Which recent GNSS/INS innovations have been most helpful in advancing bathymetry? Which upcoming ones will be?
Miguel Amor
“Development of PPP removed reliance on shore-based RTK base stations, allowing operation almost anywhere on the oceans. Continued performance improvement in FOG and MEMS INS, along with bathymetric sensors, provide cost-effective solutions while also providing more accurate seabed maps. The future will see increased PPP accuracy with faster convergence and continued improvement in INS, coupled with increased resolution of bathymetric sensors, leading to more of the oceans mapped using autonomous platforms.” Miguel Amor, Hexagon Positioning
Bernard Gruber
“While GNSS has been a clear contributor to Earth mapping, it is an altogether different dilemma to solve ‘submarine topography’ mapping. Given recent developments in the IMU and lidar markets, one can readily utilize these sensors to correct for roll, pitch, and yaw, and produce digital maps, respectively. Combining these sensors with GNSS receivers, mounted on a drone for example, can allow for precise measurements in areas of tidal shifts or dynamic variations of water depth.” Bernard Gruber, Northrop Grumman
New service provides PPP convergence for centimeter-level accuracy on land, air and marine applications around the world
Research from Hexagon’s Autonomy & Positioning division has resulted in breakthrough innovations in precise point positioning (PPP) that enable nearly instant global centimeter-level accuracy. These developments pave the way to bring “RTK from the Sky” performance to worldwide users through correction service products and GNSS receivers from Hexagon.
RTK from the Sky technology provides the quick accuracy of an RTK solution with the high accessibility and availability of PPP. Users will no longer have geographic or regional infrastructure restrictions — they will be free to operate anywhere around the world with the same premium level of positioning performance.
RTK from the Sky technology removes the traditional PPP barrier of long convergence times as well as internet and radio communication limitations, delivering instantaneous convergence anywhere in the world. This breakthrough establishes the foundation for assured positioning with no downtime in marine, agriculture, and autonomous applications.
To achieve these results, there must be masterful attention to detail throughout the entire positioning ecosystem: no errors conveniently cancelled and no errors ignored. All errors are carefully estimated and removed from the final GNSS position faster and more reliably than ever before.
This end-to-end fine-tuning of measurement quality and error mitigation establishes the foundation for RTK from the Sky performance. No matter the location or application, users will be able to rely upon the highest availability and accuracy of corrections anywhere in the world, without the convergence time, Hexagon said.
“In 2020, PPP has become RTK — without the mobility limitations,” said Sandy Kennedy, VP of Innovation at Hexagon’s Autonomy & Positioning division. “RTK from the Sky has been a very satisfying development. To see this kind of positioning performance available anywhere in the world is the realization of the next step of innovation for GNSS.”
RTK from the Sky technology will be the foundation for future correction service products and applications from Hexagon built for diverse applications.
As the skipper of Galileo 4, a 50-foot sailboat on the Columbia River, I instruct my crew to alert me if the water under the keel drops below 10 feet and take immediate action if it drops below 5 feet, because I cannot constantly monitor my chart to avoid running aground. Yet, the huge cargo ships that navigate the river for 100 miles from its mouth at Astoria to the Port of Portland sometimes have as little as two feet of vertical clearance.
This feat of navigation is made possible by the knowledge, experience and electronic equipment used by the river pilots who steer the ships, the hydrographers who survey the river, and the dredge operators who perform the Sisyphean task of maintaining the required depth of the navigation channel. Each additional inch of draft they enable allows a ship to carry additional cargo worth up to several million dollars.
In similar ways, marine professionals around the world cooperate to chart ocean bottoms and to keep ports, harbors and navigable waterways safe for the more than 90% of trade that is carried by ships. Additionally, off-shore installations—such as fiber optic cables, pipelines, drilling platforms and wind turbines—all require accurate surveys of the ocean floor. Finally, population growth in coastal areas and sea level rise due to climate change are driving the need for bathymetric data for planning and emergency management.
Bathymetry
For centuries, mariners recorded water depth using nothing more than a lead line, a compass, a sextant and a rudimentary nautical chart. This was such a time-consuming process, however, that they could only perform it for a tiny percentage of the world’s oceans and coastlines. Today’s technology makes the process not only more accurate, but also vastly more efficient.
In deep waters, depth data is collected using huge multi-beam echo sounders (MBES) that operate at very low frequencies. As the depth decreases, smaller devices are used that operate at higher frequencies and, therefore, have higher resolution. However, close to shore, the efficiency of these devices drops dramatically, as the cone of their sound signal is cut off by the slope of the shelf. This is where airborne lidar sensors become a much more efficient means of collecting depth data.
In addition to data from the sounders, bathymetry requires data about the vessel’s location and attitude. The former, an obvious requirement for any kind of mapping, are collected by differential GNSS receivers. The latter, collected by an inertial measurement unit (IMU), are used to compensate for variations in the depth measurement depending on the vessel’s rotational movements (roll, pitch and yaw) and translational movements (heave, surge and sway). This is the same reason that aerial photogrammetrists use IMUs on aircraft.
Challenges
Traditionally, MBES systems have been large, complex and expensive. However, they are rapidly becoming smaller, cheaper, quicker to deploy, and easier to use thanks in part to the introduction of inertial systems that use microelectromechanical systems (MEMS), said Ludovic Bazin, technical support manager for SBG Systems, which specializes in MEMS technology. “You can see that the new systems are being increasingly deployed in smaller autonomous vehicles, on smaller autonomous surface vessels (ASV), and even smaller vessels. So, people can go quickly in operation,” he said. An additional advantage, he pointed out, is that they do not require an export license.
A key to accurate bathymetric surveys is reducing the error budget aboard the vessel, where the survey positions are tied back to a GNSS antenna. “You have errors all the way through the system,” said Richard Turner, vice president of global marine sales for Hexagon’s Autonomy & Positioning division, which caters mostly to the market for survey related to oil and gas. He attributes the largest improvements in recent years to the increase in accuracy using precise point positioning (PPP). “If you are out of range of real-time kinematic (RTK) and any other near-shore positioning, the accuracy of PPP is constantly improving,” he said. “It is getting down into the five-centimeter range horizontal or better than that.”
Turner also pointed to the tight integration of inertial navigation system (INS) technology with other systems. “Every time you improve the accuracy of your system the specs go up,” he said. Therefore, the challenge is to ensure that the equipment is installed properly, which requires very accurate offset measurements. “It is no good having two centimeters position accuracy if your heading or your offsets are wrong.” Generally, he points out, boats are not designed for this type of installation, due to such things as long cable runs.
Hexagon will send surveyors out with equipment from Leica, one of its divisions, to do the dimensional control and to calibrate the gyroscopes, which are another source of error. In 2014, Hexagon acquired Veripos. “Many of the people in the Veripos organization come from the offshore survey world or the dredging world, so it is very marine focused,” said Turner. “No other providers have the marine experience that we do.”
For bathymetric software companies, the main current challenge is “keeping up with all the modern and cheaper hardware,” including RTK receivers, echo sounders, and side scan sonars, said Leon Steijger, owner and programmer at Eye4Software B.V., which makes the Hydromagic software.
Requirements and capabilities
To get accurate data, all position and depth records must be timestamped with high precision so that the location of the echo sounder pings can be calculated during post-processing, Steijger noted. “The software needs to be able to generate elevation maps, depth contours, and 3D terrain views and must support volume calculations to calculate how much water there is in a basin, or to determine how much material has been removed during dredging operations.”
Hydromagic uses “plugins,” which are pieces of software that are loaded optionally to interface sensors with the software. “For some hardware we also offer a plugin containing a user interface that can be used to, for instance, upload a planned route to an automatic pilot or to control the signal processing parameters of an echo sounder.” Operators only need to specify the dimensions of their vessel and correct for the sound velocity and the static draft (the distance between the water surface and transducer). They see the vessel’s track in real time, but the rest of the data are post-processed.
Hexagon controls its own correction services and the network that delivers them. “We obviously build our own GPS receivers, so we can tightly integrate inertial systems,” said Turner. “We use third-party inertial systems. However, because we have access to the tracking loops on the GNSS boards, we can tightly integrate that inertial system so it gives a level of coupling that’s difficult unless you are actually building those boards yourself.” While near-shore operations can use RTK or post-processing, he pointed out, “the offshore guys often use real-time positioning to collect data for oil and gas. And that is really where we come to the party, because we have all those services too.”
SBG Systems designs, manufactures, and calibrates its own IMUs, then integrates them with GNSS boards, creating OEM products. “We also design and produce our own firmware algorithms to merge all those datasets,” said Bazin. “From the selection of the MEMS sensor to the final product, SBG will design, manufacture, develop, and produce the entire systems. We also provide tools for people to integrate our systems to develop their own libraries or to integrate our libraries into their systems and work with some integrators for APIs so they can control our systems from their own application.” The company’s post-processing system, Qinertia, integrates GNSS corrections with raw IMU data. “So, when we do post-processing, we reprocess an entire solution at the end for position, but also for stabilization for pitch, roll and heading,” Bazin explained. One of the benefits is the ability to remove many multipath effects.
For bathymetric surveys using an unmanned aerial vehicle (UAV), the control software must keep the platform at a constant altitude and speed over the surface of the water, because the echo sounder is dragged through the water at the end of a cable, explained Alexey Dobrovolsky, CTO of SPH Engineering, based in Riga, Latvia, which delivers UAV-related software. Therefore, he said, “missions should be executed in a fully automated mode.” His company’s software only requires the UAV’s operator to define the survey area, set the direction of the survey lines, and specify the distance between them. The software will handle everything else. “We automatically recalculate the depth measured from the echo sounder to the real depth in our data files using data from a radar altimeter,” he said. “Our software contains a high-end model of the echo sounder, which has a tilt sensor and a pitch sensor.”
Of course, dragging an echo sounder from a UAV only works for small areas, such as in open pit mines where the liquid can be very contaminated. “The flight time with an echo sounder of the most popular UAV will be around 20 minutes,” said Dobrovolsky. “That determines the maximum length of the survey lines that can be covered by a single flight.”
A couple of years ago, SPH began to provide some UAV-based bathymetry solutions that use low frequency ground-penetrating radar (GPR). There are two scenarios when GPR can be useful for bathymetry, Dobrovolsky explained. The first one is to do bathymetry through ice on the surface of lakes or rivers, which would require drilling holes to use an echo sounder. “With GPR, you can do bathymetry through the ice layer,” he said. The second scenario is mountain rivers with extremely strong currents, when it is not possible to use a standard manned or unmanned boat, because GPR works without contact with the water.
Bathymetric systems are now also deployed on autonomous underwater vehicles (AUVs) that are only one to three feet long. “MEMS INS are compact and can be integrated directly with MBES systems, which provide an all-in-one compact system that can be easily deployed and operated because they are lightweight and their mechanical alignments are known and fixed,” said Bazin. “Some of these systems can go 2,000 meters below the surface of the water.” In post-processing, he pointed out, some MEMS INS can have an angular accuracy as low as 0.07 degrees for the vessel’s pitch and roll and a heading accuracy of as little as 0.01 degrees.
Outputs
To integrate diverse sensors with a UAV, SPH developed an onboard computer, called UgCS SkyHub, that logs data from the sensors. In the case of the echo sounder, it can be an NMEA stream or just a stream of current depth measurements, said Dobrovolsky. The device is also connected to the UAV’s autopilot, so it logs the platform’s position and speed, and with the altimeter. UgCS SkyHub can record three types of data files: a CSV file containing the coordinates, depths, and a few additional parameters; a file in NMEA 0183 format, which is also standard for bathymetry; and a SEG-Y file containing the full echo sounder data, including, for example, sediments and objects in the water.
SBG Systems’ software has two kinds of outputs, Bazin explained. First, a proprietary binary format, as well as NMEA and ASCII formats, that are used to provide stabilization and navigation for the platform in real-time. Second, a standard as-built survey format for post-processing. “Then, we have very powerful tools to output ASCII files that are completely configurable from header to footer,” he added.
Eye4Software’s main outputs are volume reports or plot sheets for end customers containing a map with depth colors and depth contours, as well as cross section views or XYZ export files for further processing in, for instance, AutoDesk Civil 3D and AutoCAD.
Feature image: A UAV from SPH Engineering tows a bathymetric sonar just under the surface of a river. (Photo: SPH Engineering)
Septentrio’s SECORX-S GPS/GNSS receiver product line offers sub-decimeter accuracy without the need for additional positioning service subscriptions.
The mosaic-Sx module. (Photo: Septentrio)
Septentrio has expanded its SECORX-S product line. The multi-constellation multi-frequency GNSS receivers of the SECORX-S family deliver sub-decimeter positioning out of the box, without the need for any additional correction service subscription or maintenance.
Users benefit from always-on high accuracy provided by a PPP-RTK correction service integrated directly into Septentrio’s latest core GNSS technology. The SECORX-S product line, already including GNSS OEM boards, now also offers a compact mosaic-Sx module as well as a ruggedized receiver in an IP68 chassis, AsteRx SB Sx.
By adding modules and boxed receivers to the SECORX-S product line, Septentrio brings its innovative approach of plug-and-play accurate positioning to industrial applications including precision agriculture, UAV, robotics and construction.
The AsteRs-m2-Sx. (Photo: Septentrio)
Receivers of the SECORX-S family offer lifelong sub-decimeter accuracy in U.S. and Europe. The PPP-RTK correction service integrated in these receivers uniquely combines near-RTK accuracy with short convergence time.
“By launching the SECORX-S product family a few months ago, we have taken a ground-breaking step towards easy-to-use and accessible high-accuracy positioning,” said Francois Freulon, head of product management at Septentrio. “Our SECORX-S product range now includes compact modules, versatile OEM boards as well as boxed receivers. With this expansion of the product family our customers now have the flexibility to choose from a wider range of receivers, the one that perfectly fits their needs.”
By R. Eric Phelts, Kazuma Gunning, Juan Blanch and Todd Walter
Innovation Insights with Richard Langley
AS WE NOTED IN THE LAST INNOVATION COLUMN, integrity — at least from a safety viewpoint — is the most important characteristic of a navigation system. Yes, accuracy, availability and continuity are also required but, without integrity, the advertised accuracy of a system might become meaningless and perhaps misleading. While GPS and user receivers are highly reliable, we cannot presume that there will never be an erroneous signal transmitted by a GPS satellite that would result in a receiver outputting a hazardously misleading position solution. While “supervisory” systems such as satellite-based augmentation systems monitor GPS signals and can alert users about defective satellites within a very short period of time, it is advantageous for a user receiver to autonomously detect problematic satellites and quarantine them so that they do not perturb the position solution.
It is for this reason that receiver autonomous integrity monitoring (RAIM) techniques were developed. As we know, a receiver needs signals from a minimum of four satellites simultaneously to determine its 3D position and its clock offset. However, typically there are more than four satellites in view, and so multiple solutions using subsets of four satellites are possible. If five satellites are visible, then it is possible to determine that one of them is faulty, but not which one (geometry plays a role here). This is called fault detection (FD). And if six satellites are visible, the faulty satellite can be determined and then excluded from the position solution (fault detection and exclusion, or FDE). This is the basic principle of RAIM.
Advanced RAIM (ARAIM) extends RAIM to other constellations beyond GPS. ARAIM enables the use of the newer GNSS constellations to provide better levels of performance than RAIM with GPS alone. It also uses dual-frequency measurements for enhanced vertical positioning reliability.
Central to positioning techniques providing a safety-of-life service is the notion that the uncertainty of a provided position must be conservatively estimated and provide for both nominal uncertainty and the uncertainty of a faulted solution such as that detected using RAIM. These conservative estimates are known as the horizontal and vertical protection levels. The horizontal protection level (HPL) is the radius of a circle in the horizontal plane with its center at the true position, which describes the region that is assured to contain or bound the provided horizontal position to a very high probability. The vertical protection level is half the length of a segment in the vertical direction with its center at the true position, which describes the region that is assured to contain or bound the provided vertical position to a very high probability. The probability levels are typically taken to be 99.9999998 and 99.99999% for HPL and VPL, respectively.
The usual approach for RAIM and ARAIM is to use the so-called “snapshot” approach, where measurements are assumed to be uncorrelated epoch to epoch. In this month’s column, a team of authors from Stanford University discusses a superior approach for ARAIM using the technique of precise point positioning.
Advanced Receiver Autonomous Integrity Monitoring (ARAIM) is implemented using solution separation in positioning and navigation software. Solution separation computations presume one or more GNSS satellites may be faulty, and they iteratively compute multiple position solutions comprised of subsets of the n satellites in view (n, n-1, n-2, and so on) to ensure that at least one of the solutions is fault-free. Using assumptions on the nominal and faulted uncertainty of the solutions, the software can compute conservative horizontal and vertical protection levels (PLs) by bounding the uncertainty from all the solutions. This assures (to a targeted level of probability) that the user position is contained within these limits.
Traditional solution separation techniques generally operate as a “snapshot.” The basic measurements are dual-frequency, carrier-smoothed pseudorange (code), and errors are generally assumed to be uncorrelated from epoch to epoch. This procedure requires that errors at each time step are conservatively bounded with large uncertainties (sigmas) designed to protect the user against the worst-case error. These assumptions minimize the complexity and computational cost of the solution by providing a robust, provably safe bound. However, the PLs computed are relatively large. In addition, they can change suddenly from one epoch to the next due to changes in available satellites or platform dynamics. This can make meeting performance goals (such as continuity) for aircraft approaches more challenging.
Solution separation procedures using techniques based on precise point positioning (PPP) implement an extended Kalman filter (EKF) to filter measurements over time. In this case, the basic measurements are dual-frequency code and carrier phase, and errors are assumed to have some correlation between each time step to the next. Accordingly, these techniques leverage higher quality measurements (that is, carrier-phase-based as opposed to code-based) to smooth and reduce large sigmas and to estimate (and calibrate) errors over time. The complexity associated with defining and characterizing the decorrelation models for the errors, so that the nominal covariance produced by the EKF conservatively describes the actual error, is significant. Also, the computational cost of estimating the error states may be substantially higher than with the traditional snapshot approach. However, the computed protection levels provide integrity and are often significantly smaller. In addition, the filtering makes them more robust to platform dynamics, which makes them well-suited for aircraft in flight.
Flight Data: Outages and Cycle Slips. ARAIM performance may be significantly affected by aircraft dynamics. Specifically, banking can induce satellite outages and cycle slips. Outages weaken the constellation geometry and can cause sudden changes in the protection level. Frequent cycle slips prevent code measurements from being smoothed, potentially inflating protection levels of carrier-phase-smoothed code measurements for extended periods of time.
When the outages and cycle slips are computed as a rate, a trend can be seen. Both increase notably as the relative elevation angle to the satellites decrease. FIGURE 1 shows an example of outages as a function of the apparent elevation angle of the satellites (relative to the aircraft). Cycle slips on GPS L1-L5 and Galileo El-E5a are plotted in FIGURES 2 (a) and (b), respectively.
FIGURE 1. Outages as a function of body frame or apparent elevation angle during aircraft banking. (Image: Authors)FIGURE 2a. Cycle-slip rate (per satellite-second) for GPS L1-L5. (Image: Authors)FIGURE 2b. Cycle-slip rate (per satellite-second) for E1-E5a. (Image: Authors)
For this article, we have used the flight data from one of our earlier papers on the effect of aircraft banking on ARAIM performance (see Further Reading). With this data, we show that significant advantages of PPP can be retained even during aircraft maneuvers when outages and cycle slips threaten ARAIM continuity and availability the most.
MODEL ASSUMPTIONS
The traditional snapshot solution separation approach is well-established and was implemented according to the standards established by a working group operating under the U.S.-European Union Agreement on GPS-Galileo Cooperation, which has been extended to all constellations (see Further Reading). For this article, we limited the constellations to GPS and Galileo, and the prior probabilities assumed for satellite and constellation faults were as follows:
Psat = 10-5, Pconst,GPS = 10-8 and Pconst,GAL = 10-4
We implemented the PPP algorithm with solution separation using an EKF using dual-frequency code and carrier-phase measurements (from GPS and Galileo) with estimated parameters comprising the receiver position and velocity, clock biases for each constellation in use, a residual tropospheric delay, carrier-phase float ambiguities for each tracked carrier, multipath error, receiver differential code bias, and broadcast orbit and clock error. Modeled (not estimated) effects include solid Earth tide modeling, ocean loading, an initial tropospheric delay and relativistic effects. Many of the details of the implementation can be found in our paper “Design and Evaluation of Integrity Algorithms for PPP in Kinematic Applications” (see Further Reading).
PPP techniques typically utilize precise ephemeris information obtained from a global network of ground reference stations such as those operating in the network coordinated by the International GNSS Service. Snapshot solution separation techniques, however, use only ephemeris information broadcast from the satellites themselves. For a proper comparison of the protection levels computed by each technique, the PPP filter was constrained to use this broadcast information.
The model we have applied is mostly typical of a traditional PPP implementation with one significant exception — the state tracking the error contribution of the broadcast orbit and clock on each line-of-sight signal. The error contributed by the broadcast orbit and clock is handled by the filter leveraging a characterization of the rate of change of the error, then including it as an estimation state for each line of sight and only adding enough process noise to capture the slowly changing error. We have previously characterized the rate of change of the error in the broadcast orbit and clock and process noise (for GPS). Complete tables of initial state uncertainties and additional settings for process and measurement noise were provided in our earlier work (see Further Reading).
RESULTS
Flight data collected over a period of approximately one year was used to evaluate ARAIM performance through momentary outages and cycle slips due to aircraft dynamics. A multi-constellation, multi-frequency receiver tracked GPS (L1 C/A and L5) and Galileo (E1 and E5a) satellites. This receiver is installed in a Global 5000 jet owned and operated by the FAA William J. Hughes Technical Center. It records and stores GNSS measurements whenever flights are taken. The data we used for this article included data recorded over approximately 35 flights from September 2017 to April 2018.
FIGURE 3 shows the trajectory and altitude information corresponding to a single flight (Flight #6) taken on Sept. 20, 2017, and FIGURE 4 compares the corresponding horizontal and vertical protection levels computed using snapshot and “broadcast” PPP techniques. For an additional reference, we also computed protection levels using PPP with precise orbits and clocks (we call this precise PPP despite the terminology redundancy) and plotted these in Figure 4, too.
FIGURE 3b. Altitude information for Flight #6 (Sept. 20, 2017). (Image: Authors)FIGURE 4a. Horizontal protection levels for Flight #6 (Sept. 20, 2017); red circles indicate a satellite being dropped or reentering the solution. (Image: Authors)FIGURE 4b. Vertical protection levels for Flight #6 (Sept. 20, 2017); red circles indicate a satellite being dropped or reentering the solution. (Image: Authors)
Several things are readily apparent from these comparisons. First, after the initial time required for convergence, there is a substantial reduction in the PLs using the broadcast-PPP-based approach. The precise PPP PLs, as expected, produce the largest reduction, but use additional information not available to the snapshot method. In addition, the snapshot solution separation PLs vary significantly due to cycle slips and momentary satellite outages. FIGURE 5 shows the number of satellites tracked by the receiver during this flight; red circles plotted on the snapshot protection-level line indicate when satellites are coming into and out of view. Despite numerous abrupt changes in number of measurements and measurement quality, the EKF of the PPP techniques produces PLs that are relatively smooth and continuous.
FIGURE 5. Number of satellites tracked for Flight #6 (Sept. 20, 2017). (Image: Authors)
FIGURE 6 shows the trajectory and altitude information corresponding to Flight #4 taken on Sept. 15, 2017.
FIGURE 6a. Flight path for Flight #4 (Sept. 20, 2017). (Image: Authors)FIGURE 6b. Altitude information for Flight #4 (Sept. 20, 2017). (Image: Authors)
FIGURE 7 compares the horizontal and vertical PLs for snapshot solution separation and the PPP-based techniques.
FIGURE 7. Horizontal protection levels for Flight #4 (Sept. 15, 2017); red circles indicate a satellite being dropped or reentering the solution. (Image: Authors)FIGURE 7b. Vertical protection levels for Flight #4 (Sept. 15, 2017); red circles indicate a satellite being dropped or reentering the solution.
As in the case shown in Figure 4, the PLs in Figure 7 reveal a substantial reduction in the mean PLs computed using the PPP-based approach. And the snapshot solution separation approach displays even more variations due to momentary satellite outages. Some of the cycle slips affected enough satellites to introduce brief spikes in the PPP solution as well. These reconverge quickly, but they suggest that some tuning of the EKF can still be done to mitigate these interruptions. Still, the filtered approach produces PLs that are more robust to the outages and are substantially smaller than with the snapshot method.
FIGURE 8 compares the horizontal and vertical PLs computed using snapshot solution separation and PPP techniques for Flight #20 — where the airplane remained stationary on the runway. In the absence of flight dynamics, the levels for all the approaches were relatively smooth. However, a few discontinuities can still be observed for the snapshot case. Also note, in the case of the broadcast PPP, the convergence time is noticeably longer. This is likely because the integer ambiguity resolution in the solution took longer to converge without platform motion.
FIGURE 8a. Horizonta protection levels for a stationary aircraft (Flight #20, Dec. 4, 2017); red circles indicate a satellite being dropped or reentering the solution. (Image: Authors)FIGURE 8b. Vertical protection levels for a stationary aircraft (Flight #20, Dec. 4, 2017); red circles indicate a satellite being dropped or reentering the solution. (Image: Authors)
The mean horizontal and vertical PLs for both techniques are summarized in FIGURE 9. (There were issues with the data from Flight #14 and it was not processed.) The PPP approach consistently produces protection levels anywhere from 30 to 75% smaller than those computed using the snapshot approach. The mean PLs for the PPP techniques were always below those computed with the snapshot method.
FIGURE 9a. Comparison of mean horizontal PLs for “snapshot” vs. a PPP-based technique. (Image: Authors)FIGURE 9b. Comparison of mean vertical PLs for “snapshot” vs. a PPP-based technique. (Image: Authors)
CONCLUSIONS
Data from 35 flights was used to compare ARAIM protection levels computed by the traditional “snapshot” solution separation versus a PPP-based approach during both in-flight and several static scenarios. We observed that the filtering of PPP methods yields mean PLs approximately 30 to 75% of those computed using traditional methods in all cases. This improvement can be attributed to exploiting — through filtering and estimation — carrier-phase-based measurements and a time-correlation of the errors. In addition, the EKF employed by the PPP approach demonstrated improved robustness to outages and cycle slips induced by aircraft dynamics. Despite the increased complexity and computational cost, we believe that PPP approaches hold promise for significantly improving ARAIM performance.
ACKNOWLEDGMENT
This article is based on the paper “Evaluating the Application of PPP Techniques to ARAIM Using Flight Data” presented at ION ITM 2020, the 2020 International Technical Meeting of The Institute of Navigation, San Diego, California, Jan. 21–25, 2020.
MANUFACTURER
The flight data was recorded using a Trimble BX935-INS receiver fed by an Antcom Avionic II GNSS antenna.
R. ERIC PHELTS is a research associate in the Department of Aeronautics and Astronautics at Stanford University, California. He received a Ph.D. in mechanical engineering from Stanford University in 2001. His research involves signal deformation monitoring for SBAS and flight-data analyses for ARAIM.
KAZUMA (KAZ) GUNNING is a Ph.D. candidate in the GPS Laboratory at Stanford University working under the guidance of Todd Walter. He is also the navigation algorithms and architecture lead at Xona Space Systems in San Mateo, California. His research interests are in precise point positioning and integrity.
JUAN BLANCH is a senior research engineer at Stanford University, where he works on integrity monitoring algorithms for radionavigation. He received a Ph.D. in aeronautics and astronautics from Stanford University in 2003. He has received The Institute of Navigation (ION) Parkinson and Early Achievement awards.
TODD WALTER is a research professor in the Department of Aeronautics and Astronautics at Stanford University. He received his Ph.D. in applied physics from Stanford University in 1993. His research focuses on implementing high-integrity air navigation systems. He has received the ION Thurlow and Johannes Kepler awards. Walter is also a Fellow of the ION and has served as its president.
“A Baseline RAIM Scheme and a Note on the Equivalence of Three RAIM Methods” by R.G. Brown in Navigation, Vol. 39, No. 3, Fall 1992, pp. 301–316.
Advanced Receiver Autonomous Integrity Monitoring
“SBAS Corrections for PPP Integrity with Solution Separation” by K. Gunning, J. Blanch and T. in Proceedings of ITM 2019, the 2019 International Technical Meeting of The Institute of Navigation, Reston, Virginia, Jan. 28–31, 2019, pp. 707–719.
“Design and Evaluation of Integrity Algorithms for PPP in Kinematic Applications” by K. Gunning, J. Blanch, T. Walter, L. de Groot and L. Norman in Proceedings of ION GNSS+ 2018, the 31st International Technical Meeting of the Satellite Division of The Institute of Navigation, Miami, Florida, Sept. 24–28, 2018, pp. 1910–1939.
“Effect of Aircraft Banking on ARAIM Performance” by R.E. Phelts, J. Blanch, K. Gunning, T. Walter and P. Enge in Proceedings of ION GNSS+ 2018, the 31st International Technical Meeting of the Satellite Division of The Institute of Navigation, Miami, Florida, Sept. 24–28, 2018, pp. 2632–2641.
“Precise Point Positioning” by J. Kouba, F. Lahaye and P. Tétreault, Chapter 25 in Springer Handbook of Global Navigation Satellite Systems, edited by P.J.G. Teunissen and O. Montenbruck, published by Springer International Publishing AG, Cham, Switzerland, 2017.
This insight column from Septentrio explains the role of GNSS corrections in precise positioning. It explores the three most popular correction methods: RTK, PPP and PPP-RTK.
Let’s say you need reliable accurate global positioning in your technology. You do some research and decide to get yourself a multi-frequency GPS/GNSS receiver. You order an evaluation kit, but how to get your receiver to deliver the high accuracy that it promises?
GNSS receivers rely on external corrections to compensate for GNSS errors to achieve decimeter- or centimeter-level accuracy as fast as possible.
Correcting GNSS errors
GNSS-based positioning is calculated using a method that, by itself, is limited in accuracy due to several errors caused by GNSS satellites as well as the Earth’s atmosphere.
Even the advanced clocks on board GNSS satellites experience minute drifts that cause clock errors.
The movement of GNSS satellites is predicted as they orbit the Earth. These predictions are not perfect, which results in orbit errors.
Satellite equipment introduces small signal errors, which are modeled as satellite biases.
Atmospheric errors caused by distortions and delays are experienced by the signal as it passes through the Earth’s ionosphere (outer layer) and troposphere (layer near the Earth’s surface).
The local environment around the receiver as well as the receiver itself can introduce errors. For example, satellite signals can be reflected off buildings and tall structures (multipath).
A GNSS receiver cannot correct satellite and atmospheric errors by itself; it relies on data provided by an external source. Clock and orbit errors are satellite-dependent, and so are the same around the world. Atmospheric errors, on the other hand, depend on the path the signal takes as it travels from the satellites to the user, differing depending on the receiver’s location.
To overcome both satellite and atmospheric errors, a reference station (also known as a base station) can be used. A reference station — a GNSS receiver installed at a fixed and precisely known location — estimates GNSS errors and sends them in the form of GNSS corrections to the user receiver. A reference network consists of interconnected reference receivers spread over a geographic area.
A user receiver gets data sent from a GNSS reference station to correct satellite and atmospheric errors. (Image: Septentrio)
Receiver-side errors can only be handled partially, by robust receiver technology and careful operation. Depending on which type of corrections are applied, it can take a few seconds to several minutes of initialization time for high accuracy to be achieved.
Types of corrections for high-accuracy positioning
Until recent years, RTK and PPP have been the established methods of providing GNSS corrections to user receivers. But the demand for high-accuracy positioning is on the rise, paving the way for new positioning techniques such as the hybrid PPP-RTK.
RTK: Highest level of accuracy. With the RTK (real-time kinematic) method, a user receiver gets correction data from a single base station or a local reference network. It then uses this data to eliminate most of the GNSS errors.
RTK is based on the principle that the base station and the user receiver are located close together (a maximum 40 kilometers or 25 miles apart) and therefore “see” the same errors. For example, since the ionospheric delays are similar for both the user and the reference station, they can be cancelled out of the solution, allowing higher accuracy.
While in the RTK method corrections are provided for a specific location, in the PPP and PPP-RTK methods, a correction model is broadcast to a larger area, but with slightly lower accuracy. To transmit this correction model, a message format called SSR (Space State Representation) can be used. There is some confusion in the industry about the term “SSR” since it is often associated with the newer PPP-RTK method. But be careful, since “SSR” is occasionally used as a buzzword to refer to traditional PPP services as well.
PPP: Globally accessible and accurate, but at a cost. Precise point positioning (PPP) corrections contain only the satellite clock and orbit errors. Since these errors are satellite specific, and thus independent of the user’s location, only a limited number of reference stations is needed around the world. Because atmospheric errors are not included in PPP corrections, only a lower accuracy level can be achieved with this method. Also, a longer initialization time is expected of up to 20-30 minutes, which may not be practical for some applications. PPP has been traditionally used in the maritime industry; today it has expanded to various land applications such as agriculture as a convenient way to get global GNSS corrections.
PPP-RTK: Best of both worlds? PPP-RTK (a.k.a. SSR) is the latest generation of GNSS correction services, combining near-RTK accuracy and quick initialization times with the broadcast nature of PPP. A reference network, with stations about every 150 kilometers (100 miles), collects GNSS data and calculates both satellite and atmospheric correction models.
As explained above, atmospheric corrections are regional, and so a denser reference network is needed than for PPP. These corrections are then broadcast to subscribers in the area via internet, satellite or telecom services. Subscribed receivers use the broadcast correction model to deduce their location-specific corrections, resulting in sub-decimeter accuracy.
Comparing the three GNSS correction methods
The table below compares the three correction methods, highlighting their strengths and weaknesses.
Table: Septentrio
The infrastructure density and initialization time for all three methods vary with the different kinds of errors that are corrected. The broadcast nature of PPP-RTK and PPP, as well as the lighter infrastructure that they require, makes these methods scalable for mass-market applications.
Types of errors that are corrected by each of the three methods. (Image: Septentrio)
Some GNSS receivers also incorporate advanced positioning algorithms to compensate for receiver-side issues such as multipath (for example, see Septentrio APME+), jamming and spoofing. This adds reliability and robustness to high-accuracy positioning.
Getting GNSS corrections
Modern industrial receivers often get their GNSS corrections via a subscription service, delivered via internet (using NTRIP protocol), satellite or 4G/5G. Today, there is a boom in the correction-service market driven by high-accuracy demands of the automotive industry, automation and smart consumer devices. Automotive suppliers and many other new players are deploying infrastructure to set up services for centimeter-level positioning around the globe.
User receivers often get their GNSS corrections via a subscription service delivered via internet, satellite or 4G/5G. (Image: Septentrio)
PPP and PPP-RTK corrections can even be transmitted directly by the GNSS satellites, as in the Japanese CLAS service from the QZSS constellation, or in the planned High-Accuracy Service (HAS) from Galileo. Depending on the network density and quality of the error modeling, different initialization times and accuracies can be achieved. This means that positioning quality can vary from one service provider to another.
Major telecom companies such as Deutsche Telekom as well as the Japanese Softbank and NTT are equipping their infrastructure with GNSS receivers to enable new corrections services. 3GPP, which provides specifications for mobile telephony including LTE, 4G and 5G, now covers broadcasting of GNSS satellite corrections in its mobile protocol. Since reference receivers are becoming part of critical infrastructure, such as telecom towers, it is essential that they have a high level of security to protect them from potential jamming or spoofing attacks (for example, Septentrio AIM+ technology).
Which corrections are right for me?
The right correction service for your technology will depend on your location and service area, your accuracy and reliability needs, as well as your budget. Because the corrections market keeps expanding, it is now more important than ever that integrators or GNSS manufacturers assist you in selecting the best correction method for your industrial application.
If you choose a GNSS receiver which does not “lock” you to a certain correction service, you will be free to choose a correction method which is most suitable for your application and its location. Such “non-locking” open-interface receivers also offer customers flexibility to switch to another more beneficial service in the future, as correction methods keep evolving.
Klau Geomatics has released processing that brings precise point positioning (PPP) and post processed kinematic (PPK) together in an optimized solution.
The autonomous solution can work anywhere without any other user inputs, such as base station data and radio/GSM links, the company added.
According to Klau Geomatics, the solution works on its own to achieve high accuracy, regardless of the location of the user. Accurate datum and tectonic plate motion corrections, specific to different countries and regions, are automatically applied to deliver the most accurate solutions.
In addition, Klau Geomatics’ NRT technology gives users — specifically those in the drone inspection industry — the ability to attain absolute accuracy to analyze change over time on 3D assets, the company said. The precise corrections are applied to data from custom-tuned KlauPPK GNSS receivers in the KlauPPK post processing software to enable centimeter-level accuracy anywhere in the world without the need for RTK, CORS or local base station data.
Finally, Klau Geomatics’ hybrid terrestrial multi station and PPP algorithm are offering even more refined accuracy in areas such as the U.S., Europe, Japan, New Zealand and Australia. Data from as many as 15 reliable long-range CORS stations, where available, are applied to the processing. The enhanced PPP solution achieves 1-3cm XYZ absolute accuracy in many parts of the world.
The same KlauPPK software workflow applies, to synchronise camera events, apply lever arm corrections, manage coordinate systems and geoids, apply site localizations, capture ground points and more. Instead of choosing a base station, which should be within 20 miles of the site, or setting up an RTK radio link, users with an active KlauPPK subscription can process a high accuracy trajectory, anywhere, without any other inputs, Klau Geomatics said.
By Kazuma Gunning, Juan Blanch and Todd Walter, Stanford University, and Lance de Groot and Laura Norman, Hexagon Positioning Intelligence
UAV and autonomous platforms can greatly benefit from an assured position solution with high integrity error bounds. The expected high degree of connectivity in these vehicles will allow users to receive real-time precise clock and ephemeris corrections, which enable the use of precise point positioning (PPP) techniques.
Until now, these techniques have mostly been used to provide high accuracy, rather than focusing on high-integrity applications. The authors apply the methodology and algorithms used in aviation to determine position error bounds with high integrity (or protection levels) for a PPP position solution.
PPP techniques can provide centimeter accuracy without local reference stations in kinematic applications. These techniques have so far mostly been used to provide high accuracy, and it is only recently that they have been proposed to provide integrity, that is, position error bounds with a very low probability of exceeding them.
There has been preliminary work on the application of integrity to PPP, but it remains a challenge to translate the benefits of PPP to accuracy while maintaining high integrity. Most of the integrity work in PPP and real-time kinematic (RTK) has dealt more with the ambiguity resolution process under nominal error conditions and less on the integrity of the position solution under fault conditions.
The authors overview their PPP filter implementation, and describe the threat model as well as two classes of integrity algorithms: solution separation and sum of squared residuals based (also called residual-based [RB], a misnomer, as all autonomous integrity monitors are based on the residuals.)
They present data sets used to evaluate the algorithms, compare the protection levels (PLs) obtained with different algorithms, and present the results obtained with the most promising PL formulation in four different data sets: static, dynamic in open-sky conditions, dynamic in midtown suburban conditions, and in flight.
Concluding, they state: “We have formulated RAIM protection-level formulas using either solution separation or the sum of residual squares. Both formulations consist of straightforward adaptations of snapshot RAIM to a Kalman filter solution.
“For solution separation, we have shown an implementation where the computational cost of running a bank of filters is far from being proportional to the cost of one filter. Instead, we could run 50 additional filters for the cost of one.
“For residual based RAIM we have developed a set of formulas to update the sum of square residuals from one time step to the next one. Because this test statistic is exactly the same as the one used in snapshot RAIM (when we consider the problem as a batch least squares), we could use the formula that ties the slope of a fault mode to the standard deviation of the solution separation. The slope can therefore also be updated recursively.”
Finally, “we have refined the PPP filter, added one scenario (suburban driving conditions), and examined the effect of considering multiple faults in the formulation of the test statistics and the protection levels. The results are very promising: protection levels below 2 m appear to be achievable, and the computation load is lower than expected.”
Spaceopal has launched NAVCAST, a GNSS precise point positioning (PPP) service featuring high-accuracy positioning enhancement for end users worldwide. NAVCAST aims to actively support and to accelerate widespread adoption of Galileo.
NAVCAST provides Galileo and GPS real time orbit and clock corrections based on an algorithm RETICLE (REal-TIme CLock Estimation), developed by the German Aerospace Centre (DLR e.V.).
Galileo and GPS observations, from more than 100 receivers of the worldwide IGS network, are used to estimate the current corrections which are broadcast to registered users relaying on the standard NTRIP protocol.
NAVCAST corrections improve the user error down to the centimeter level, making it attractive for a large number of applications, the company said.
Users can appraise the accuracy levels and convergence times achievable using NAVCAST (Galileo + GPS) corrections combined with a precise point positioning (PPP) engine, on the Spaceopal website. The underlying PPP engine (dual-frequency, ionosphere-free observations) estimates the local troposphere delays and fixes the carrier-phase integer ambiguities.
NAVCAST can be considered as proof of concept and Spaceopal’s contribution to high-accuracy GNSS services. NAVCAST corrections, which are broadcast over the Internet, could be in future via satellite constellation (such as MEO satellites).
From November 2010 until end of June 2017, Spaceopal was the prime contractor responsible for Galileo operations under the Galileo Full Operational Capability (FOC) Operations Framework contract, the company said. Spaceopal GmbH will continue to operate the Galileo satellite fleet under the Galileo Service Operator (GSOp) contract. Spaceopal is actively supporting the completion of the system to expand the services up to full operational capability by 2020.
SBG Systems is launching the Navsight Land & Air Solution, high-performance inertial navigation designed to make surveyors’ mobile data collection easier, whether for mobile mapping, GIS or road inspection.
SBG Systems will release the Navsight Land & Air Solution at the Intergeo show in Frankfurt, Germany, Oct. 16-18.
The solution consists of an inertial measurement unit (IMU), available at two different performance levels, connected to Navsight, a rugged processing unit embedding fusion intelligence and a GNSS receiver. It also has connections for external equipment such as lidar, cameras or computer.
Photo: SBG Systems
The Navsight Land & Air Solution is the result of more than 10 years of experience in the mobile positioning industry, especially in the unmanned industry where position reliability is mandatory. SBG’s fusion algorithms allow the company to get the best performance from inertial, odometer and GNSS technologies; exclude false GNSS fixes; and improve the trajectory in complicated areas such as urban canyons, forests and tunnels.
According to the company, the Navsight Land & Air Solution supports all GNSS constellations, real-time kinematic (RTK) and precise point positioning services such as Omnistar and TerraStar.
SBG IMUs are easy to install, the company said. The sensor alignment and lever arms are automatically estimated and validated. Once connected to the Navsight processing unit, the web interface guides the user to configure the solution. A 3D view of the vehicle shows the entered parameters so that the user can check the installation. By choosing the vehicle, such as a plane or a car, the inner algorithms are automatically adjusted to the application. The Navsight unit also integrates LED indicators for satellite availability, RTK corrections and power.
INS/GNSS Post-Processing Software. Qinertia, the SBG post-processing software, provides access to offline RTK corrections from more than 7,000 base stations in 164 countries. Trajectory and orientation are greatly improved by processing inertial data and raw GNSS observables in forward and backward directions.
Multi-GNSS will open up PPP to a much wider range of applications.
By Francesco Basile, Terry Moore, Chris Hill, Gary McGraw and Andrew Johnson
INNOVATION INSIGHTS by Richard Langley
ARE WE THERE? In a multi-GNSS world, that is. We’ve asked that question from time to time in this column over the years. So, are we there yet? That depends. One definition of “multi” is more than one. In this sense, we were in a multi-GNSS world as long ago as 1996. In that year, we had two fully populated constellations of satellites: GPS and GLONASS. Unfortunately, the full GLONASS constellation was short-lived. Russia’s economic difficulties following the dissolution of the Soviet Union hurt GLONASS, and by 2002 the constellation had dropped to as few as seven satellites. But GLONASS was reborn, and by Dec. 8, 2011, a full 24-satellite constellation was again operational.
But another meaning of “multi” is many, implying more than two. In the late 1990s, the first satellites to host transponders for satellite-based augmentation systems were launched. So, by the mid-2000s, even though GLONASS was still undergoing its rejuvenation, we were already in a three-constellation world. And receivers then on the market provided the necessary raw measurement data to yield positioning solutions from this system of systems with potentially more continuity and greater accuracy than those obtained using GPS alone.
And so in July 2008, we featured the article “The Future is Now: GPS + GLONASS + SBAS = GNSS.” And then in June 2010, we had “GPS, GLONASS, and More: Multiple Constellation Processing in the International GNSS Service.” In the introduction to that article, we asked that same question: Are we there yet? We concluded that, for early adopters of GPS plus GLONASS data and products, we were. With Galileo test satellites in orbit and an early version of the BeiDou system operational, it was already clear that by the end of the current decade, it wouldn’t just be the early adopters who would be benefiting from multi-GNSS but virtually all users of satellite-based positioning and navigation.
Although we aren’t quite there with fully operational Galileo and BeiDou constellations, we are getting pretty close. And so researchers are looking hard at how to make the best use of multiple-constellation observations in a variety of positioning and navigation scenarios. In this month’s column, a team of such researchers examines the potential benefit of combining GPS and Galileo observations for improving precise point positioning in urban environments, following the advice we read in the Book of Ecclesiastes: “Two are better than one.”
Over the years, precise point positioning (PPP) has been applied to many real-time applications that require sub-decimeter-level accuracy over a wide area or on a global scale. It is currently a standard in scenarios characterized by open-sky conditions, where a receiver is likely to have continuous track of GNSS satellites. On the other hand, PPP’s typically long convergence time means the technique has not been widely used in constrained and transient signal environments associated with urban areas. Analysis with both simulated and real data has shown that, once Galileo reaches final operational status, the PPP convergence time will be cut by more than half when using both GPS and Galileo observations. Accordingly, multi-GNSS will open up PPP to a much wider range of applications.
To begin, we assessed the positioning performance of GPS and Galileo signals, alone or used together, in open-sky conditions. A Simulink-based software simulator was used to simulate 24-hour-long observation sessions from 10 static (fixed location) receivers spread worldwide, which were then processed with the POINT software (developed by the University of Nottingham and three other British universities) in static (receiver assumed fixed) PPP mode with an elevation cutoff angle of 10° and with carrier-phase ambiguities estimated as real or floating-point values. For each station, the simulator was run 55 times to provide a sufficient number of data points to characterize the general behavior of the processing algorithms; therefore, a total of 550 points were considered.
For better GPS-Galileo interoperability, PPP results based on the ionosphere-free (IF) combination between GPS L1 and L5 and Galileo E1 and E5a observables were considered.
The metrics used to define the positioning performance are the errors in the north, east and down components of the position once all of a daily file has been processed and the time these errors take to converge below 10 centimeters.
The open-sky condition always guarantees excellent geometry and signal continuity even considering only one constellation.
PPP Results. TABLE 1 shows the root mean square (RMS) of the errors and convergence times of the three components of position for the different configurations for the 550 points considered. Both single- and dual-constellation systems are able to provide a sub-decimeter-level accuracy after a few tens of minutes. On average, positioning with Galileo E1-E5a IF performs better that GPS L1-L5 IF: the Galileo solution is more accurate and converges faster than the GPS solution.
TABLE 1. Comparison between GPS-only, Galileo-only and GPS plus Galileo PPP results. RMS of the positioning errors and convergence times for the stations considered.
The reason for this behavior is the assumed lower noise on Galileo pseudoranges. It is well known that the quality of the pseudoranges affects the convergence time of the PPP solution.
For this reason, one would expect some improvements by employing the Galileo Alternative BOC (AltBOC) modulated E5 signal. Thanks to its very large signal bandwidth of at least 51 MHz, Galileo E5 is characterized by excellent rejection properties of both long-range and short-range multipath. However, as shown in Table 1, when comparing the PPP solutions obtained using the Galileo E1-E5 IF and E1-E5a IF combinations, they have nearly the same performance. The reason for this apparent contradiction can be found in the use of the IF combination with E1. Given that E1 represents the dominant source of error in the IF combinations, its noise is amplified by a factor of 2.34 in the IF combination with E5 and by a factor of 2.26 when combined with E5a. Also, the smaller errors (with respect to E1) in E5a are amplified by 1.26, while the one in E5 is amplified by 1.34. Therefore, depending on the noise level in the Galileo pseudoranges, there might be instances where the noise in the E1-E5 IF combination is close to the one in the E1-E5a IF combination.
The number and the geometry of the observed satellites also affect the convergence time. For this reason, when using the two systems together, the time the vertical errors take to go below 10 centimeters was reduced by 50 percent with respect to the GPS-only case and by 18 percent with respect to the Galileo-only case.
URBAN ENVIRONMENTS
The poor signal visibility and continuity associated with urban environments, together with the slow (re)convergence time of PPP, usually make the technique unsuitable for land navigation in cities. However, as demonstrated in the previous section, using a dual-constellation not only improves the visibility conditions, but also reduces the PPP convergence time. Therefore, it might be possible to extend the applicability of PPP to land navigation in certain urban areas.
To assess the positioning performance of two-constellation GNSS in these constrained environments, we analyzed the signal availability and geometry of five different simulated sites in the neighborhood of the University College London (UCL) campus. We adopted building boundaries, which determine the minimum elevation angles above which GNSS signals can be received due to building obstruction. FIGURES 1 and 2 illustrate the location and the building boundaries for each site. FIGURE 3 shows the junction (site B) between Gower Street (site A) and University Street (site C).
FIGURE 1. Locations of the urban sites that are considered in the analysis.FIGURE 2. Building obstruction masks controlling satellite visibility for each site.FIGURE 3. Google Map image showing the junction (site B) between Gower Street (site A) and University Street (site C) in the midst of the University College London main campus.
When processing data from multi-constellation GNSS, the differences between the system time of the different constellations need to be considered. For this reason, when GPS and Galileo are used simultaneously for precise positioning, the Kalman filter state vector (in general) includes the three position components, the receiver clock offset, and the GPS-Galileo Time Offset (GGTO) — whether or not a predicted value might be available in a navigation message from one of the constellations. On the other hand, in PPP processing, the multi-constellation precise products used are based on the same system time, and therefore, in theory, it is not necessary to estimate the GGTO. However, existing intersystem biases may affect the PPP performance, and so it is advisable to estimate them in the Kalman filter.
Traditionally in PPP, the state vector also includes the residual zenith wet tropospheric delay and the carrier-phase ambiguities. Therefore, the minimum number of satellites required for GPS plus Galileo PPP is six. The geometry conditions are also an important factor for assessing the GNSS positioning performance. For land navigation, the horizontal dilution of precision (HDOP), which provides information about the achievable horizontal precision (and, assuming a bias-free solution, accuracy), is particularly relevant. For many land applications, such as precision agriculture and urban positioning, horizontal accuracy is more critical than vertical accuracy. Assuming that the ranging error in the carrier phase is 20 centimeters, to have decimeter-level horizontal accuracy HDOP needs to be no larger than 5. In most cases, HDOP values as small as 2 are desired.
TABLE 2 gives an overview of the visibility and geometry conditions at the selected sites. A dual-constellation (GPS and Galileo) receiver placed at one of the two road junctions will always, or almost always, see at least six satellites with an HDOP better than 5. At sites A and C, these minimum requirements for signal availability and geometry are met for more than 75 percent of the day. Obstructions due to high buildings, such as at site E, allows us to have at least six satellites for only 13 percent of the time.
TABLE 2. Percentage of epochs in 24 hours for which dual-constellation GNSS meets the minimum visibility (number of satellites, N) and geometry requirements (horizontal dilution of precision, HDOP).
From our preliminary study, it seems clear that high-accuracy positioning in urban environments is possible, but only in some areas where buildings are relatively short, providing good signal availability and geometry. Things can slightly improve by considering additional systems, such as GLONASS and BeiDou, and by exploiting the non-line-of-sight (reflected) signals. However, it is well known that an additional obstacle for PPP in urban environments is signal discontinuity. Indeed, when a GNSS receiver loses lock on the carrier, the positioning filter needs to be reinitialized, meaning that further tens of minutes are required before reconvergence.
To test the reconvergence time of PPP in transient signal environments, a pedestrian carrying a multi-GNSS receiver was simulated to be walking along the path in FIGURE 4. The receiver was simulated to be located for the first half hour of the simulation in the front yard of UCL’s Wilkins Building (where the simulation begins and ends), before starting to move. This is to allow the initial convergence of the PPP filter.
FIGURE 4. The measured trajectory of the simulated pedestrian kinematic test.
FIGURE 5 shows the visibility for a given GNSS satellite. Only the epochs when the receiver is moving are considered. Therefore, the first 30 minutes, when the receiver is static, are not included in the plot. Data gaps due to building obstructions are visible, with the largest being about 12 minutes and the average less than 2 minutes. As a consequence, the carrier-phase ambiguities need to be estimated all over again; and, as previously mentioned, this process usually requires tens of minutes before reconvergence.
FIGURE 5. Satellite availability during the kinematic test.
FIGURE 6 shows the HDOP and the number of visible satellites for the kinematic test, while FIGURE 7 shows the RMS, over 50 simulations, of the horizontal components of the positioning error when GPS L1 and L2 and Galileo E1 and E5, linearly combined into the IF combination, are processed in kinematic PPP mode with the POINT software. At the beginning of the kinematic test, when the HDOP is well below 5, the horizontal error is at the centimeter level, while, after 33 minutes from the beginning of the simulation, building obstructions don’t permit a converged solution below the 20-centimeter accuracy level.
FIGURE 6. Horizontal dilution of precision and number of visible satellites for the kinematic test.FIGURE 7. RMS of the position errors for the kinematic test.
This short example clearly demonstrates that two-constellation PPP has, in theory, the potential to precisely navigate ground vehicles in some urban environments; however, it is too sensitive to signal discontinuity. Slow solution reconvergence to the few decimeter/centimeter level still represents the main limitation to the use of PPP for high-accuracy applications in cities. Nonetheless, GPS plus Galileo PPP easily enables sub-meter-level horizontal accuracy for most of the simulations we have carried out. After signal loss, it only took a few tens of seconds to have a horizontal accuracy of better than a meter.
SMOOTHED CORRECTIONS
As an alternative to ambiguity-fixing methods aimed to improve the (re)convergence time, we propose a method that mitigates the effect of the ionosphere and which thereby reduces the reconvergence time of the PPP solution after initial convergence has been achieved. In this new approach, while the two-frequency carrier phases are linearly combined in the traditional IF combination, the uncombined pseudoranges are corrected by a pre-smoothed ionospheric delay (via a Hatch filter), computed using the geometry-free combination of two-frequency pseudoranges.
Once the Hatch filter has converged, ideally we have IF pseudoranges with lower noise than the traditional ones. Therefore, in case the PPP filter needs to restart, we can obtain a quicker reconvergence thanks to the lower noise on the ionosphere-corrected pseudoranges. Indeed, provided that the signal gap is not very large, the ionosphere smoothing filter doesn’t need to be restarted from the raw values.
It is possible to predict the ionospheric delay computed from two-frequency carrier-phase measurements using a linear fitting model from previous measurements within a sliding time window. As an example, high-rate data recorded on July 25, 2017, from station DAEJ in Daejeon, Republic of Korea, were used to analyze the ionosphere prediction error.
In FIGURES 8 and 9, the RMS of the prediction errors for different time windows have been plotted against the data gap length. The prediction error depends on both the time latency of the observation and the elevation angle of the satellite. It increases with the data gap length, but larger time windows can damp the divergence of the error. A time window of 120 seconds was used both for satellites above and below 30° elevation angle. In this case, the error for a 5-minute prediction is about 4 centimeters for a satellite above 30° and 7 centimeters for satellites with a low elevation angle. These values are much smaller than the noise in the pseudorange measurements and can, therefore, be neglected.
FIGURE 8. RMS of the prediction errors vs. data gap length for satellite elevation angles greater than 30°.FIGURE 9. RMS of the prediction errors vs. data gap length for satellite elevation angles less than than 30°.
Multi-Frequency Combinations. The method introduced in the previous section allows users to be free from the constraint of IF observables and, therefore, to look for multi-frequency combinations aimed to minimize the noise on the pseudoranges. The next-generation GNSS satellites will broadcast open signals over three frequencies. The triple-frequency, geometry-preserving combination aimed to reduce the noise, instead of mitigating the ionosphere, can be used for positioning purposes.
TABLE 3 summarizes the assumed values for the ratios ni between the noise on different GPS and Galileo pseudoranges and the ones on L1/ E1. FIGURE 10 shows a color map of the noise amplification factor associated with different linear combinations between GPS L1, L2 and L5. The x-axis is α3, the coefficient multiplying the pseudorange on L5 in the combination, while the y-axis is the ionosphere amplification factor of the triple-frequency combination with respect to L1, q. The noise for this combination can be as little as 0.57 times the noise on L1, while the corresponding ionosphere amplification factor is 1.49. Once the smoothed ionosphere correction has converged, we can potentially have an IF pseudorange 81 percent less noisy than the L1-L2 IF, and, therefore, a much faster reconvergence.
TABLE 3. Assumed noise, ni, on GPS and Galileo pseudoranges, i, and their ionospheric delay, q, with respect to L1/ E1.FIGURE 10. Geometry-preserving surface in the space q-α3-n (ionosphere amplification factor – L5 pseudorange multiplier – noise amplification factor) for GPS L1-L2-L5 combinations.
Similar conclusions can be drawn by considering Galileo signals. Using triple-frequency combinations with E1, E5a and E5b, we can obtain 81 percent less noise than E1-E5a IF, while a reduction of the noise in the IF pseudorange up to 90 percent was observed using E5 alone. Triple-frequency combinations involving E5 don’t bring such large improvements with respect to using E5 alone. Indeed, a maximum of 16 percent less noise can be registered when combining E1, E5a and E5 with respect to the E5 uncombined case. TABLE 4 illustrates the minimum noise amplification factor for each triple-frequency combination and its ionosphere amplification factor.
TABLE 4. Minimum noise achievable through GPS and Galileo triple-frequency pseudorange combinations and their ionospheric delay with respect to L1/ E1.
The noise associated with the ionosphere-corrected multi-frequency pseudorange combination is as large as meter level before converging to centimeter level. For this reason, a proper weighting method, which considers the varying noise on the ionosphere correction, needs to be employed.
To test the benefit of the new approach for the reconvergence time, three hours of simulated GPS and Galileo data from a static site in La Misere, Seychelles, were processed with the POINT software in kinematic mode. After 90 minutes, the PPP filter was forced to restart to simulate reconvergence. The multipath time constant was set to 5 seconds, which is a typical value for kinematic multipath. The performance of the traditional L1- L2 IF combination was compared with the triple-frequency pseudorange combination, corrected by the smoothed ionosphere delay coming from the Hatch filter.
FIGURE 11 shows the precision (RMS error over 50 simulations) of the horizontal components after filter restart. The new approach has much faster reconvergence than the traditional PPP method based on the IF combination. Indeed, while the traditional method takes about 11 minutes to have a horizontal error below 10 centimeters, using the low-noise combination, this accuracy is achieved after 171 seconds. Even better performance can be achieved considering the Galileo E5 signal (see FIGURE 12).
FIGURE 11. RMS error of the horizontal position components of static site using GPS data after filter restart.FIGURE 12. RMS error of the horizontal position components of static site using Galileo data after filter restart.
The E1-E5 IF combination requires 10 minutes for the horizontal convergence, while using E5 with the Hatch filter we have the horizontal solution converged in about 30 seconds. It is worth noticing that in the presence of static multipath, the proposed weighting method may lead to an overly optimistic weighting of the pseudorange measurements in the PPP filter and to a slower reconvergence of the positioning solution. Indeed, the long correlation time in the static multipath, of the order of a few minutes, makes it hard to filter out by the Hatch filter, hence the corrected measurements have larger errors than expected.
The effect of static multipath in the new configuration is visible in FIGURE 13, where the reconvergence of the horizontal component for the L1-L2 IF combination is compared with the new approach. In this case, the time constant of the simulated multipath was set to 1 minute. In this scenario, the triple-frequency low-noise combination corrected by the smoothed ionosphere combination quickly converges below 20 centimeters; however, it takes significantly longer than the L1-L2 IF combination to reach the 10-centimeter accuracy level.
FIGURE 13. RMS error of horizontal position component of static site using GPS data after filter restart with 1-minute multipath time constant.
Also, the new method was tested with the kinematic simulation as in the previous section. Here, the GPS triple-frequency combined pseudorange and Galileo E5 pseudorange (both corrected with the smoothed ionosphere) are processed in kinematic PPP mode with the POINT software. FIGURE 14 compares the RMS of the horizontal errors with the IF configuration. Less than a minute after the receiver lost lock on the satellites, the solution reconverged below the 20-centimeter level, while it took less than 30 seconds to go below 50 centimeters.
FIGURE 14. RMS error of the horizontal position components of kinematic trajectory using GPS and Galileo data and the smoothed ionosphere approach after filter restart.
CONCLUSIONS
In this article, we described a comparison that we carried out between GPS-only, Galileo-only and GPS plus Galileo PPP. Results based on simulated open-sky conditions demonstrated that Galileo performs better than GPS thanks to an assumed lower E1-E5a IF noise with respect to L1-L5. Two-constellation PPP enables faster (re)convergence compared to the single constellation case.
An analysis of GNSS signal availability, continuity and satellite geometry was also performed to study the feasibility of PPP in urban environments. Preliminary results, based on simulations, showed that dual-constellation (GPS plus Galileo) PPP is possible in urban areas with relatively short buildings in which a satellite minimum availability requirement is met most of the time. However, signal discontinuity still represents the major problem for traditional PPP in urban environments, due to long reconvergence times.
Finally, we proposed a new PPP configuration based on triple-frequency combinations, intended to minimize the noise on the pseudorange and corrected by a smoothed ionospheric delay. This configuration seems to provide faster reconvergence than the traditional PPP with the IF combination if applied to kinematic scenarios. In static applications, the very slow varying multipath error makes the proposed weighting method, based on the error in the smoothed ionosphere correction, overly optimistic. In such cases, the IF combination reconverges more quickly to high-accuracy levels better than 20 centimeters.
ACKNOWLEDGMENTS
The research described in this article was sponsored through a studentship agreement between the University of Nottingham and Rockwell Collins UK Limited. The article is based on the paper “Multi-Frequency Precise Point Positioning Using GPS and Galileo Data with Smoothed Ionospheric Corrections” presented at the 2018 IEEE/ION Position, Location and Navigation Symposium, held in Monterey, California, April 23–26, 2018. All figures attributed to the authors unless otherwise specified.
FRANCESCO BASILE is a postgraduate research student at the Nottingham Geospatial Institute of the University of Nottingham in the United Kingdom. He received his M.Sc. in space and astronautic engineering from the University of Rome – La Sapienza and his B.Sc. in aerospace engineering from the University of Naples – Federico II, both in Italy.
TERRY MOORE is the director of the Nottingham Geospatial Institute where he is the Professor of Satellite Navigation. He is a fellow and the president of the Royal Institute of Navigation (RIN) and also a fellow and a member of council of the Institute of Navigation (ION).
CHRIS HILL is an associate professor in the Faculty of Engineering at the University of Nottingham and a member of the Nottingham Geospatial Institute research group. He holds a Ph.D. in satellite laser ranging and he is a fellow of the RIN.
GARY MCGRAW is a technical fellow with the Rockwell Collins Advanced Technology Center in Cedar Rapids, Iowa. McGraw is a fellow of the ION and is a senior member of the IEEE.
ANDREW JOHNSON is a chief engineer at Rockwell Collions UK in Winnersh, Berkshire, United Kingdom. Johnson has a B.Sc. in electronic and electrical engineering from the University of Surrey in Guildford, United Kingdom.
FURTHER READING
Authors’ Conference Paper
“Multi-Frequency Precise Point Positioning Using GPS and Galileo Data with Smoothed Ionospheric Corrections” by F. Basile, T. Moore, C. Hill, G. McGraw and A. Johnson in Proceedings of PLANS 2018, the Institute of Electrical and Electronics Engineers / Institute of Navigation Position, Location and Navigation Symposium, Monterey, California, April 23–26, 2018, pp. 1388–1398, doi: 10.1109/PLANS.2018.8373531.
“Multi-Constellation GNSS Performance Evaluation for Urban Canyons Using Large Virtual Reality City Models” by L. Wang, P.D. Groves and M.K. Ziebart in Journal of Navigation, Vol. 65, No. 3, July 2012, pp. 459–476, doi: 10.1017/S0373463312000082.
“Potential Benefits of GPS/GLONASS/GALILEO Integration in an Urban Canyon – Hong Kong” by S. Ji, W. Chen, X. Ding, Y. Chen, C. Zhao and C. Hu in Journal of Navigation, Vol. 63, No. 4, October 2010, pp. 681–693, doi: 10.1017/S0373463310000081.
Multi-Constellation Use in Aviation Applications
“Assessment of Alternative Positioning Solution Architectures for Dual Frequency Multi-Constellation GNSS/SBAS” by G. McGraw, B.A. Schnaufer, P.Y. Hwang and M.J. Armatys in Proceedings of ION GNSS+ 2013, the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation, Nashville, Tennessee, Sept. 16–20, 2013, pp. 223–232.
“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, 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, Vol. 56, No. 2, Summer 2009, pp. 135–149, doi: 10.1002/j.2161-4296.2009.tb01750.x.
Hatch Filter
“Combinations of Observations” by A. Hauschild, Chapter 20 in Springer Handbook of Global Navigation Satellite Systems, edited by P.J.G. Teunissen and O. Montenbruck, published by Springer International Publishing AG, Cham, Switzerland, 2017.
“The Synergism of GPS Code and Carrier Measurements” by R. Hatch in Proceedings of the Third International Geodetic Symposium on Satellite Doppler Positioning, Las Cruces, New Mexico, Feb. 8–12, 1982, Vol. II, pp. 1213–1232.
Dilution of Precision
“Dilution of Precision” by R.B. Langley in GPS World, Vol. 10, No. 5, May 1999, pp. 52–59.
Kalman Filtering
“Least-Squares Estimation and Kalman Filtering” by S. Verhagen and P.J.G. Teunissen, Chapter 22 in Springer Handbook of Global Navigation Satellite Systems, edited by P.J.G. Teunissen and O. Montenbruck, published by Springer International Publishing AG, Cham, Switzerland, 2017.
Galileo and BeiDou observation data are now included with Trimble VRS Now subscriptions in North America.
Photo: Trimble
The addition of the Galileo and BeiDou constellations allow users to make use of more satellites, enabling more robust performance when working in harsh GNSS environments such as in urban canyons and under canopy, the company said.
Trimble VRS Now in North America fully supports GPS, GLONASS, QZSS and now, Galileo and BeiDou satellite systems.
The service is powered by the Trimble Pivot Platform GNSS real-time network software, Trimble said. As a true five-constellation solution, it delivers improved real-time positioning performance for customers in North America.
VRS Now is designed for surveying, mapping and GIS, construction and agriculture professionals who require high-accuracy positioning in their workflows.
Adding Galileo and BeiDou observation data provides significant benefits by enabling users to:
Operate in environments where traditional GPS + GLONASS systems’ performances are limited
Improve accuracy and reliability of GNSS solutions
Minimize the effects of multipath and interference
“By including Galileo and BeiDou data, customers can achieve greater accuracy and positioning performance than ever before,” said Patricia Boothe, vice president of Trimble’s Advanced Positioning Division.
With the addition of North America, Trimble VRS Now networks worldwide now support all five GNSS constellations. Besides North America, coverage is available throughout Europe, Australia and New Zealand when using a compatible GNSS receiver or display.
Subscriptions are available through Trimble’s Authorized Business Partners or Trimble’s online store at tpsstore.trimble.com.
VRS Now provides positioning professionals with instant access to real-time kinematic (RTK) and post-processing (PP) corrections using a network of permanent (fixed) continuously operating reference stations (CORS). Professional management and monitoring 24/7 by a global operations team provides peak performance and high reliability, Trimble said.
