authors and do not reflect the official policy or position of the United States Air Force, Department of Defense, or the U.S. Government.

    Acknowledgment

    This article is based on the paper “Vision-Aided Integrity Monitor for Precision Relative Navigation Systems” presented at ITM 2015, the 2015 International Technical Meeting of The Institute of Navigation held in Dana Point, Calif., Jan. 26–28, 2015.

    SEAN CALHOUN is the managing director at CAL Analytics, Columbus, Ohio, and is pursuing his Ph.D. degree at the Air Force Institute of Technology (AFIT), Wright-Paterson Air Force Base, Ohio.

    JOHN RAQUET is the director of the Autonomy and Navigation Technology Center at AFIT, where he is also a professor of electrical engineering.

    GILBERT L. PETERSON is a professor of computer science at AFIT and vice chair of the International Federation for Information Processing Working Group 11.9, Digital Forensics.

    FURTHER READING

    • Authors’ Conference Paper

    “Vision-Aided Integrity Monitor for Precision Relative Navigation Systems” by S.M. Calhoun, J. Raquet and G. Peterson in Proceedings of ITM 2015, the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, Calif., Jan. 26–28, 2015.

    • Image-Sensor Navigation

    “Flight Test Evaluation of Image Rendering Navigation for Close-Formation Flight” by S.M. Calhoun, J. Raquet and J. Curro in Proceedings of ION GNSS 2012, the 25th International Technical Meeting of the Satellite Division of The Institute of Navigation, Nashville, Tenn., Sept. 17–21, 2012, pp. 826–832.

    Using Predictive Rendering as a Vision-Aided Technique for Autonomous Aerial Refueling by A.D. Weaver, M.S. thesis, Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio, March 2009.

    “Fusing Low-Cost Image and Inertial Sensors for Passive Navigation” by M. Veth and J. Raquet in Navigation: Journal of The Institute of Navigation, Vol. 54, No. 1, Spring 2007, pp. 11–20. doi: 10.1002/j.2161-4296.2007.tb00391.x.

    “Automated Rendezvous and Docking Sensor Testing at the Flight Robotics Laboratory” by J.D. Mitchell, S.P. Cryan, D. Strack, L.L. Brewster, M.J. Williamson, R.T. Howard and A.S. Johnston in Proceedings of 2007 IEEE Aerospace Conference, Big Sky, Mont., March 3–10, 2007, doi: 10.1109/AERO.2007.352723.

    “Performance of Integrated Electro-Optical Navigation Systems” by T. Hoshizaki, D. Andrisani II, A.W. Braun, A.K. Mulyana and J.S. Bethel in Navigation: Journal of The Institute of Navigation, Vol. 51, No. 2, Summer 2004, pp. 101–121, doi: 10.1002/j.2161-4296.2004.tb00344.x.

    • Simultaneous Localization and Mapping

    “A Review of Recent Developments in Simultaneous Localization and Mapping” by G. Dissanayake, S. Huang, Z. Wang and R. Ranasinghe in Proceedings of 6th IEEE International Conference on Industrial and Information Systems, Kandy, Sri Lanka, Aug. 16–19, 2011, pp. 477–482, doi: 10.1109/ICIINFS.2011.6038117.

    • Navigation Integrity

    “Developing a Framework for Image-based Integrity” by C. Larson, J.F. Raquet and M.J. Veth in Proceedings of ION GNSS 2009, the 22nd International Technical Meeting of the Satellite Division The Institute of Navigation, Savannah, Ga., Sept. 22–25, 2009, pp. 778–789.

    “From RAIM to NIOAIM: A New Integrity Approach to Integrated Multi-GNSS Systems” by P.Y. Hwang and R.G. Brown in Inside GNSS, Vol. 3, No. 4, May-June 2008, pp. 24–33.

    Minimum Aviation System Performance Standards for Local Area Augmentation System (LAAS), DO-245A, by RTCA SC-159 WG-4, RTCA Inc., Washington, D.C., December 2004.

    • Camera Calibration

    “Flexible Camera Calibration by Viewing a Plane from Unknown Orientations” by Z. Zhang in Proceedings of ICCV’99, the Seventh IEEE International Conference on Computer Vision, Kerkya, Greece, Sept. 20–27, 1999, Vol. 1, pp. 666–673, doi: 10.1109/ICCV.1999.791289.

    • Digital Image Processing

    Digital Image Processing, 4th Ed., by W.K. Pratt, published by John Wiley & Sons, New York, 2007.

    Digital Image Processing, 3rd Ed., by R.C. Gonzalez and R.E. Woods, published by Prentice Hall, Upper Saddle River, N.J., 2007.

    • Signals and Noise

    Detection of Signals in Noise, 2nd Ed., by R. N. McDonough and A.D. Whalen, published by Academic Press, Inc., Waltham, Mass., 1995.

    An Introduction to Signal Detection and Estimation, 2nd Ed., by H.V. Poor, published by Dowden & Culver, an imprint of Springer, New York. 1994.

     

  • Innovation: Carrier-Phase RF Ranging

    Innovation: Carrier-Phase RF Ranging

    Precise, Accurate and Multipath-Resistant Distance and Speed Measurements

    In this month’s column, we take a look at a short-distance two-way ranging system using a 5.8-GHz carrier to supply not only precise and accurate distance measurements but also complementary measurements of speed.

    By Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor

    INNOVATION INSIGHTS by Richard Langley
    INNOVATION INSIGHTS by Richard Langley

    THERE IS A LONG HISTORY of determining distances using radio waves with a large number of techniques being developed over the years for positioning, navigation, situational awareness and other purposes.

    Of course, we are all familiar with the latest and greatest distance-measuring technology: GPS and its GNSS brethren. The distance to each observable satellite is determined by measuring the time it takes for the radio signal to travel from the transmitting antenna of the satellite to the receiver’s antenna and then, using the speed of light in a vacuum (which is also the speed of radio waves), converting the signal travel time into a distance. Distances can be determined from either the signal’s modulation (the pseudorandom noise codes) or the carrier phase. Both approaches require modeling and estimation to account for various errors or biases.

    GPS is an example of one-way ranging. Other systems, notably radar, are two-way systems relying on reflections (passive ranging) or transponders (active ranging) to return a signal to the point of transmission.

    Radar was developed during Word War II although radio-ranging technologies and techniques existed before the war started (to measure the height of the ionosphere, for example) and allowed radar’s rapid development and use during the war.

    Besides ranging to terrestrial objects, radar has been used extraterrestrially. Independent experiments in the United States and Hungary in 1946 resulted in the first detections of radar reflections from the moon. Radar has been used subsequently to range to other solar system bodies as well.

    Also developed during World War II were several radio-based systems for aircraft navigation. An outgrowth of these were the Loran-C and Omega hyperbolic positioning systems. They operated with networks of coordinated transmitters using frequencies at the low end of the radio spectrum. With widespread GPS availability, Omega was shut down in September 1997 followed by the North American Loran-C chains in 2010. Other chains are threatened with closure. However, there is an ongoing debate about bringing Loran-C back to North America in the form of Enhanced Loran (eLoran) as an autonomous backup for GPS. The United Kingdom has already implemented an eLoran network. Among other improvements, eLoran uses range measurements from multiple transmitters to determine position fixes.

    The first terrestrial electromagnetic-distance-measurement or EDM device using microwave signals was the Tellurometer. Developed for surveying in 1954, it initially used a 3-GHz carrier modulated by frequencies near 10 MHz and was capable of accurately measuring distances up to at least 50 kilometers (line of sight).

    Ranging can be performed with virtually any radio signal, and viable positioning techniques have been developed to use so-called signals of opportunity such as AM, FM and TV signals. And purpose-designed systems have been developed using ultra-wideband and other short-distance radio technologies.

    An issue with any radio-based ranging system is multipath where, in addition to a direct line-of-sight signal, interfering signals are received after being reflected off nearby structures. Multipath degrades the system’s achievable precision and accuracy. Better performance can be obtained by using measurements on the signal’s carrier rather than on its modulation, and the higher the carrier frequency, generally the smaller will be the multipath error in the distance measurement. In this month’s column, we take a look at a short-distance two-way ranging system using a 5.8-GHz carrier to supply not only precise and accurate distance measurements but also complementary measurements of speed.

    “Innovation” is a regular feature that discusses advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering, University of New Brunswick. He welcomes comments and topic ideas. Email him at lang @ unb.ca.

    Reliable measurements of distance and speed are a critical aid to integrated positioning and navigation systems. Several different sensor technologies can provide such measurements including a variety of radio frequency (RF) ranging techniques. Previous work by the authors based on round-trip time-of-flight RF ranging using the baseband code phase of direct sequence spread spectrum (DSSS)-modulated signals achieves centimeter-level distance estimation performance. This DSSS ranging implementation approaches the Cramér-Rao lower bound in a benign RF channel (the theoretical lower bound on the variance or corresponding standard deviation of any unbiased estimator of a deterministic parameter — the best we can ever expect to achieve). A distance measuring radio (DMR) produced by our company is shown in FIGURE 1.

    FIGURE 1. Distance measuring radio. The dimensions of the radio are 160 × 69 × 13.3 millimeters with a mass of 180 grams.
    FIGURE 1. Distance measuring radio. The dimensions of the radio are 160 × 69 × 13.3 millimeters with a mass of 180 grams. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

    Our baseband ranging capability has been demonstrated on a direct conversion radio operating in the unlicensed 5.8-GHz industrial, scientific and medical (ISM) band with approximately 20 MHz RF signal bandwidth, and has been previously implemented in the 2.4 GHz and 915 MHz ISM bands. The system uses an 11-megachip-per-second chipping rate and a symbol rate of about 687 kHz per channel (16 chips per symbol). This method has been implemented with both binary phase-shift keying (BPSK) and quadrature phase-shift keying (QPSK) modulation. The same signal that is used for ranging is also used for data communications. A decentralized asynchronous carrier-sense multiple access with collision avoidance (CSMA/CA) networking layer supports networked operation.

    The DMR performs real-time digital signal processing on a Kintex-7 field-programmable gate array (FPGA) baseband processor to compute ranging observables on the received baseband packet structure. A round-trip measurement duration under three milliseconds allows for approximately 350 measurements per second for a single pair of DMRs. Measurements do not require a priori synchronization of the remote radios nor high-performance reference oscillators, as remote oscillator behavior is observed in the ranging operation. The measurement is highly compatible with frequency agility techniques. A system of ranging radios provides networked operation for measurements between multiple platforms.

    The primary limitation of DSSS code-phase ranging is degraded accuracy and reliability in challenging multipath environments. This is somewhat mitigated by a “quality factor” observation on the characteristics of the received DSSS baseband signal, which can be used to de-weight or exclude corrupted baseband ranging measurements from an integrated navigation or positioning filter. However, it is desirable to provide a ranging measurement that has improved robustness against multipath corruption in all environments.

    Multipath Effects on Carrier Phase

    The carrier phase of the DSSS ranging signal in space can be used as an additional ranging measurement. Each 5.8-GHz RF carrier-wave cycle has a length of about 52 millimeters. Phase measurements on the received carrier phase in a round-trip ranging exchange are proportional to the propagation distance of the RF signal over the air. These measurements of the carrier phase can be made precisely, and they are inherently more tolerant to multipath than baseband phase measurements.

    Consider a simplified two-ray RF channel model, where there is a direct RF line-of-sight (LOS) path and a multipath (MP) reflection. The two signals will have a phase difference between MP and LOS of θm and an amplitude ratio of MP to LOS of α, which lumps together the attenuation due to the additional path length of the MP signal, the reflection coefficient of the reflecting surface, the difference in antenna gain at the incidence angles and other factors. The received signal will be a superposition of the two signals with a phase difference between this composite and the original LOS of θc. This phase difference is the multipath-induced error on the received carrier phase. The worst-case error will occur when there is a small difference in total path length. In this case, the LOS and MP are inseparable by the DSSS receiver, and the error is bounded by Equation 1. The error is reduced for MP with much longer path length due to both a reduced amplitude coefficient α of the MP signal, as well as separation by the DSSS receiver due to the baseband spreading codes.

    E-1  (1)
    The multipath carrier-phase error bounds are ±90 degrees for α ≤ 1, which is satisfied when there is an RF LOS signal present. In practice, α is typically much less than 1. For a more practical case of α = 0.1, the maximum carrier-phase error is less than ±6 degrees. At 5.8 GHz RF, ±6 degrees corresponds to about 0.1 millimeters. A plot of this response for various values of α is shown in FIGURE 2.

    FIGURE 2. Carrier-phase error due to multipath interference for various values of relative multipath amplitude.
    FIGURE 2. Carrier-phase error due to multipath interference for various values of relative multipath amplitude. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

    As a physical interpretation, the carrier-phase error goes to zero when there is zero phase difference between LOS and MP signals as the signals happen to be in phase already, and at ±180 degrees where the MP signal is in phase with the LOS signal but with inverted polarity, and serves to reduce the magnitude of the received signal, which is the case in a deep multipath fade. MP signals arrive at a dynamic receiver with an unpredictable distribution of relative phase to the LOS signal  due to platform motion. This resistance to multipath is highly desirable for use in an RF ranging system. The following sections will present a ranging method that leverages this useful behavior.

    Carrier-Phase Ranging Measurement

    Each DMR round-trip ranging exchange consists of transmission and reception of a packet between two cooperating DMR devices, typically termed “originator” and “transponder” with roles determined by software configuration. For baseband ranging, the code phase is computed on the oversampled shape of the DSSS correlator output and exchanged in the round-trip measurement. The number of elapsed baseband clock periods between receive and transmit on the transponder and between transmit and receive on the originator are also observed to compute a round-trip coarse time. These measurements, plus a calibration offset due to cabling and other systematic delays, are used to perform baseband ranging.

    Two additional observations are required for carrier-phase ranging: the carrier phase of the received DSSS signal in space and the carrier-frequency offset of the received carrier with respect to the local oscillator on the receiving radio. These observables are exchanged in a round-trip transaction, generating carrier-phase range (CPR), the magnitude of carrier-phase velocity (CPV) and clock-offset measurements. This section will describe the background of the CPR and CPV measurements.

    Assuming the communicating DMRs operate with identical carrier frequencies, the round-trip carrier-phase ranging measurement is a function of the RF carrier wavelength λC = c/fC and the received phase on each DMR (φO and φT) in units of radians. The measurement is ambiguous by Namb half-wavelengths, as shown in Equation 2.

    E-2(2)
    The frequency offsets measured at each receiver (SO and ST) in units of hertz will reflect the Doppler-based velocity offset between the two receivers, as shown in Equation 3.

    E-3 (3)
    While the velocity measurement is absolute, the carrier-phase ranging measurement is ambiguous within a half-wavelength in a round-trip measurement. There are several ways to overcome this limitation including using the velocity measurement to “unwrap” sequential carrier-phase observations, using baseband phase measurements to establish absolute offsets, by aiding the measurement with a strapdown inertial measurement unit (IMU) and by other means. The primary error source for carrier-phase ranging in practice is the solution of integer ambiguity, not the actual phase measurements. The quality of the phase measurements becomes the limiting factor when the integer ambiguity is resolved perfectly. An analysis of the Cramér-Rao lower bound (CRLB) for carrier-phase ranging and carrier-frequency velocity measurements along with measured performance is presented in the following section.

    Measurement Performance Bounds

    The CRLB for estimation of phase and frequency of a sinusoid based on a number of data samples in additive white Gaussian noise has been previously treated in the literature and can be interpreted to provide a best case, lower bound on how well the measurements could perform. The CRLBs for carrier-frequency and phase estimation are computed in terms of the sinusoid’s signal-to-noise ratio, SNR, the number of observed samples of the phase of the signal NS and the sample rate of the measurement system fS.

    The CRLB for the standard deviation of carrier-phase ranging measurements is presented in Equation 4 in units of radians. In general, the standard deviation of carrier-phase measurements improves with the square root of NS and the square root of SNR.

    E-4 (4)
    The CRLB for carrier-phase estimation can be used to compute the CRLB for carrier-phase ranging by scaling each measurement by λC

    E-5 (5)
    This CRLB can be interpreted for the carrier-phase ranging observable generation process used in this DMR system. NS can be expanded to Equation 6, with NC = 12 chips out of a 16-chip pseudorandom noise code, α = 400 symbols typically tracked (assuming 100 symbrols are consumed in automatic gain control out of a 512-symbol preamble), and fSample/fChip = 44 MHz/11 MHz = 4. [Note different use of the character α here than in the section on multipath.] This gives NS = 400 · 12 · 4 = 19,200 in a typical usable DMR preamble as currently implemented.

    E-6(6)
    FIGURE 3 shows the CRLB for carrier-phase ranging measurement evaluated over a range of SNR and with a varying number of symbols used in the ranging preamble, with typical α = 400 in the current implementation. Evaluating the phase CRLB at a conservatively low SNR = 10 dB and typical NS = 19,200 on a 5.8-GHz RF carrier yields a lower bound of about 27 micrometers standard deviation for a round-trip carrier-phase ranging measurement.

    FIGURE 3. Cramér-Rao lower bound for carrier-phase ranging with different numbers of symbols used in the ranging preamble.
    FIGURE 3. Cramér-Rao lower bound for carrier-phase ranging with different numbers of symbols used in the ranging preamble. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

    The CRLB for the standard deviation of carrier-frequency-offset measurements is presented in Equation 7 in units of hertz. In general, the standard deviation of carrier-frequency observation improves with NS3/2 and the square root of SNR.

    E-7(7)
    The CRLB for carrier-frequency estimation can be used to compute the CRLB for carrier-phase velocity by scaling each measurement by λC to convert to meters per second, and reducing the standard deviation by the square root of 2 due to the two independent phase measurements being conducted in the round-trip experiment as shown in Equation 8.

    E-8(8)
    Evaluating the round-trip carrier-phase velocity CRLB at a conservatively low SNR = 10 dB and typical NS = 19,200 on a 5.8-GHz RF carrier yields a lower bound of about 10 centimeters per second velocity standard deviation. FIGURE 4 shows the CRLB for velocity measurement evaluated over a range of SNR and with varying number of symbols used in the ranging preamble.

    FIGURE 4. Cramér-Rao lower bound for carrier-phase velocity with different numbers of symbols used in the ranging preamble.
    FIGURE 4. Cramér-Rao lower bound for carrier-phase velocity with different numbers of symbols used in the ranging preamble. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

    These CRLB levels predict that excellent CPR with precision much better than millimeter level and CPV precision much better than a meter per second should be achievable with the designed system assuming a perfect carrier-frequency generation circuit operating in additive white Gaussian noise. The practical limiting factor for these measurements at high SNR is typically the phase-noise performance of the reference oscillators themselves.

    Measurement Results

    CPR measurements have been implemented in our DMRs and tested in a variety of environments. In a static data collection, CPR demonstrates a stationary precision of approximately 0.1 millimeters at one sigma as shown in the histogram in FIGURE 5. The red line indicates the best-fit to a Gaussian curve of the measurement data, showing very well behaved data.

    FIGURE 5. Histogram showing carrier-phase range precision.
    FIGURE 5. Histogram showing carrier-phase range precision. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

    A static collection of CPV measurements demonstrates a precision of approximately 15 centimeters per second at one sigma as shown in the histogram of CPV data in FIGURE 6, which also has the best fit Gaussian distribution overlaid. The performance of these measurements approaches the CRLB.

    FIGURE 6. Histogram showing carrier-phase velocity precision.
    FIGURE 6. Histogram showing carrier-phase velocity precision. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

    To further quantify the accuracy of CPR, a test was conducted comparing CPR to the distance measured by a survey-grade total station laser rangefinder. The transponding radio was mounted on a tripod and moved to varying distances away from the originating radio, which was located near the total station. FIGURE 7 shows the distance-measurement results. The blue dots are the baseband distance measurements and the red dots are the unwrapped carrier-phase range distance measurements. The mean distance and scatter within each stationary period were used to evaluate the precision and accuracy of CPR versus the total station rangefinder values.

    FIGURE 7. Distance determined from baseband ranging (blue) and carrier-phase ranging (red) data collected during a test with varying distances between originating and transponding radios and using a total station to provide ground-truth.
    FIGURE 7. Distance determined from baseband ranging (blue) and carrier-phase ranging (red) data collected during a test with varying distances between originating and transponding radios and using a total station to provide ground-truth. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

    FIGURE 8 shows the outcome of the laser-based total station ground-truth validation of the carrier-phase distance measuring performance in an outdoor LOS environment. The red lines indicate the ±8 millimeter experimental accuracy of the laser ground-truth test setup. The error from each surveyed point is within the uncertainty of the test, with an experimental precision of 0.6 millimeters at one sigma indicated by the vertical error bars on each data point.

    FIGURE 8. Range comparison between CPR and a total station.
    FIGURE 8. Range comparison between CPR and a total station. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

    System Integration

    CPR and CPV measurements have been successfully integrated into a pedestrian tracking dual boot-mounted inertial system. In this configuration, one industrial-grade microelectromechanical systems IMU operating at 400 Hz (three-axis accelerometer, three-axis gyro and three-axis magnetic compass) is mounted on the heel of each boot, and a DMR with CPR/CPV capability is attached to the medial side of each boot. The DMRs perform inter-boot ranging and velocity measurements at 360 Hz throughout system operation. The walking motion generates a very high-dynamic, high-multipath environment that is challenging for RF systems.

    FIGURE 9 shows four strides of walking data collected in this configuration. Periodic walking motion is clearly visible on CPR and CPV as the range between boots increases up to 0.6 meters at the extents of strides and passes near zero during foot crossings. CPV measurements are internally consistent with CPR. The first difference of CPR is equivalent to the independent Doppler-based CPV measurement. A significant benefit of the CPV measurement as opposed to the first difference of CPR is that CPV is an absolute measurement with no integer ambiguity.

    FIGURE 9. CPR and CPV data for four strides from boot-mounted distance measuring radios.
    FIGURE 9. CPR and CPV data for four strides from boot-mounted distance measuring radios. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

    For this system, IMU data is integrated using both interpreted zero-velocity updates (ZUPTs) and ranging measurements to determine dead-reckoning motion of each individual boot. The high-precision, multipath-tolerant CPR and CPV measurements are used to constrain inter-boot position and velocity in a centralized extended Kalman filter (CEKF). CPR and CPV residuals from the CEKF are shown in FIGURE 10 and FIGURE 11, representing measurement accuracy in a challenging, high-dynamic environment. All system errors including antenna phase response, integrated IMU errors, and others are included in these histograms, so the true CPR and CPV measurement errors are likely significantly lower, even for this high-multipath environment. This is why we believe our results are a good estimate of the system’s accuracy capability.

    FIGURE 10. Histogram showing carrier-phase range accuracy.
    FIGURE 10. Histogram showing carrier-phase range accuracy. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)
    FIGURE 11. Histogram showing carrier-phase velocity accuracy.
    FIGURE 11. Histogram showing carrier-phase velocity accuracy. (Image: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor)

    While the overall CPR measurement accuracy of about 11 millimeters is two orders of magnitude worse than the stationary measurement precision of 0.1 millimeters, it should be noted that this includes all measurement biases in the system and various error sources.

    CPV achieves an in-system measurement accuracy of 0.31 meters per second, which is approximately a factor of two degraded from the stationary, LOS collection (0.15 meters per second). In this sense, CPV is shown to be an extremely robust measurement in the presence of multipath and non-ideal antenna patterns throughout actual walking motion.

    Conclusions

    This article presents a new method to perform highly precise, accurate and multipath-resistant measurements of distance and velocity using a small portable radio. Measurements that are as accurate as a laser require only milliseconds to complete and are insensitive to multipath interference. This opens up a wide range of applicability as an aiding sensor to integrated navigation systems. Performance has been demonstrated in the high-dynamic and high-multipath environment between the boots of a walking pedestrian, and similar performance is expected in industrial and military applications. By employing a conventional communications link, measurements of CPR and CPV should be scalable to longer distances with the availability of the measurements roughly comparable to the availability of the communications link.

    CPR and CPV achieve stand-alone measurement precision of much better than 1 millimeter standard deviation, and about 15 centimeters per second velocity respectively at a rate of hundreds of measurements per second. In-system performance of CPR and CPV measurement residuals demonstrates 1-centimeter CPR accuracy and 30 centimeters per second CPV accuracy. The measurements presented in this article are typically 100 times more precise than typical baseband round-trip RF measurements in a similarly challenging RF environment.

    Acknowledgments

    The work described in this article was sponsored by ENSCO Inc.

    Manufacturers

    The distance measuring radio is manufactured by ENSCO Inc. The inertial measurement unit used in the boot test was a Memsense LLC model H3, while the total station used for calibration was a Leica Geosystems AG model TS30.

    BRADLEY D. FARNSWORTH is the chief engineer for positioning, navigation and timing (PNT) at ENSCO Inc., Springfield, Va. He holds several U.S. patents and has expertise in real-time signal processing, autonomous systems and mixed-signal design. He received his B.S. summa cum laude and M.S. degrees in electrical engineering from Case Western Reserve University, Cleveland, Ohio.

    E.J. KREINAR is with ENSCO Inc. and holds B.S. and M.S. degrees in electrical engineering from Case Western Reserve University. He has expertise in optimal estimation using Kalman filters, real-time signal processing and autonomous systems.

    DAVID W.A. TAYLOR is the director of technology development and business area lead for PNT at ENSCO Inc., where he leads R&D programs developing sensors and systems for national security applications. He holds several U.S. patents and is an expert in GPS-denied navigation technologies. Taylor holds a B.S. in physics from Rhodes College, Memphis, Tenn. and a Ph.D. in geophysics from Virginia Polytechnic Institute and State University (Virginia Tech), Blacksburg, Va.

    FURTHER READING

    • Authors’ Conference Paper on which the Article is Based

    “Precise, Accurate, and Multipath-Resistant Networked Round-Trip Carrier Phase RF Ranging” by B.D. Farnsworth, E.J. Kreiner and D.W.A. Taylor in Proceedings of ITM 2015, the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, Calif. January 26–28, 2015, pp. 651–656.

    • Radio Frequency Ranging

    “Where Are We? Positioning in Challenging Environments Using Ultra-Wideband Sensor Networks” by Z. Koppanyi, C.K. Toth and D.A. Grejner-Brzezinska in GPS World, Vol. 26, No. 3, March 2015, pp. 44–49.

    “Hybrid Positioning: A Prototype System for Navigation in GPS-Challenged Environments” by C. Rizos, D.A. Grejner-Brzezinska, C.K. Toth, A.G. Dempster, Y. Li, N. Politi, J. Barnes, H. Sun and L. Li in GPS World, Vol. 21, No. 3, March 2010, pp. 42–47.

    RF Ranging for Location Awareness by S.M. Lanzisera and K. Pister, Technical Report No. UCB/EECS-2009-69, Dept. of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, Calif., May 19, 2009.

    “Opportunistic Navigation: Finding Your Way with AM Signals of Opportunity” by J. McEllroy, J.F. Raquet and M.A. Temple in GPS World, Vol. 18, No. 7, July 2007, pp. 44–49.

    “GPS + LORAN-C: Performance Analysis of an Integrated Tracking System” by J. Carroll in GPS World, Vol. 17, No. 7, July 2006, pp. 40–47.

    “Prime Time Positioning: Using Broadcast TV Signals to Fill GPS Acquisition Gaps” by M. Martone and J. Metzler in GPS World, Vol. 16, No. 9, September 2005, pp. 52–60.

    • Direct Sequence Spread Spectrum Radio Frequency Ranging

    “High-Precision 2.4 GHz DSSS RF Ranging” by B.D. Farnsworth and D.W.A. Taylor in Proceedings of ITM 2011, the 2011 International Technical Meeting of The Institute of Navigation, San Diego, Calif., January 24–26, 2011, pp. 178–183.

    “High Precision Narrow-Band RF Ranging” by B.D. Farnsworth and D.W.A. Taylor in Proceedings of ITM 2010, the 2010 International Technical Meeting of The Institute of Navigation, San Diego, Calif., January 25–27, 2010, pp. 161–166.

    • Estimating Phase and Frequency of Noisy Signals

    Phase and Frequency Estimation: High-Accuracy and Low-Complexity Techniques by Y. Liao, Master’s thesis, Dept. of Electrical and Computer Engineering, Worcester Polytechnic Institute, Worcester, Mass., May 2011.

    Equation images: Bradley D. Farnsworth, E.J. Kreinar and David W.A. Taylor

  • Innovation: Robustness to Faults for a UAV

    Innovation: Robustness to Faults for a UAV

    Integrated Navigation Systems Using Parallel Filtering

    The authors look at the development of a robust navigation system employing a GNSS receiver, accelerometers, gyroscopes, magnetometers, an airspeed device and dead reckoning to supply a blended navigation solution to a flight control system on a small, unmanned aerial vehicle.

    By Trevor Layh and Demoz Gebre-Egziabher

    INNOVATION INSIGHTS by Richard Langley
    INNOVATION INSIGHTS by Richard Langley

    THE NUMBER FOUR has special significance to humankind.  According to Penelope Merritt (a Samuel Beckett scholar) “[f]our has long been a number of completion, stability and predictability, as well as the representation of all earthly things.” And so it is with navigation systems. There are four important requirements of any navigation system: accuracy, availability, continuity, and integrity. To quickly review:

    Accuracy describes how well a measured value agrees with a reference value, typically the true value.

    Availability refers to a navigation system’s ability to provide the required function and performance within the specified coverage area at the start of an intended operation.

    Continuity is the ability of a navigation system to function without interruption during an intended period of operation.

    Integrity refers to the trustworthiness of a navigation system. A system might be available at the start of an operation, and we might predict its continuity at an advertised accuracy during the operation. But what if something unexpectedly goes wrong? If some system anomaly results in unacceptable navigation accuracy, the system should detect this and declare that it can no longer be used for navigation at the expected accuracy level. GPS, for example, has built into it various checks and balances to ensure a fairly high level of integrity. The same may be said of other global navigation satellite systems. Satellite performance is continuously monitored and a satellite is set unhealthy when an anomaly is detected. Some receivers have built-in receiver autonomous integrity monitoring to detect and isolate problematic satellite signals and navigation support systems (such as the Wide Area Augmentation System) independently monitor the health of satellite signals and supply a timely warning in the case of anomalous signal behavior.

    However, an aircraft, vessel, vehicle or some other platform still needs to be able to navigate if an independent primary navigation system becomes unavailable. This requires a back-up system of some kind and may take the form of an inertial navigation system, another radionavigation system such as eLoran, celestial navigation or just dead reckoning. Ideally, the platform’s navigation system should have multiple integrated sensors so that it continues to operate seamlessly even in the event of a sensor failure. We would call such a system robust. While we often use this word to describe a person with a strong healthy constitution, we can apply it to systems to refer to their ability to tolerate perturbations that might affect their functionality. A robust navigation system employs multiple sensors and uses appropriate filtering systems to autonomously detect anomalies, such as a failed sensor, and then to isolate it from the combined navigation solution.

    It is important to catch navigation sensor failures early, ideally instantaneously, to reduce integrity risk as much as possible. This is not a trivial operation, and it requires clever software design and operation.

    In this month’s column, we look at the development of such a robust navigation system employing a GNSS receiver, accelerometers, gyroscopes, magnetometers, an airspeed device and dead reckoning to supply a blended navigation solution to a flight control system on a small, unmanned aerial vehicle.

    While the number four has special significance in religion, science and other aspects of our lives, the number five may be considered equally important — denoting, for example, how many digits we have on our hands and feet. For those mathematically inclined, it is the first safe prime number. And perhaps we should use it to more fully characterize a navigation system, denoting its accuracy, availability, continuity, integrity and robustness.

    “Innovation” is a regular feature that discusses advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering, University of New Brunswick. He welcomes comments and topic ideas. Email him at lang @ unb.ca.

    Multi-sensor navigation systems generate an estimate of a vehicle’s state vector by fusing information from a disparate set of sensors. In many instances the sensors used in these systems provide redundant information. For example, in GNSS receivers, more than four (the minimum number required) satellite measurements are used to generate a position, navigation and time or PNT solution. This redundancy is beneficial because it enhances accuracy. It also enhances integrity or robustness because it allows the detection and possibly the isolation of failed sensors. However, fault detection and isolation schemes do not work instantaneously because once a sensor has failed, it takes some time before this can be detected. This is especially true for failures that are drift-like in nature as opposed to step-like. Drift-like errors grow slowly and, thus, fault detection schemes that monitor filter residuals cannot detect them until they have grown to a point where they are sufficiently large to exceed preset thresholds.

    The time between the onset of a fault and its detection — called the detection time — depends on the fault magnitude and thresholds of the fault detection algorithms. For a given fault magnitude, the length of the detection time represents a compromise between a navigation system’s continuity performance (or false alarm rate) and integrity risk (missed detection probability). The fact that faults cannot be detected instantaneously is an issue particularly for systems that have some form of dead reckoning (such as inertial navigation or velocity-based odometry) integrated with aiding sensors such as GNSS or radars. A failure in the aiding system (for example, a pseudorange fault in GPS) will lead to a corruption of the dead-reckoning solution. Once the GNSS fault has been detected and subsequently removed, the error induced by this failure has already propagated into the dead-reckoning solution. How does one deal with these types of errors? In this article, we discuss a solution to this challenge, which we call parallel filtering.

    Solutions for dealing with the problem exist. For example, one approach that has been used is based on the idea of delayed measurements. In this approach, integration of aiding sensor measurements in the navigation solution is delayed until a period equal to the fault detection time has elapsed. If no faults are detected during this period, then the delayed measurements are extrapolated forward in time and integrated into the navigation solution. Alternately, we can rewind the dead-reckoning solution backwards in time, integrate the delayed measurements and fast-forward the integrated solution up to the current time epoch. While this approach works, it has several shortcomings, of which we will mention just two. First, it requires buffering sensor data. Second, the most current navigation solution is not as accurate as it can be, because it does not incorporate the most recent sensor measurements (that is, the delayed measurements). The parallel filtering approach and fault tolerance we describe in this article deals with both of these shortcomings. Of course, like any other engineering solution, it represents a compromise between competing requirements. We will discuss these compromises and their impacts later in the article. For now, we will concentrate on describing the mechanics of parallel filtering and its performance when implemented in an integrated flight control system used for navigation, guidance and control of small unmanned aerial vehicles or UAVs.

    Parallel Filtering

    To understand parallel filtering, consider the schematic in FIGURE 1, which represents the conventional way in which an integrated navigation system fuses the information from N sensors. All the measurements from the N sensors are integrated in a single sensor-fusion algorithm. In the context of what we are describing here, the algorithm consists of a navigation filter and a fault-detection filter. The sensor-fusion algorithm integrates the measurements from all N sensors and generates a single, optimal estimate of the navigation state vector.

    FIGURE 1. Conventional (centralized) sensor fusion architecture.
    FIGURE 1. Conventional (centralized) sensor fusion architecture.

    In contrast to this, the schematic shown in FIGURE 2 is the parallel filtering approach introduced in this article. In this case, the same N sensors are divided up into M separate sensor clusters.

    FIGURE 2. Parallel filtering architecture.
    FIGURE 2. Parallel filtering architecture.

    The measurements from the sensors in the jth cluster is processed in a sensor-fusion algorithm to generate an estimate of the state vector denoted xj and a covariance matrix Pj. Each pair (xj, Pj) is then sent to a blending filter that generates a single optimal estimate Inn-x and P. The estimate  is a weighted sum of the estimates from the M filters:

    Inn-E1  (1)

    where Bj are blending weights that function as switches, which can be “opened” (set to zero) to isolate a parallel filter momentarily or permanently when a failed sensor is detected. The analogy with a physical switch should not be taken literally, however, because they are not “hard on-off” switches. Instead, they are matrices, which serve to change the emphasis put on a particular parallel filter. The blending weights are calculated so that the estimate Inn-x is an unbiased minimum-variance estimate. In mathematical terms, this means that they minimize the trace of the final covariance P. We will give more detail on how to calculate the weights shortly, but before we do that, let us describe, at a high level, how all of this works.

    Consider that one of the sensors in the Inn-lth cluster fails. TheInn-lth fault detection filter will identify the fault and try to isolate it. If the fault is non-isolable, the Inn-lth fault detection filter will raise an alarm. This can be done in various ways including inflation of the Inn-lth filter covariance Inn-Pl. An increasing covariance matrix Inn-Pl leads to a decreasing value of the corresponding blending weight Inn-Bl . For a non-isolable fault, Inn-Bl  will eventually approach zero, which effectively isolates the Inn-lth cluster from the navigation solution. If the fault was just a momentary glitch, then Inn-x and Inn-xl  are reset. In the simplest case, Inn-xl  can be reset to a weighted sum of remaining M-1 parallel state estimates. This is then blended with all of the other parallel estimates for generating the new Inn-x. This does not require setting aside buffers to store delayed measurements. Neither does it require rewinding the solution back in time when recovering from a faulted sensor scenario.

    Mathematical Formulation

    Providing a detailed derivation of the parallel filter is beyond the scope of this short article. Instead, we will just summarize the steps in the parallel filtering algorithm with the key formulas that are used in determining the blending weights. For simplicity, we will assume that we are working with a system with two parallel filters (M = 2 in Figure 2). How this extends to systems with more parallel filters or complex interlinking between the filters will become apparent later in the article when we present the results from a case study.

    To start, let us define some notation. We assume that the two parallel filters are extended Kalman filters (EKFs) generating estimates of the state vectors x1 and x2. We will denote these estimates Inn-x1 and Inn-x2. The covariances for these estimates are denoted by P1 and P2, respectively. The output of the blending filter is an estimate of the state vector x, which is a subset of x1 and x2. In mathematical terms, this means that we can define two mapping matrices M1 and M2 whose entries are either “1” or “0” and:

    Inn-E2   (2)

    The output of the blending filter Inn-x is, thus, given by:

    Inn-E3. (3)

    The blending weights are computed from:

    Inn-E4  (4)

    Inn-E5  (5)

    where

    Inn-E6  (6)

    Inn-E7 (7)

    Inn-E8. (8)

    The covariance of Inn-x is given by:

    Inn-E9(9)

    where Inn-E9b  and Π is given by:

    Inn-E10(10)

    where P12 is the cross-correlation between the states of parallel filter #1 and #2. We will say more about this shortly. In the meantime, note that in Equation (9), P1 and P2 are the covariances computed by the parallel filters after the measurement update. This computation requires knowledge of K1 and K2, which are the EKF gains for parallel filters. The matrices H1 and H2 are the observation matrices for filters #1 and #2. They relate the measurements y1 and y2 of the two parallel filters to their respective state vectors as follows (refer to Figure 2):

    y1 = H1x1 + v1   (11)

    y2 = H2x2 + v2  (12)

    where v1 and v2 are the measurement noises. Thus, the blending filter has to have knowledge of the measurement model and the gains of each parallel filter.

    Finally, note that P12 is zero if the dynamic models (time update equations) for the two parallel filters are completely independent. However, if they share sensors then there will be a correlation and P12 ≠ 0. This is the case for the example we present later in this article. In this case, P12 needs to be propagated between measurement updates. This can be done with the covariance time update equation (Lyapunov equation) for the joint state vector

    Inn-joint.

    Note that the architecture depicted in Figure 2 is meant to be a high-level depiction of the idea of parallel filtering. It should not be interpreted as an actual system architecture schematic. This will become apparent in the case study we present later in this article. The system we will consider there consists of three filters of which two are run in series (cascaded so that the output of the first is the input of the second) and each, in turn, is run in parallel with the third filter.

    It is important to note that the proper blending of the various filters’ outputs hinges on an accurate estimate of the individual covariances. This is particularly true when a fault has occurred. An individual filter that has detected a failed sensor must inflate its covariance to reflect its faulted state. How a filter does this is the problem of fault-detection filter design and is beyond the scope of this short article. For the work presented here, we used fault-detection filters, which monitored the EKF measurement residuals to detect sensor faults. When these filters detected a fault, they immediately inflated the faulted sensor’s output noise covariance matrix. We cannot overemphasize, therefore, the importance of having a well-designed fault-detection filter that responds in a timely and accurate manner to sensor faults.

    Case Study: Small UAV Flight Control

    detection/isolation scheme described above, we discuss the results of a blending filter, which was used on the University of Minnesota UAV Laboratory Goldy flight control system (FCS) shown in FIGURE 3. The Goldy FCS is used for navigation, guidance and control of small UAVs. The results presented below were obtained by post-processing flight test data.

    FIGURE 3. Goldy flight control system.
    FIGURE 3. Goldy flight control system.

    The architecture of the parallel filtering scheme used is shown in FIGURE 4. There are three separate filters whose outputs are blended: a GNSS-aided inertial navigation system (INS) filter, an attitude heading reference system (AHRS) filter and an airspeed-based dead-reckoning (DR) filter. Two blending filters are used to fuse the outputs from these three filters. The first blending filter fuses the attitude estimates from a GNSS-aided INS and an AHRS. The second blending filter fuses the position solutions from the GNSS-aided INS and the airspeed-based DR system. The AHRS and the airspeed-based DR filters are a pair of filters, which are cascaded to generate an estimate of the UAV navigation state vector. Thus, in the case of GNSS-denied operations, it can provide a position, velocity and attitude estimate to the flight control system. All of the sensors and software required to run these filters are part of the Goldy FCS. Before we present results of the parallel filter’s performance, we will briefly describe these three systems below.

    FIGURE 4. Goldy parallel filtering architecture. The three-axis magnetometer (Mag.) feeding the attitude heading reference system (AHRS) filter is part of the inertial measurement unit (IMU) device. The device’s accelerometer and gyro outputs feed both the GNSS-INS and AHRS filters. A pitot tube device supplies airspeed measurements to the airspeed-based dead-reckoning (DR) filter.
    FIGURE 4. Goldy parallel filtering architecture. The three-axis magnetometer (Mag.) feeding the attitude heading reference system (AHRS) filter is part of the inertial measurement unit (IMU) device. The device’s accelerometer and gyro outputs feed both the GNSS-INS and AHRS filters. A pitot tube device supplies airspeed measurements to the airspeed-based dead-reckoning (DR) filter.

    The GNSS-aided INS uses a consumer/automotive grade inertial measurement unit (IMU) to generate a position, velocity and attitude solution at a rate of 50 Hz. A 1-Hz measurement update from GPS is used to arrest drift errors inherent in inertial navigation systems, especially those mechanized using low cost consumer/automotive grade sensors. The GPS position updates also allow estimation of the inertial sensor biases. The state vector for this GNSS-aided INS is denoted x1 and consists of the following 15 states: latitude (Λ), longitude (λ), altitude (h), north velocity (Vn), east velocity (Ve), down velocity (Vd), roll angle (φ), pitch angle (θ), yaw angle (ψ), three gyro biases (bp, bq and br) and three accelerometer biases (bax, bay and baz).

    The second and third filters are a pair of estimators connected in series. The AHRS filter generates attitude estimates, which are fed to the airspeed-based DR filter. The AHRS uses the same IMU as the GNSS-aided INS to estimate roll (φ), pitch (θ) and yaw (ψ) attitude states of the vehicle as well as the three gyro biases (bp, bq and br). This AHRS filter’s six-dimensional state vector is denoted x2. The attitude is then used to resolve airspeed measurements from the body frame of the UAV to the north-east-down coordinate frame. After adding an estimate of the local winds to this, a single integration yields a position solution. This is done at a rate of 50 Hz. A periodic 1-Hz update from GPS is used to arrest the inherent DR drift. It also allows estimation of the magnitude of the local winds. The state vector of the airspeed-DR is denoted x3 and consists of the following 11 states: latitude (Λ), longitude (λ), altitude (h), local north wind speed (Wn), local east wind speed (We), yaw angle offset (Δψ), pitch angle offset (Δθ), three airspeed-measurement biases (Ub, Vb and Wb), and altitude offset (Δh).

    In the UAV flight control system, the blended states of interest are position (Λ, λ and h) and attitude (φ, θ and ψ). This implies that four mapping matrices are required for the fusion. First, matrices are needed for the attitude blending using the GNSS-aided INS (M1a) and the AHRS (M2). Then, additional matrices are needed for the position blending using the GNSS-aided INS (M1b) and the airspeed-based DR (M3). The shaping matrices are given by:

    Inn-E13   (13)

    Inn-E14   (14)

    Inn-E15   (15)

    Inn-E16   (16)

    where Ij×k is a j × k identity matrix and Zj×k is a j × k matrix of zeros.

    Filter Performance

    Validation of the parallel filtering scheme was accomplished by post-processing data from a series of flight tests where the Goldy FCS was installed on a UAV flying around a box-shaped trajectory.

    The first set of results was from a case where GPS was available from the moment the FCS is turned on until shortly after takeoff. Thus, GPS was available during initialization, take off roll and initial climb of the UAV. Then, GPS services were interrupted for a three-minute period during flight and restored shortly before the UAV landed. The GPS interruption was simulated by cutting out the 1-Hz measurement updates to the GNSS-aided INS and the AHRS/airspeed-DR system. In the background, however, there was another GNSS-aided INS that had an uninterrupted GPS service throughout the entire flight. This additional GNSS-aided INS solution is referred to as the reference solution and is used as ground-truth for assessing the performance of the parallel filtering scheme. For example, error plots shown below were generated by taking the difference between the various filtering schemes under consideration and this reference solution.

    FIGURE 5 shows the errors in the attitude of all three filters during this flight test. It shows that the blended estimates of heading, pitch and roll tend to oscillate closer to zero error than either of the individual filters themselves. This is reflected in TABLE 1, where it can be noted that the root-mean-square (RMS) error of the blended solution is lower than either the GNSS-aided INS or the AHRS in each of the three attitude solutions.

    FIGURE 5. Attitude errors. The gray vertical lines indicate when GPS availability was interrupted and then restored.
    FIGURE 5. Attitude errors. The gray vertical lines indicate when GPS availability was interrupted and then restored.
    Table 1. RMS orientation errors of different solutions (in degrees).
    Table 1. RMS orientation errors of different solutions (in degrees).

    FIGURE 6 shows the position errors of all three systems and illustrates one of the primary advantages of the proposed architecture. FIGURE 7 and FIGURE 8 show the blending weights matrices B1 and B2 before, during, and after the GPS outage. What is shown in these figures are the diagonal elements of these matrices.

    FIGURE 6. Position errors during a GPS outage.
    FIGURE 6. Position errors during a GPS outage.
    FIGURE 7. Attitude blending weights.
    FIGURE 7. Attitude blending weights.
    FIGURE 8. Position blending weights.
    FIGURE 8. Position blending weights.

    The INS exhibits extreme drift errors after only three minutes of unaided operation. The blending algorithm detects this inaccuracy and places more weight on the slow-drifting AHRS-DR solution, as shown in Figure 8. When GPS services are restored, the GNSS-aided INS error is “reset,” and the position weights are re-established to their pre-outage levels with minimal transient responses.

    We next show data from another flight test where an unplanned but fortuitous fault in the GPS sensor occurred. The cause of this fault has not been definitively determined, but potential reasons for it include loose cabling or outdated firmware. Nevertheless, this fault provided useful flight data for our architecture as no fictitious or simulated data was used. FIGURE 9 shows the GPS altitude measurements during this flight test. At t = 44 seconds a large oscillatory GPS error occurred. Similar errors were present in the GPS measurements of the velocities, latitude and longitude.

    FIGURE 9. GPS sensor errors during a fault.
    FIGURE 9. GPS sensor errors during a fault.

    Thus, all filters were initialized and operated correctly for the first 44 seconds. Between 44 and 132 seconds, the GPS receiver output was in error. This time period corresponds to the taxi, takeoff and initial climb phase of the UAV’s flight. A “reference” GNSS-aided INS, which did not employ the fault detection and isolation scheme that was employed in the parallel filtering system, was running in real time for this flight test. However, the UAV was under manual control (fortunately). As shown by the gray solution in FIGURE 10, the “reference” (non-fault-tolerant) system running in the background diverged and never converged.

    FIGURE 10. Attitude solution during an actual GPS sensor failure.
    FIGURE 10. Attitude solution during an actual GPS sensor failure.

    The dark traces in Figure 10 show the performance of the fault detection and isolation algorithm paired with the parallel filtering scheme described in this article. It is seen to be fault-tolerant and ignores the invalid measurements. Although nearly no aiding was provided until after the GPS sensor converged back to a stable state, the fault tolerant filter provided a much more accurate solution.

    A bird’s eye view of the ground track of the UAV shows a similar trend. This can be seen in the position plot of FIGURE 11, which shows a roughly 60-second segment of the flight.

    FIGURE 11. GPS sensor failure performance: north vs. east.
    FIGURE 11. GPS sensor failure performance: north vs. east.

    This north vs. east plot demonstrates that a non-fault-tolerant GNSS-aided INS provides an unstable position solution similar to the attitude shown in Figure 10. By contrast, the fault-tolerant system described in this article provides a smooth position estimate that ignores the “bad” GPS measurements and tracks the “good” measurements after they convergence back to the truth. Therefore, the safety of the aircraft would not have been in question, and the UAV could have completed multiple segments of fully autonomous waypoint navigation in spite of the faulty sensor measurements provided earlier.

    Summary

    The parallel filtering approach discussed in this article has the potential for providing a systematic way of designing multi-sensor navigation systems, which are robust to sensor faults. Unlike prior approaches, it obviates the need to maintain data buffers to store data, which can be played back in the event of a sensor fault. As noted earlier, like any engineering solution to problems, this one is a comprise between many competing requirements. As such, it has some drawbacks when compared to traditional approaches. We note two of them here as they are the focus of ongoing work. First, the computational overhead associated with this approach can be high especially if a large number of parallel filters are used. Thus, methods for streamlining the computations so that they are not computer-resource intensive will be important.

    The second issue that needs further exploration is the way in which blending weights are computed. A key input to calculating the weights (as well as the “triggers” for the fault detection and isolation algorithm) are the covariances estimated by the various parallel filters. This can be problematic if the covariances used by the parallel filters do not match the true statistics. This can lead to turning off a particular filter when no faults had occurred or, worse, retaining a filter with a failed sensor in the blended solution.

    For more detail about the Goldy FCS, go to www.uav.aem.umn.edu.

    Acknowledgments

    This article is based, in part, on the paper “A Fault-Tolerant, Integrated Navigation System Architecture for UAVs” presented at ION ITM 2015, the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, Calif., January 26–28, 2015. The contents of this article reflect the views of the authors, who are responsible for the facts and the accuracy of the information presented herein. The authors acknowledge the United States Department of Homeland Security for supporting the work reported here through the National Center for Border Security and Immigration under grant number 2008-ST-061-BS0002. However, any opinions, findings, conclusions or recommendations in this article are those of the authors and do not necessarily reflect views of the United States Department of Homeland Security.

    Manufacturers

    The Goldy FCS uses a Hemisphere GNSS Crescent OEM board and an Analog Devices ADIS16405 iSensor MEMS inertial measurement unit.

    Trevor Layh is a M.S. candidate in the Department of Aerospace Engineering and Mechanics at the University of Minnesota in Minneapolis. He obtained his B.S. in mechanical engineering from South Dakota State University, Brookings, S.D., and his research interests include backup navigation systems to GPS-aided inertial navigation systems.

    Demoz Gebre-Egziabher is an associate professor in the Department of Aerospace Engineering and Mechanics at the University of Minnesota. His research focuses on the design of multi-sensor navigation systems. He holds a Ph.D. in aeronautics and astronautics from Stanford University, Stanford, Calif.

    FURTHER READING

    • Authors’ Conference Paper

    “A Fault-Tolerant, Integrated Navigation System Architecture for UAVs” by T. Layh and D. Gebre-Egziabher in Proceedings of ITM 2015, the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, Calif. January 26–28, 2015, pp. 702–712.

    • Attitude Heading Reference System and Airspeed-Based Dead Reckoning Filters

    Correlated-Data Fusion and Cooperative Aiding in GNSS-Stressed or Denied Environments by H. Mokhtarzadeh, Ph.D. dissertation, University of Minnesota UAV Laboratories, 2014.

    “A Recovery System for SUAV Operations in GPS-Denied Environments Using Timing Advance Measurements” by T. Layh, J. Larson, J. Jackson, B. Taylor and D. Gebre-Egziabher in Proceedings of ITM 2015, the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, Calif. January 26–28, 2015, pp. 293–303.

    • UMN UAV Research Lab and Goldy Flight Control System

    “Infrastructure” website, University of Minnesota UAV Laboratories, July 2014.

    • Navigation in GPS-Denied Environments

    Impact and Mitigation of GPS-Unavailability on Small UAV Navigation, Guidance and Control by D. Gebre-Egziabher and B. Taylor, Technical Report 2012-2, University of Minnesota, Department of Aerospace Engineering and Mechanics, November 2012. Available through online request.

    • Avionics Reliability

    Introduction to Avionics Systems, 2nd Edition, by R.P.G Collinson. Published by Kluwer Academic Publishers, Boston, Mass., 2003.

    Civil Avionics Systems by I. Moir and A. Seabridge. AIAA Education Series. Published by American Institute of Aeronautics and Astronautics, Reston, Va., 2003.

    • Example of a Fault-Tolerant Avionics System

    “Performance of Honeywell’s Inertial/GPS Hybrid (HIGH) for RNP Operations” by  C. Call, M. Ibis, J. McDonald and K. Vanderwerf in Proceedings of PLANS 2006,  the Institute of Electrical and Electronics Engineers / Institute of Navigation Position, Location and Navigation Symposium, Coronado (San Diego), Calif., April 25–27, 2006, pp. 244–255, doi: 10.1109/PLANS.2006.1650610.

    • GNSS Integrity

    “Digging into GPS Integrity: Charting the Evolution of Signal-in-Space Performance by Data Mining 400,000,000 Navigation Messages” by L. Heng, G.X. Gao, T. Walter and P. Enge in GPS World, Vol. 22, No. 11, November 2011, pp. 44–49.

    “Integrity for Non-Aviation Users: Moving Away from Specific Risk” by S. Pullen, T. Walter and P. Enge in GPS World, Vol. 22, No. 7, July 2011, pp. 28–36.

    “The Integrity of GPS” by R.B. Langley in GPS World, Vol. 10, No. 3, March 1999, pp. 60–63.

    • Multi-Sensor Systems

    “Toward a Unified PNT — Part 1: Complexity and Context: Key Challenges of Multisensor Positioning” by P. D. Groves, L. Wang, D. Walter, H. Martin and K. Voutsis in GPS World, Vol. 25, No. 10, October 2014, pp. 18, 27–34, 47–49.

    “Toward a Unified PNT — Part 2: Ambiguity and Environmental Data: Two Further Key Challenges of Multisensor Positioning” by P. D. Groves, L. Wang, D. Walter and Z. Jiang in GPS World, Vol. 25, No. 11, November 2014, pp. 18, 27–35.

  • Innovation: Carrier-Phase Ambiguity Resolution

    Innovation: Carrier-Phase Ambiguity Resolution

    Handling the Biases for Improved Triple-Frequency PPP Convergence

    By Denis Laurichesse

    Precise point positioning (PPP) can be considered a viable tool in the kitbag of GPS positioning techniques. One precision aspect of PPP is its use of carrier-phase measurements rather than just pseudoranges. But there is a catch. Often many epochs of measurements are needed for a position solution to converge to a sufficiently high accuracy. In this month’s column, we look at how using measurements from three satellite frequencies rather than just two can help.

    INNOVATION INSIGHTS by Richard Langley
    INNOVATION INSIGHTS by Richard Langley

    PPP? WHAT’S THAT? This acronym stands for precise point positioning and, although the technique is still in development, it has evolved to a stage where it can be considered another viable tool in the kitbag of GPS positioning techniques. It is now supported by a number of receiver manufacturers and several free online PPP processing services. You might think, looking at the name, that there’s nothing particularly special about it. After all, doesn’t any kind of positioning with GPS give you a precise point position including that from a handheld receiver or a satnav device? They key word here is precise.

    The use of the word precise, in the context of GPS positioning, usually means getting positional information with precision and accuracy better than that afforded by the use of L1 C/A-code pseudorange measurements and the data provided in the broadcast navigation messages from the satellites. A typically small improvement in precision and accuracy can be had by using pseudoranges determined from the L2 frequency in addition to L1. This permits the real-time correction for the perturbing effect of the ionosphere. Such an improvement in positioning is embodied in the distinction between the two official GPS levels of service: the Standard Positioning Service provided through the L1 C/A-code and the Precise Positioning Service provided for “authorized” users, which requires the use of the encrypted P-code on both the L1 and L2 frequencies. Civil GPS users will have access to a similar level of service once a sufficient number of satellites transmitting the L2 Civil (L2C) code are in orbit. However, this capability will only provide meter-level accuracy. The PPP technique can do much better than this.

    It can do so thanks to two additional precision aspects of the technique. The first is the use of more precise (and, again, accurate) descriptions of the orbits of the satellites and the behavior of their atomic clocks than those included in the navigation messages. Such data is provided, for example, by the International GNSS Service (IGS) through its global tracking network and analysis centers. These so-called precise products are typically used to process receiver data after collection in a post-processing mode, although real-time correction streams are now being provided by the IGS and some commercial entities.

    Now, it’s true that a user can get high precision and accuracy in GPS positioning using the differential technique where data from one or more base or reference stations is combined with data from the user receiver. However, by using precise products and a very thorough model of the GPS observables, the PPP technique does away with the requirement for a directly accessed base station.

    The other precision aspect of PPP is its use of carrier-phase measurements rather than just pseudoranges. Carrier-phase measurements have a precision on the order of two magnitudes (a factor of 100) better than that of pseudoranges. But there is a catch to the use of carrier-phase measurements: they are ambiguous by an integer multiple of one cycle. Processing algorithms must resolve the value of this ambiguity and ideally fix it at its correct integer value. Unfortunately, it is difficult to do this instantaneously, and often many epochs of measurements are needed for a position solution to converge to a sufficiently high accuracy, say better than 10 centimeters. Researchers are actively working on reducing the convergence time, and in this month’s column, we look at how using measurements from three satellite frequencies rather than just two can help.

    “Innovation” is a regular feature that discusses advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering, University of New Brunswick. He welcomes comments and topic ideas. To contact him, see the “Contributing Editors” section on page 6.

    While carrier-phase measurements typically have very low noise compared to pseudorange (code) measurements, they have an inherent integer cycle ambiguity: the carrier phase, interpreted as a range measurement, is ambiguous by any number of cycles. However, integer ambiguity fixing is now routinely applied to undifferenced GPS carrier-phase measurements to achieve precise positioning. Some implementations are even available in real time. This so-called precise point positioning (PPP) technique permits ambiguity resolution at the centimeter level.

    With the new modernized satellites’ capabilities, performing PPP with triple-frequency measurements will be possible and, therefore, the current dual-frequency formulation will not be applicable. There is also a need for a generalized formulation of phase biases for Radio Technical Commission for Maritime Services (RTCM) State Space Representation (SSR) needs. In this RTCM framework, the definition of a standard is important to allow interoperability between the two components of a positioning system: the network side and the user side.

    Classical Formulation

    In this section, we review the formulation of the observation equations. We will use the following constants in the equations:

    Eq-0

    where f1 and f2 are the two primary frequencies transmitted by all GPS satellites and c is the vacuum speed of light. For the GPS L1 and L2 bands, f1 = 154f0 and f2 = 120f0, where f0 = 10.23 MHz.

    The pseudorange (or code) measurements, P1 and P2, are expressed in meters, while phase measurements, L1 and L2, are expressed in cycles. In the following, we use the word “clock” to mean a time offset between a receiver or satellite clock and GPS System Time as determined from either code or phase measurements on different frequencies or some combination of them.

    The code and phase measurements are modeled as:

    Eq1  (1)

    where:

    • D1 and D2 are the geometrical propagation distances between the emitter and receiver antenna phase centers at f1 and f2 including troposphere elongation, relativistic effects and so on.
    • W is the contribution of the wind-up effect (in cycles).
    • e is the code ionosphere elongation in meters at f1. This elongation varies with the inverse of the square of the carrier frequency and is applied with the opposite sign for phase.
    • Δh = hi – hj is the difference between receiver i and emitter j ionosphere-free phase clocks. Δhp is the corresponding term for code clocks.
    • Δτ = τi – τj is the difference between receiver i and emitter j offsets between the phase clocks at f1 and the ionosphere-free phase clocks. By construction, the corresponding quantity at f2 is γΔτ. Similarly, the corresponding quantity for the code is Δτp (time group delay).
    • N1 and N2 are the two carrier-phase ambiguities. By definition, these ambiguities are integers. Unambiguous phase measurements are therefore L1 + N1 and L2 + N2.

    Equations (1) take into account all the biases related to delays and clock offsets. The four independent parameters, Δh, Δτ, Δhp, and Δτp, are equivalent to the definition of one clock per observable. However, our choice of parameters emphasizes the specific nature of the problem by identifying reference clocks for code and phase (Δhp and Δh) and the corresponding hardware offsets (Δτp and Δτ). These offsets are assumed to vary slowly with time, with limited amplitudes.

    The measured widelane ambiguity, nw , (also called the Melbourne-Wübbena widelane) can be written as:

    Eq2(2)

    where Nw is the integer widelane ambiguity, μ j is the constant widelane delay for satellite j and μi is the widelane delay for receiver i (which is fairly stable for good quality geodetic receivers). The symbol brackets means that all quantities have been averaged over a satellite pass.

    Integer widelane ambiguities are then easily identified from averaged measured widelanes corrected for satellite widelane delays. Once integer widelane ambiguities are known, the ionosphere-free phase combination can be expressed as

    Eq3  (3)

    where  Eq-8   is the ionosphere-free phase combination computed using the known Nw ambiguity, Dc is the propagation distance, hi is the receiver clock and h j is the satellite clock. N1 is the remaining ambiguity associated to the ionosphere-free wavelength λc (10.7 centimeters).

    The complete problem is thus transformed into a single-frequency problem with wavelength λc and without any ionosphere contribution. Many algorithms can be used to solve Equation (3) using data from a network of stations. If Dc is known with sufficient accuracy (typically a few centimeters, which can be achieved using a good floating-point or real-valued ambiguity solution), it is possible to simultaneously solve for N1 , hi and h j. The properties of such a solution have been studied in detail. A very interesting property of the h j satellite clocks is, in particular, the capability to directly fix (to the correct integer value) the N1 values of a receiver that was not part of the initial network.

    The majority of the precise-point-positioning ambiguity-resolution (PPP-AR) implementations are based on the identification and use of the two quantities μ j and h j. These quantities may be called widelane biases and integer phase clocks, a decoupled clock model or uncalibrated phase delays, but they are all of the same nature.

    A Real-Time PPP-AR Implementation

    A PPP-AR technique was successfully implemented by the Centre National d’Etudes Spatiales (CNES) in real time in the so-called PPP-Wizard demonstrator in 2010 and has been subsequently improved. In this demonstrator and in the framework of the International GNSS Service (IGS) Real-Time Service (RTS) and the RTCM, the GPS and GLONASS constellation orbits and clocks are computed. Additional biases for GPS ambiguity resolution are computed and broadcast to the user. The demonstrator also provides an open-source implementation of the method on the user side, for test purposes. Centimeter-level positioning accuracy in real time is obtained on a routine basis.

    Limitations of the Bias Formulations. The current formulation works but it has several drawbacks:

    • The chosen representation is dependent on the implemented method. Even if the nature of the biases is the same, their representation may be different according to the underlying methods, and this makes it difficult for a standardization of the bias messages.
    • The user side must implement the same method as the one used on the network side. Otherwise, the user side would have to convert the quantities from one method to another, leading to potential bugs or misinterpretations.
    • It is limited to the dual-frequency case. There are only two quantities to be computed in the dual-frequency case (uj12 and hj12), but in the triple-frequency case, there are many more possible combinations. For example, one can have (this is a non-exhaustive list) uj12, uj15, uj25,hj12, hj15, hj25, where the indices refer to different pairs of frequencies, and other ionosphere-free combinations such as phase widelane-only or even phase ionosphere-free and geometry-free combinations are possible.

    New RTCM SSR Model

    The new model, as proposed by the RTCM Special Committee 104 SSR working group for phase bias messages is based on the idea that the phase bias is inherent to each frequency. Thus, instead of making specific combinations, one phase bias per phase observable is identified and broadcast.

    It is noted that this convention was adopted a long time ago for code biases. Indeed, in the RTCM framework, and unlike the standard differential code bias (DCB) convention where code biases are undifferenced but combined, the RTCM SSR code biases are defined as undifferenced and uncombined. The general model for uncombined code and phase biases is therefore:

    Eq4   (4)

    Time group delays, τ, and phase clocks, h, in Equation (1) are replaced by code and phase biases (ΔbP and ΔbL respectively). RTCM SSR code and phase biases correspond to the satellite part of these biases. The prime notation denotes the “unbiasing” process of the measurements. Here, the clock definition is crucial. As the biases are uncombined, they are referenced to the clocks. The convention chosen for the standard is natural: it is the same as the one used by IGS, that is, ΔhP in our notation.

    This new model can be extended to the triple-frequency case very easily, as it does not involve explicit dual-frequency combinations:

    Eq5    (5)

    This new model simplifies the concept of phase biases for ambiguity resolution. This representation is very attractive because no assumption is made on the method used to identify phase biases on the network side. All the implementations are valid if they respect this proposed model. It also allows convenient interoperability if the network and user sides implement different ambiguity resolution methods.

    TABLE 1 summarizes the different messages used for PPP-AR in the context of RTCM SSR:

    TABLE 1. RTCM SSR messages for PPP-AR.
    TABLE 1. RTCM SSR messages for PPP-AR.

    Bias Estimation in the Dual-Frequency Case. The new phase biases identification in the dual-frequency case is straightforward. There are two biases (bL1, bL2 ) to be estimated using two combinations (µ and h). The problem to be solved is described in FIGURE 1.

    FIGURE 1. Phase biases estimation in the dual-frequency case.
    FIGURE 1. Phase biases estimation in the dual-frequency case.

    It can be solved very easily on the network side by means of a 2 × 2 matrix inversion:

    Eq6   (6)

    with

    Eq7

    Note: All the quantities denote the satellite part of the Δ operator defined above.

    Bias Estimation in the Triple-Frequency Case. The triple-frequency bias identification is tricky due to the need, using only three biases, to keep the integer nature of phase ambiguities on all viable ionosphere-free combinations, and in particular combinations that were not used in the identification process. At this level, one cannot make assumptions on what kind of combinations will be employed by a user. The problem to be solved is described in FIGURE 2.

    FIGURE 2. Phase biases estimation in the triple-frequency case.
    FIGURE 2. Phase biases estimation in the triple-frequency case.

    As an example, a naïve solution would be to identify the extra-widelane phase biases,uj25, using the dual-frequency widelane approach, and then identify thebL5bias. Given the large wavelength of the extra-widelane combination, such identification would be very easy. However, the corresponding bias would be only helpful for extra-widelane ambiguity identification, and its noise would prevent its use for widelane 15 (L1/L5) ambiguity resolution or other useful combinations available in the triple-frequency context.

    Each independent phase bias can be directly estimated in a filter; however, in order to keep ascending compatibility with the dual-frequency case during the deployment phase of the new modernized satellites, we have chosen to stay in the old framework, that is, to work with combinations of biases. The resolution method is the following:

    • The widelane biases, that is, the identification of all the bLi – bLj quantities, are solved. For this computation and in order to have an accurate estimate of these biases, the two MW-widelane biases µ12 and µ15 are used coupled to an additional phase bias, which is given by the triple-frequency ionosphere-free phase combination with the integer widelane ambiguities already fixed. This last combination using only phase measurements is much more accurate than MW-widelanes. The system to be solved is redundant and the noise of the different equations has to be chosen carefully.
    • The remaining bias (bLi ) is estimated using the traditional ionosphere-free phase combination of L1 and L2.

    This computation has been implemented in the CNES real-time analysis center software, and since September 15, 2014, CNES broadcasts phase biases compatible with this triple-frequency concept on the IGS CLK93 real-time data stream.

    Real Data Analysis

    To prove the validity of the concept, at CNES, we compute several ambiguity combinations using real data. The process is the following:

    • Look for good receiver locations having a large number of GPS Block IIF satellites (transmitting the L5 signal) in view for a period of time exceeding 30 minutes, and choose among them, one participating in the IGS Multi-GNSS (MGEX) experiment. The station CPVG (Cape Verde) in the Reseau GNSS pour l’IGS et la Navigation (REGINA) network was chosen for the time span on September 28, 2014, between 19 and 20 hours UTC. During this period, four Block IIF satellites were visible simultaneously (PRNs 1, 6, 9, 30) for a total of 14 GPS satellites in view.
    • Record a compatible phase-bias stream. The CLK93 stream is recorded during the time span of the experiment.
    • Perform a PPP solution using the measurements, CLK93 corrections and biases to estimate the propagation distance, the troposphere delay and the receiver clock and phase ambiguity estimates according to Equation (5).
    • For different ambiguity estimates, compute and plot the obtained residuals.

    We present in the following graphs various ambiguity residuals for the four Block IIF satellites in view. The values of each ambiguity are offset by an integer value for clarity purposes.

    Melbourne-Wübbena Extra-Widelane. FIGURE 3 represents the MW extra-widelane (between frequencies L2 and L5) ambiguity estimation using our process. The MW extra-widelane ambiguity has a wavelength of 5.86 meters. The noise of the combination expressed in cycles is very low, and the integer nature of ambiguities in this combination is clearly visible.

    FIGURE 3. Ambiguity residuals for the extra-widelane 5-2 combination.
    FIGURE 3. Ambiguity residuals for the extra-widelane 5-2 combination.

    Melbourne-Wübbena Widelanes. FIGURE 4 represents the MW-widelanes (the regular 1-2 and 1-5 combinations). Here again, the integer nature of the four ambiguities is clearly visible.

    FIGURE 4. Ambiguity residuals for widelane combinations; top: 1-2 widelane, bottom: 1-5 widelane.
    FIGURE 4. Ambiguity residuals for widelane combinations; top: 1-2 widelane, bottom: 1-5 widelane.

    Widelane-Only Ionosphere-Free Phase. In the triple-frequency context, there is a possibility of forming an ionosphere-free combination of the three phase observables. This combination has an important noise amplification factor (>20), but would allow us to perform decimeter-accuracy PPP using only the solved widelane integer ambiguities and if the corresponding phase biases are accurate. In addition, it can be shown that the wavelength of the widelane ambiguity when the extra-widelane ambiguity is solved is about 3.4 meters. It means that the remaining widelane using this combination can be solved if the position is accurate enough (a few tens of centimeters) and the extra-widelane is known. FIGURE 5 shows such a case, that is, the residuals of the widelane ambiguity using this combination and assuming that the extra-widelane is already solved for.

    FIGURE 5. Ambiguity residuals for widelane-only 1-2-5 ionosphere free combinations.
    FIGURE 5. Ambiguity residuals for widelane-only 1-2-5 ionosphere free combinations.

    Such a case where the solution is the most biased  is shown (the dark blue curve). This behavior is mainly due to the difficulty in estimating the phase biases on this combination accurately using only a few Block IIF satellites. We hope that in the future the increasing number of modernized satellites will help such bias estimation.

    N1 Ionosphere-Free Phase. FIGURES 6 to 8 show the three possible ambiguity estimates using the ionosphere-free phase combination with two measurements (we assume that the corresponding widelane has already been solved). In each case, the computed biases allow us to easily retrieve the integer nature of the N1 ambiguity.

    FIGURE 6. Ambiguity residuals for the N1 combination using a fixed 1-2 widelane.
    FIGURE 6. Ambiguity residuals for the N1 combination using a fixed 1-2 widelane.
    FIGURE 7. Ambiguity residuals for the N1 combination using a fixed 1-5 widelane.
    FIGURE 7. Ambiguity residuals for the N1 combination using a fixed 1-5 widelane.
    FIGURE 8. Ambiguity residuals for the N1 combination using a fixed 2-5 widelane.
    FIGURE 8. Ambiguity residuals for the N1 combination using a fixed 2-5 widelane.

    Application to Triple-Frequency PPP

    The results presented above show that the integer ambiguity nature of phase measurements is conserved for various useful observable combinations and prove the validity of the model. Another experiment has been carried out to estimate the impact of ambiguity convergence in the triple-frequency context. For that, in order to maximize the observability of the GPS Block IIF constellation and thus the accuracy of the biases, a network of ten stations across Europe has been chosen for the phase biases computation (see FIGURE 9). The station REDU (in green) was the test station to be positioned. The test occurred on January 10, 2015, around 11:00 UTC. At that time, four Block IIF satellites were visible simultaneously (PRNs 1, 3, 6, 9) for a total of 10 satellites in view.

    FIGURE 9. Network used for the triple-frequency PPP study.
    FIGURE 9. Network used for the triple-frequency PPP study.

    The PPP-Wizard open source client was used to perform PPP in real time. The advantage of this implementation is that it directly follows the uncombined observable formulation described in Equations (5). The strategy for ambiguity resolution is a simple bootstrap approach.

    Convergence of the Widelane-Only Solution. In this test, a PPP solution was performed, but only the fixing of the widelane ambiguities was implemented. As noted in the previous section, the wavelength of the widelane ambiguity when the extra-widelane ambiguity is solved is about 3.4 meters, so it is expected that all the widelanes can be fixed in a very short time. Despite the amplification factor of about 20 of the equivalent unambiguous phase combination, we expect to obtain an accuracy of about 10 centimeters with such a solution.

    FIGURE 10 shows the convergence time of several PPP runs in this context (16 different runs of five minutes are superimposed), in terms of horizontal position error.

    FIGURE 10. Widelane-only triple-frequency PPP convergence (horizontal position error).
    FIGURE 10. Widelane-only triple-frequency PPP convergence (horizontal position error).

    The extra-widelanes are fixed instantaneously; the remaining widelanes are fixed in about two minutes on average to be below 30 centimeters (this is represented by the different sharp reductions of the errors). This new configuration, available in the triple-frequency context, is very interesting as it provides an intermediate class of accuracy, which converges very quickly and which is suitable for applications that do not demand centimeter accuracy. Another interesting aspect of this combination is the gap-bridging feature. In PPP, gap-bridging is the functionality that allows us to recover the integer nature of the ambiguities after a loss of the receiver measurements over a short period of time (typically a pass through a tunnel or under a bridge). This is done usually by means of the estimation of a geometry-free combination (ionosphere delay estimation) during the gap. Realistic maximum gap duration in the dual-frequency case is about one minute. In the triple-frequency case, the wavelength of the geometry-free combination involving the widelane (if the extra-widelane is fixed) is 1.98 meters. With such a large wavelength, the gaps are much easier to fill, and we can safely extend the gap duration to several minutes. In addition, the widelane combinations are wind-up independent, so there is no need to monitor a possible rotation of the antenna during the gap, as in the dual-frequency case.

    Overall Convergence (All Ambiguities). Another PPP convergence test has been carried out with all ambiguities fixing activated (four different runs of 15 minutes are superimposed). Results are shown in FIGURE 11.

    FIGURE 11. All ambiguities triple-frequency PPP convergence (horizontal position error).
    FIGURE 11. All ambiguities triple-frequency PPP convergence (horizontal position error).

    The centimeter accuracy is obtained in this configuration within eight minutes, which is a significant improvement in comparison to the dual-frequency case. Further improvement of this convergence time is expected with an increase in the number of Block IIF satellites and, subsequently, GPS IIIA satellites.

    Convergence Time Comparison Between the Dual- and Triple-Frequency Contexts. Thanks to these new results, a realistic picture for PPP convergence in the dual- and triple-frequency contexts can be drawn. To do so, polynomial functions have been fitted over the data points obtained in the previous studies. Two data sets were used:

    • Standard dual-frequency convergence (GPS only, 10 satellites in view).
    • Triple-frequency convergence (GPS only, 10 satellites in view, four Block IIF satellites).

    FIGURE 12 represents the comparison between the two polynomials (horizontal error).

    FIGURE 12. Realistic PPP convergence comparison between dual- and triple-frequency contexts (horizontal position error).
    FIGURE 12. Realistic PPP convergence comparison between dual- and triple-frequency contexts (horizontal position error).

    Conclusion

    The new phase-bias concept proposed for RTCM SSR has been successfully implemented in the CNES IGS real-time analysis center. This new concept represents the phase biases in an uncombined form, unlike the previous formulations. It has the advantage of the unification of the different proposed methods for ambiguity resolution, and it prepares us for the future; for example, for a widely available triple-frequency scenario. The validity of this concept has been shown; that is, the integer ambiguity nature of phase measurements is conserved for various useful observable combinations.

    In addition, we have also shown that the triple-frequency context has a significant impact on ambiguity convergence time. The overall convergence time is drastically reduced (to some minutes instead of some tens of minutes) and there is an intermediate combination (widelane-only) that has some interesting properties in terms of convergence time, accuracy and gap-bridging for non-demanding centimeter-level applications.

    Acknowledgments

    The contributions of colleagues contributing to the IGS services are gratefully acknowledged. Geo++ is thanked for useful discussions on the standardization of phase bias representation.

    DENIS LAURICHESSE received his engineering degree and a Diplôme d’études appliquées (an advanced study diploma) from the Institut National des Sciences Appliquées in Toulouse, France, in 1988. He has worked in the Spaceflight Dynamics Department of the Centre National d’Etudes Spatiales (CNES, the French Space Agency) in Toulouse since 1992, responsible for the development of the onboard GNSS Diogene navigator. He was involved in the performance assessment of the EGNOS and Galileo systems and is now in charge of the CNES International GNSS Service real-time analysis center. He specializes in navigation, precise satellite orbit determination and GNNS-based systems. He was the recipient of The Institute of Navigation Burka Award in 2009 for his work on phase ambiguity resolution.

    Further Reading

    Undifferenced Ambiguity Resolution

    “Phase Biases Estimation for Undifferenced Ambiguity Resolution” by D. Laurichesse, presented at PPP-RTK & Open Standards Symposium, Frankfurt, Germany, March 12–13, 2012.

    “Undifferenced GPS Ambiguity Resolution Using the Decoupled Clock Model and Ambiguity Datum Fixing” by P. Collins, S. Bisnath, F. Lahaye, and P. Héroux in Navigation, Journal of The Institute of Navigation, Vol. 57, No. 2, Summer 2010, pp. 123–135, doi: 10.1002/j.2161-4296.2010.tb01772.x.

    “Integer Ambiguity Resolution on Undifferenced GPS Phase Measurements and Its Application to PPP and Satellite Precise Orbit Determination” by D. Laurichesse, F. Mercier, J.-P. Berthias, P. Broca, and L. Cerri in Navigation, Journal of The Institute of Navigation, Vol. 56, No. 2, Summer 2009, pp. 135–149, doi: 0.1002/j.2161-4296.2009.tb01750.x.

    “Resolution of GPS Carrier-Phase Ambiguities in Precise Point Positioning (PPP) with Daily Observations” by M. Ge, G. Gendt, M. Rothacher, C. Shi, and J. Liu in Journal of Geodesy, Vol. 82, No. 7, pp. 389–399, doi: 10.1007/s00190-007-0187-4. Erratum: 10.1007/s00190-007-0208-3.

    Real-Time Precise Point Positioning

    “Coming Soon: The International GNSS Real-Time Service” by M. Caissy, L. Agrotis, G. Weber, M. Hernandez-Pajares, and U. Hugentobler in GPS World, Vol. 23, No. 6, June 2012, pp. 52–58.

    “The CNES Real-time PPP with Undifferenced Integer Ambiguity Resolution Demonstrator” by D. Laurichesse in Proceedings of ION GNSS 2011, the 24th International Technical Meeting of The Satellite Division of the Institute of Navigation, Portland, Ore, September 20–23, 2011, pp. 654–662.

     RTCM PPP State Space Representation

    “PPP with Ambiguity Resolution (AR) Using RTCM-SSR” by G. Wübbena, M. Schmitz, and A. Bagge, presented at IGS Workshop, Pasadena, Calif., June 23–27, 2014.

    “The RTCM Multiple Signal Messages: A New Step in GNSS Data Standardization” by A. Boriskin, D. Kozlov, and G. Zyryanov in Proceedings of ION GNSS 2012, the 25th International Technical Meeting of The Satellite Division of the Institute of Navigation, Nashville, Tenn., September 17–21, 2012, pp. 2947-2955.

    “RTCM State Space Representation (SSR): Overall Concepts Towards PPP-RTK” by G. Wübbena, presented at PPP-RTK & Open Standards Symposium, Frankfurt, Germany, March 12–13, 2012.

    Precise Point Positioning

    Improved Convergence for GNSS Precise Point Positioning by S. Banville, Ph.D. dissertation, Department of Geodesy and Geomatics Engineering, Technical Report No. 294, University of New Brunswick, Fredericton, New Brunswick, Canada. Recipient of The Institute of Navigation 2014 Bradford W. Parkinson Award.

    “Precise Point Positioning: A Powerful Technique with a Promising Future” by S.B. Bisnath and Y. Gao in GPS World, Vol. 20, No. 4, April 2009, pp. 43–50.