New features are now available for TerraGo Magic, including laser-rangefinder integration, offset data capture, Apple and Google turn-by-turn navigation, and proximity alerts. Also new is extended waypoint guidance for finding off-road assets and infrastructure.
TerraGo Magic is a zero-code platform-as-a-service that enables customers to build their own custom mobile apps without writing any code by choosing from a menu of available, field-tested features.
TerraGo Magic is also the underlying platform used to build TerraGo Edge, which includes these latest features in version 4.1, available for download from the iTunes App Store and Google Play.
“With the addition of laser positioning and offsets for remote data collection, TerraGo helps us rapidly capture high-accuracy data for more assets and infrastructure, even those in difficult to reach locations,” said Fernando Mutia, IS supervisor for San Jose Water Company.
Partnership with Laser Technology
TerraGo is now partnering with Laser Technology Inc. (LTI) to enable all custom apps built by TerraGo Magic to seamlessly utilize LTI’s professional-grade laser rangefinders.
TerraGo Magic partners and customers can now add TruPulse rangefinder support to their custom iOS and Android apps with the click of a button using the TerraGo Magic zero-code app platform.
Also, Seiler Instrument – Geospatial, a partner of both LTI and TerraGo, will now add TruPulse support to its new Field2GIS app, which was built using TerraGo Magic and is now available from iTunes and Google Play.
“We’re very happy to launch this partnership that we feel responds directly to our customers’ goals and the industry’s demand for improving the quality and productivity of their field data collection work,” said Derrick Reish, senior product manager at LTI. “By leveraging laser precision and cloud-based mobility, we can help our joint customers collect the accurate data they need at a level of efficiency that wasn’t possible just a few years ago.”
“With TerraGo Magic, we totally change the traditional way of thinking about how custom mobile app versions get built, released and upgraded,” said Dave Basil, vice president of product development at TerraGo. “When we publish a new feature in Magic, it’s immediately available to all customer apps but doesn’t force it on all customers or require an upgrade beyond their control.”
“With TerraGo Magic’s platform-as-a-service, customers can evaluate and include features based on their priorities, timeline, business requirements and users’ needs, giving them the flexibility and control of a custom solution without the cost of custom app development,” Basil said.
Webinars
TerraGo is hosting a webinar on Aug. 15 at 12 p.m. ET with a live demonstration of the latest features in TerraGo Magic Apps and TerraGo Edge.
To learn more about the technical details and operational benefits, join TerraGo and LTI in the webinarAdvanced Mobile Data Collection Finds the Range with Laser-Precision, on Aug. 22 at 12 p.m. ET.
In this article, author Urs Hugentobler looks at the history of laser ranging to navigation satellites, how that ranging has improved the accuracy of the orbits of those satellites and what the future portends for this important contribution to space geodesy.
INNOVATION INSIGHTS with Richard Langley
THE LASER. It might not be in the top 10 of the most important inventions of all time, but Time magazine rated it among the most important developments of the 20th century, listing it fifth after the automobile, the radio, the television and the transistor. Lasers are now ubiquitous: they scan our purchases at the supermarket checkout; they let us read and write data on compact discs; they have replaced the scalpel in many operating theaters; and they play major roles on the battlefield with laser-guided munitions. However, one of the first practical uses of the laser was in precisely determining the orbits of satellites.
Initial experiments in ranging to satellites carrying corner-cube retroreflectors began in 1964 just a few years after the laser was invented in 1960. Satellite laser ranging (SLR) stations were built in several countries, and a number of multi-instrument satellites with retroreflectors were launched by the U.S. and other nations along with dedicated spherical satellites with no electronic instrumentation — just the retroreflectors covering the satellite’s surface. The first of these was the Laser Geodynamics Satellite, or LAGEOS. It was designed by NASA and launched in 1976. LAGEOS and the other satellites carrying retroreflectors played a significant part in NASA’s Crustal Dynamics Project (CDP). Initiated in 1979, the CDP promoted the use of SLR and very long baseline interferometry to improve our understanding of plate tectonics, the rotational dynamics of the Earth, and the structure of the Earth’s gravity field.
As a post-doctoral fellow at the Massachusetts Institute of Technology and later at the University of New Brunswick, I participated in the CDP with analyses of lunar laser ranging (LLR) data. Ranging to reflectors placed on the moon’s surface by Apollo astronauts as well as those on the Russian Lunokhod rovers was a bit more difficult than ranging to satellites given the larger distances to the reflectors and the much weaker return pulses. Among other advances, LLR was the first technique to confirm the existence of variations in the spin of the Earth with a periodicity of around 50 days.
But let’s get back to SLR. Today, thanks in large measure to the International Laser Ranging Service, ranging data is routinely collected on more than 70 satellites and lunar reflectors. Included is a growing list of GNSS satellites equipped with corner-cube retroreflectors. Laser ranging to GNSS satellites is instrumental is better modeling the orbits of these satellites. Among other benefits, better GNSS satellite orbits result in better receiver position accuracies — accuracies needed to improve monitoring of crustal strain, for example, including that associated with earthquakes.
In this month’s column, we take a look at the past, present and future of laser ranging to GNSS satellites and how laser ranging and microwave ranging are mutually beneficial. They are truly kindred spirits.
Nighttime ranging at NASA’s Next Generation SLR system at Goddard Space Flight Center, Maryland. (Credit: Felipe Hall/HTSI)
Satellite laser ranging or SLR has been an indispensable independent tool for validating the precise orbits determined for GNSS satellites using microwave pseudorange and carrier-phase observations for several decades. SLR has allowed researchers to identify several orbit-modeling issues. Adding albedo radiation pressure and antenna thrust, among other effects, into the GPS orbit model allowed them to eliminate the observed bias between microwave- and SLR-derived orbits. For the first Galileo satellites launched, SLR residuals indicated severe orbit modeling issues caused by the different shape of Galileo satellite bodies compared to those of GPS. In the future, all GNSS satellites will be equipped with laser retroreflectors, a big challenge for researchers concerning tracking scenarios and observation planning to make economic use of the ground equipment.
In this article, we will take a brief look at the history of laser ranging to navigation satellites, how that ranging has improved the accuracy of the orbits of those satellites, and what the future portends for this important contribution to space geodesy.
VALIDATION OF GNSS ORBITS
FIGURE 1. Operating principle of satellite laser ranging.
In 1964, only four years after Theodore Maiman built the first laser, the first laser echoes were obtained from NASA’s Explorer 22 satellite. SLR rapidly developed into an indispensable tool for precise orbit determination, gravity field determination, and Earth system research.
FIGURE 1 shows the principles of SLR operation. Essentially, an SLR station fires a series of laser pulses at passing satellites equipped with corner-cube retroreflectors, and the relatively few photons returned are collected by a telescope. The station electronics measures the round-trip travel times of the laser pulses. From these measurements, the coordinates of the SLR station or the satellite’s orbit can be determined.
Observations by a global network of SLR stations are coordinated by the International Laser Ranging Service (ILRS), which, like the International GNSS Service, is one of the space geodetic services of the International Association of Geodesy (IAG).
FIGURE 2. Retroreflector array on GPS Block IIA satellites SVNs 35 and 36.
Since the early 1990s, the ILRS has tracked GNSS satellites supporting the independent validation of the microwave-derived precise orbits. Two Block IIA GPS satellites, SVN35 and SVN36, were equipped with retroreflectors (see FIGURE 2) and they were routinely tracked from their launches in 1993 and 1994, respectively, until their decommissioning in 2013 and 2014 (actually, SVN36 was subsequently briefly reactivated in 2015 so data is available for that satellite until that year). Also in the 1990s, the ILRS started to track GLONASS satellites in support of the International GLONASS Experiment (IGEX-98). There is a retroreflector array on all GLONASS satellites (see FIGURE 3).
Range residuals of GPS and GLONASS satellites were studied in the early years by a number of different research groups. Most of their analyses showed a bias of about –5.5 centimeters for GPS satellite orbits derived from microwave tracking data by the IGS while the accuracy of the latter was estimated to about 5 centimeters. For GLONASS orbits, a negative bias of about –4 centimeters was identified, too. The accuracy of the orbits was, however, at the 10–15 centimeter level. These validation results supported several model improvements for GPS satellite orbits including, in particular, the handling of solar and Earth albedo radiation pressure and antenna thrust, reducing the observed SLR bias with respect to the IGS orbits to 1.3 centimeters with a standard deviation of about 2 centimeters.
“What are radiation pressure and antenna thrust?” you might ask. The photons making up the light coming directly from the sun or reflected from the Earth’s surface (albedo) impinge on a satellite and transfer some of their energy to it. Solar radiation pressure – the force due to the impact of the photons – is tiny, but its continuing presence has a strong perturbing effect on satellite orbits. Antenna thrust is also a small force. The transmission of GPS navigation signals results in a continuously acting reactive force in the radial direction acting on the satellite.
FIGURE 4. Retroreflector array on Galileo satellites (at bottom of satellite, below antenna array).
SLR also plays an essential role for calibrating improved radiation pressure models for the new satellite systems. All Galileo satellites have retroreflectors (see FIGURE 4), and the orbits of the first satellites to be launched, generated using the classical extended radiation pressure model of the Center for Orbit Determination in Europe (operating in the framework of the IGS Multi-GNSS Pilot Project or MGEX), had SLR residuals as large as 20 centimeters for passes with a small beta angle. (The beta angle is the angle between the sun and a satellite’s orbital plane.) The origin of this behavior is the elongated shape of the Galileo satellites compared to the more-or-less cubic shape of GPS satellites, causing much larger variations of the satellite cross-section exposed to the sun while orbiting the Earth. The observed SLR residuals triggered the development of improved radiation pressure models for Galileo satellites.
All BeiDou satellites are also believed to be equipped with retroreflectors (see FIGURE 5). As the estimated longitude of geostationary GNSS satellites such as those in the BeiDou constellation is highly susceptible to biases due to the small motion of the satellites with respect to the tracking stations, SLR may play an important role for precise orbit determination of this category of satellite.
FIGURE 5. Retroreflector array on BeiDou satellites.
The satellites of the Indian Regional Navigation Satellite System (IRNSS), also known as the Navigation with Indian Constellation system or NavIC, also carry retroreflectors (see FIGURE 6) and have been tracked by SLR stations. However, little publicly available microwave tracking data yet exists. Therefore, up to now, precise orbit determination heavily relies on SLR observations.
FIGURE 6. Retroreflector array on NavIC satellites.
MORE APPLICATIONS OF SLR FOR GNSS
Because GNSS is a one-way measurement technique, only pseudoranges and carrier phases can be measured, and clock synchronization is indispensable for positioning and orbit determination. Radial orbit errors can therefore be absorbed to a large degree by satellite clock corrections. For the very stable clocks on board Galileo satellites, the SLR residuals show the same behavior as the microwave-derived clock corrections indicating that the clock corrections are, in fact, caused by radial orbit errors. SLR therefore provides a way to break this correlation and to separate radial orbit errors and satellite clock corrections. This makes it possible to study and to characterize the physical behavior of onboard clocks including temperature-induced clock variations.
Separation of orbit errors and satellite clock variations is crucial when using the first two Full Operational Capability Galileo satellites, which were released into wrong orbits, for relativistic experiments. In a dual launch on Aug. 22, 2014, the two satellites were put into orbits with an initial eccentricity of 0.233 and orbit height of 19,800 kilometers due to a malfunction of the launcher third stage. With a sequence of maneuvers, the satellite orbit heights could be increased to 22,600 kilometers (compared to the planned height of 23,200 kilometers) and the eccentricity was decreased to 0.156. The satellites are, nevertheless, fully functional, and the very stable hydrogen masers on board should allow scientists to improve the uncertainty of the relativistic redshift parameter α beyond the current value determined in 1976 using the Gravity Probe A satellite. Regular SLR tracking of the two satellites plays an essential role in this experiment to separate clock variations due to orbit errors from those caused by the gravitational redshift.
Eventually, SLR may also be used as a tool for high-precision time synchronization of stable GNSS clocks combining one-way laser transmissions with two-way active laser operation, similar to the concept of the European Laser Timing experiment foreseen using the Atomic Clock Ensemble in Space (ACES) on the International Space Station and already tested for BeiDou satellites.
SLR TRACKING OF THE GNSS CONSTELLATIONS
In the near future, more than 100 GNSS satellites carrying retroreflectors will be operational. This includes GPS Block III satellites, which will carry retroreflectors starting with SV-9. Tracking the full GNSS constellation will pose a big challenge for the ILRS concerning economic use of its ground equipment. Optimized tracking scenarios and session planning strategies will be indispensable.
Already today, the ILRS regularly tracks a large number of GNSS satellites. TABLE 1 shows the number of SLR normal points from ranging to the various GNSS constellations available at the ILRS data centers since 2010. Normal points are compressed full-rate data obtained by averaging individual range measurements typically over five-minute intervals. As part of the Laser Ranging to GNSS Spacecraft Experiment or LARGE project of the ILRS, the tracking of GLONASS satellites was extended to the entire satellite constellation as shown in FIGURE 7.
FIGURE 7. Number of SLR normal points per month for GLONASS satellites.
To assess the capability of SLR for GNSS precise orbit determination based on the number of tracking stations and the distribution of observations, we performed a simple simulation. The covariance analysis included observations of a single SLR station compared to networks of 6 and 17 globally distributed stations. For each station, three normal points were simulated per satellite pass for a full 24-satellite Galileo constellation: two observed at 30° rising and setting elevation angles and one at maximum elevation angle. No unfavorable weather conditions were considered and observations of different stations were assumed to be uncoordinated.
Formal errors of the determined orbits are shown in FIGURE 8 for the radial, along-track, and cross-track components. As expected, orbits determined with observations from one day’s observations by a single station reach formal errors in the few 10s of kilometers range (plot on the left in the first row). If observations from three days are used for orbit determination, the errors on the middle day reduce to about 100 meters (right, first row). The situation significantly improves if a global network of six stations is considered. Even for a single day of observations, an orbit precision of a few decimeters is reached (left, second row) while the orbit uncertainty further decreases to a few centimeters if observations from three days are used (right, second row). If, however, in an effort to reduce the number of observations per pass, only measurements at satellite culmination are acquired, the orbit precision is in the kilometer range for a six-station network and observations from one day (left, third row). If observations from three days are used, the orbit precision is at the meter level (right, third row). Using three normal points per pass for a 17-station network, the orbit precision reaches a few centimeters even within one day (left, last row) and about 1 centimeter for observations from three days (right, last row). It should be noted that the covariance analysis does not consider any systematic observation or orbit modeling error.
FIGURE 8. Formal errors of Galileo orbits in radial (red), along-track (green) and cross-track (blue) directions. First row: one SLR station, 1-day arc (left), middle of 3-day arc (right); second row: six stations, 1-day arc (left), 3-day arc (right); third row: six stations with tracking only at culmination, 1-day arc (left), 3-day arc (right); fourth row: 17 stations, 1-day arc (left), 3-day arc (right). Note the different scaling for the various plots.
This simulation is very simple and not very realistic, but nevertheless indicates the capability of precise orbit determination for GNSS satellites using a limited number of observations per station. The simulations demonstrate two facts. Firstly, even with just two or three normal points per satellite of a GNSS constellation, a significant fraction of the observation time of a station is required. Typically, a mid-latitude station can acquire about 60 normal points per day for a 24-satellite constellation, amounting to several hours of observation time per day. Secondly, the improvement in formal orbit accuracy only increases with the square root of the number of stations. More important than the number of normal points is their distribution along the orbit requiring SLR observations from several stations distributed over the globe.
These two findings make it obvious that coordination among SLR stations is indispensable for making economic use of the observing time of SLR stations while providing good coverage of normal points along all satellite orbits. To cope with weather conditions, this coordinated scheduling of GNSS SLR tracking may have to be optimized in real time.
CONCLUSIONS
SLR has played an important role in validating GNSS-derived satellite orbits for the past several decades. For new GNSS constellations and new orbit types, SLR proves to be essential for calibrating radiation pressure models and allows us to separate orbit- and temperature-induced variations of onboard clocks. Eventually, the role of SLR will become even more important by contributing to the precise orbit determination of GNSS satellites. Given the large number of GNSS satellites from several constellations equipped with retroreflectors, coordination of observation scheduling among SLR stations will be crucial for optimizing the benefit-to-cost ratio.
Concerning the distribution of SLR observations over the constellations, the following conclusions may be drawn:
For the validation and calibration of radiation pressure models, it is sufficient to acquire well-distributed observations along the orbit of one satellite for each constellation block type for a range of solar beta angles, that is, of one satellite block type per orbital plane.
For contributing to precise orbit products, optimally combined with microwave GNSS observations, the tracking of all satellites of a constellation is needed. This requires a coordinated scheduling of observations among SLR stations.
For determination of the gravitational redshift parameter using the two Galileo satellites in eccentric orbits, good coverage of the orbits of both satellites is required (as long as the satellites run on one of the onboard hydrogen maser clocks).
For BeiDou and NavIC geostationary satellites, SLR coverage is needed for all satellites to resolve biases in the microwave tracking technique.
In the long term, SLR observations could contribute, together with microwave observations, in providing operational high-precision orbit products for all GNSS constellations jointly by the ILRS and the IGS in the framework of the IAG’s Global Geodetic Observing System.
ACKNOWLEDGMENTS
This article is based on the invited paper “Ranging the GNSS Constellation” presented at the 20th International Workshop on Laser Ranging held in Potsdam, Germany, Oct. 10–14, 2016. Figure 1 was adapted from an image in “Expert Advice: Laser Reflectors to Ride on Board GPS III” published by GPS World. GPS, Galileo, BeiDou and NavIC retroreflector images obtained from the ILRS. The GLONASS retroreflector image was obtained from ISS Reshetnev. Opening photo: Nighttime ranging at NASA’s Next Generation SLR system at Goddard Space Flight Center, Maryland (Credit: Felipe Hall/HTSI).
URS HUGENTOBLER is a professor of satellite geodesy at the Technische Universität München, Germany, and head of the Satellite Geodesy Research Facility in the Institute for Astronomical and Physical Geodesy. He is also a former chair of the IGS Governing Body. His research activities include precise positioning using GNSS, precise orbit determination and modeling, reference-frame realization, clock modeling and time transfer, using both the legacy and new satellite systems. Hugentobler obtained his Ph.D. from the University of Bern, Switzerland, in 1997.
FURTHER READING
Author’s Conference Paper
“Ranging the GNSS Constellation” by U. Hugentobler, presented at the 20th International Workshop on Laser Ranging held in Potsdam, Germany, Oct. 10–14, 2016.
Early Work on Satellite Laser Ranging
“Satellite Laser Ranging: Current Status and Future Prospects” by J.J. Degnan in IEEE Transactions on Geoscience and Remote Sensing, Vol. GE-23, No. 4, July 1985, pp. 398–413, doi: 10.1109/TGRS.1985.289430.
“Reflection of Ruby Laser Radiation from Explorer XXII” by H.H. Plotkin, T.S. Johnson, P. Spandin and J. Moye in Proceedings of the IEEE, Vol. 53, No. 3, March 1965, pp. 301–302, doi: 10.1109/PROC.1965.3694.
Early Work on GPS Orbit Modeling
“Extended Orbit Modeling Techniques at the CODE Processing Center of the International GPS Service for Geodynamics (IGS): Theory and Initial Results” by G. Beutler, E. Brockmann, W. Gurtner, U. Hugentobler, L. Mervart, M. Rothacher and A. Verdun in Manuscripta Geodaetica, Vol. 19, 1994, pp. 367–386.
The International Laser Ranging Service
“The International Laser Ranging Service” by M.R. Pearlman, J.J. Degnan and J.M. Bosworth in Advances in Space Research, Vol. 30, No. 2, July 2002, pp. 135–143, doi: 10.1016/S0273-1177(02)00277-6.
SLR Tracking of GNSS Constellations
“Satellite Laser Ranging to GPS and GLONASS” by K. Sósnica, D. Thaller, R. Dach, P. Steigenberger, G. Beutler and D. Arnold in Journal of Geodesy, Vol. 89, No. 7, July 2015, pp. 725–743, doi: 10.1007/s00190-015-0810-8.
“IRNSS Orbit Determination and Broadcast Ephemeris Assessment” by O. Montenbruck, P. Steigenberger and S. Riley in Proceedings of ION ITM 2015, the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, California, Jan. 26–28, 2015, pp. 185–193.
“Initial Results of Precise Orbit and Clock Determination for COMPASS Navigation Satellite System” by Q. Zhao, J. Guo, M. Li, L. Qu, Z. Hu, C. Shi and J. Liu in Journal of Geodesy, Vol. 87, No. 5. May 2013, pp. 475–486, doi: 10.1007/s00190-013-0622-7.
“Contribution of SLR Tracking Data to GNSS Orbit Determination” by C. Urschl, G. Beutler, W. Gurtner, U. Hugentobler and S. Schaer in Advances in Space Research, Vol. 39, No. 10, 2007, pp. 1515–1523, doi: 10.1016/j.asr.2007.01.038.
Effect of Radiation Pressure on GNSS Satellite Orbits
“CODE’s New Solar Radiation Pressure Model for GNSS Orbit Determination” by D. Arnold, M. Meindl, G. Beutler, R. Dach, S. Schaer, S. Lutz, L. Prange, K. Sósnica, L. Mervart and A. Jäggi in Journal of Geodesy, Vol. 89, No. 8, Aug. 2015, pp. 775–791, doi: 10.1007/s00190-015-0814-4.
“Enhanced Solar Radiation Pressure Modeling for Galileo Satellites” by O. Montenbruck, P. Steigenberger and U. Hugentobler in Journal of Geodesy, Vol. 89, No. 3, March 2015, pp. 283–297, doi: 10.1007/s00190-014-0774-0.
“Impact of Earth Radiation Pressure on GPS Position Estimates” by C.J. Rodriguez-Solano, U. Hugentobler, P. Steigenberger and S. Lutz in Journal of Geodesy, Vol. 86, No. 5, May 2012, pp. 309–317, doi: 10.1007/s00190-011-0517-4.
“Test of the Gravitational Redshift with Stable Clocks in Eccentric Orbits: Application to Galileo Satellites 5 and 6” by P. Delva, A. Hees, S. Bertone, E. Richard and P. Wolf in Classical and Quantum Gravity, Vol. 32, No. 23, 2015, doi: 10.1088/0264-9381/32/23/232003.
Context-dependent scan matching for aided navigation
By Jyh-Ching Juang, Shang-Lin Yu and Shun-Hung Chen
Context-dependent scan matching for aided navigation — finding the rotation and translation that best align two consecutive scans — provides laser-ranging data that can be blended into a GNSS navigation system. A quality index based on analysis of intra-frame point clouds assesses the scan context, accounting for variations in feature richness, to yield a robust aided navigation solution.
For robust and autonomous navigation, many different sensors have been incorporated and, indeed, fused to form a navigation suite that typically includes a GNSS receiver, inertial measurement unit, vision sensor, laser rangefinder, odometer and others. Recently, driven by the goal to achieve autonomous driving, laser range data and image data have been widely adopted in the establishment of vehicle safety and autonomy functions. Laser range data can facilitate navigation and guidance. Through the use of scan matching, vehicle motion can be detected and used in dead reckoning. The surroundings of a vehicle can also be built based on point clouds, so that a feasible path can be generated for obstacle avoidance and vehicle guidance. To some extent, the image data can also be exploited in a similar manner. The use of a visual odometry technique attempts to estimate the relative motion between two consecutive images for dead-reckoning navigation.
This article addresses a limitation in scan matching for vehicular navigation and proposes a context-dependent scheme to account for the variation of the richness of features in scan-matching-based navigation. Environmental context in terms of the richness of features is known to affect the quality of the resulting navigation performance. Thus, in scan matching, we seek to establish a quality index to quantify the quality of the resulting estimates on rotation and translation. In this manner, after fusion with other sensors, a robust positioning solution can be obtained.
Here, we briefly review the scan-matching technique and discuss the aforementioned limitation using a real-world example. We then investigate a context-dependent weighting concept, and the entropy of a scan is used to quantify the richness of its features. We find that a scan with low entropy may be prone to improper registration and an erroneous navigation result. Thus, a weighting is assigned to the scan-matching result for integrated navigation processing. To verify and demonstrate the proposed context-dependent weighting approach, the method is implemented and tested in a vehicle. The result verifies that the proposed scheme can indeed avoid improper registration and lead to robust navigation performance.
Scan Matching
Scan matching is an enabling technique in vehicle navigation, map building and obstacle avoidance, produced by laser ranging devices. Scan matching finds the rotation and translation that best align two consecutive scans. Given two point sets {pn, n = 1,2,K,N} and {qm, m = 1,2,K,M} at two consecutive instants, the scan-matching problem is to determine a correspondence n → m(n) for the registration of two scans and a rotation matrix R and translation (shift) vector s such that the objective function is minimized:
(1)
Once the mapping m(n) is determined, the optimization of (1) can be solved analytically. The determination of the mapping from n to m(n) is typically accomplished by using an iterative method. This class of methods is termed as iterative closest point (ICP), in which the mapping m(n) is determined by searching for the closest point in the target point cloud. There have been many different variations to the ICP by using a different objective function for minimization, a point-to-plane matching, the removal of boundary and/or low-quality correspondences, and so forth. By repeating the scan-matching process, the rotation matrices and translation vectors can be determined and used in the dead-reckoning navigation process to estimate the position and attitude of the vehicle. In robotics and autonomous vehicles, the scan matching is typically integrated with the map-building process for simultaneous localization and mapping (SLAM).
Figure 1 depicts a representative result when the scan-matching technique is used in the SLAM. In the figure, the vehicle moves from the bottom to the top. As the vehicle moves, the laser rangefinder collects measurements for the determination of the vehicle and the mapping of the environment. The location of the vehicle can be estimated (in green) and the environment can be mapped (in blue) by using the scan-matching and filtering techniques. However, as also depicted in the figure, as the vehicle moves to the end of the corridor the point clouds that are obtained from the laser rangefinder (in red) are constrained, and the change of the pose of the vehicle cannot be accurately determined.
Figure 1. Representative SLAM result.
Figure 2 shows the original scans at two consecutive instants (in blue and gray, respectively) and the matched scan after the scan-matching process (in red) when the vehicle moves along the corridor.
Figure 2. Scan-matching result 1.
At this point, the laser rangefinder obtains measurements that are rich in context. The rotation and translation of the vehicle can be estimated with an acceptable level of accuracy, and the vehicle can be located. In this example, the translation vector is found to be s = [11.07 0.50 –0.58]T mm and the minimal error of the objective function is 3.47. When the vehicle moves to the end of the corridor, the scans at two consecutive instants, together with the matched scan, are depicted in Figure 3.
Figure 3. Scan-matching result 2.
In this case, only the end wall is observed by the laser scanner, and the determination of the rotation and translation based on scan matching is subject to errors due to the lack of features. Indeed, by applying the scan-matching technique, the translation vector is found to be s = [9.18 –2.84 13.22]T , which is obviously incorrect in the z axis component. Also, the minimal error of the objective function is 3.20, which is smaller than the error in Figure 2. Thus, the error may not provide a fair assessment of the scan matching due primarily to the fact that the error in registration is not taken into account in the objective function (1). In short, lack of features in the environment may induce improper registration and lead to navigation error.
To account for the aforementioned limitation, several methods can be adopted. One can resort to some variations of the scan-matching techniques by, for example, using feature extraction and matching. Blending with other sensors can be employed. In this case, the vehicle can be equipped with gyros to give information on the change of attitude so that the change of translation can be better estimated. This research project addressed this issue by using a context-dependent weighting to quantify the scan-matching results.
Context-Dependent Weighting
Scan matching attempts to investigate the relationship between two consecutive scans to explore the inter-frame characteristics. However, as discussed, the quality of the scan-matching result depends on the richness of features in the scan, which is revealed by examining the intra-frame characteristic. Given a scan in 2D or 3D, some quality indices can be established to assess its characteristic. For example, principal component analysis (PCA) is a widely applied technique to quantify a scan and to obtain normal vector in a polygon environment. For vehicle navigation in an outdoor environment, the PCA approach may be limited. Here, we propose the use of entropy to assess the complexity of the environment of a scan (or image).
Given a set of K random variables, the entropy is defined as
,(2)
where pk stands for the probability of the k-th random variable. The entropy is a measure that can be used to probe the randomness of a set of random variables. As each probability is bounded by 1, the entropy in (2) ranges between 0 and log2 K.
To assess the entropy of a scan, which is characterized in terms of a combination of angle and range, the scan is converted through a kernel function to become a density-based map. Several different kernel functions can be used. With the density-based scan, the histogram can be formed to obtain an estimate of the probabilities and, consequently, (2) is used to evaluate the entropy.
Figure 4 and Figure 5 represent the original scan and the density-based scan, respectively. The entropy of the sacn in Figure 4 is evaluated to be 1.17. In contrast, the scan in Figure 6 is found to have an entropy of 0.86. Note that Figure 6 is limited in terms of its features, leading to a smaller entropy.
Figure 4. A representative laser range measurement.Figure 5. A density-based scan.Figure 6. Another scan.
By evaluating the entropy of the scan, the scan-matching result can be quantified. A weighting can indeed be assigned as a function of the entropy for integration with other sensors in the integrated navigation system. A limitation of using laser scan data for the assessment of entropy is the need of the conversion to its corresponding density-based map. In vehicular navigation, a camera is often mounted together with a laser rangefinder. As a result, it is possible to use the image data from the camera for the assessment of entropy.
Figure 7 depicts the navigation system design when the context-dependent weighting is used. The navigation suite uses laser rangefinder, camera and other navigation sensors to estimate the position, velocity and attitude of the vehicle. In this approach, the reference scan is matched with the current reading scan based on the scan-matching technique to produce estimates on the rotation and translation. In the meantime, the current scan is overlaid on the image that is obtained from the camera. The region of interest, which is the image that covers the scan points, is extracted. With respect to the region of interest of the image, the entropy is evaluated. The entropy then serves as an indicator in adjusting the weighting of the rotation and translation. The use of image data is the saving in computational complexity. A potential limitation is that the entropy may be sensitive to the variation of gray scale, or RGB values may affect the result.
Figure 7. Integrated navigation with context-dependent weighting.
Experiments
To verify the applicability of the context-dependent weighting, an experiment is conducted. The vehicle is equipped with the following navigation sensors for the determination of position, velocity and attitude.
laser rangefinder
camera
IMU
GPS receiver
odometer
In addition, a GPS real-time kinematic (RTK) receiver provides ground truth. The RTK solution is only used in the evaluation process. Figure 8 depicts the location of the sensors after installation in the test vehicle Luxgen U7.
Figure 8. Test vehicle and the locations of sensors.
The experiment was conducted at a test track of the Automotive Research and Test Center (ARTC), Taiwan, and Figure 9 depicts the track as well as the RTK result. The starting point is at the right upper corner of the track, and the vehicle moves in a counter-clockwise direction.
Figure 9. Test track at ARTC, Taiwan.
The proposed context-dependent weighting approach is evaluated. To assess the significance of the context-dependent weighting, the navigation system processes the laser rangefinder, IMU and encoder data only as these data are obtained from dead-reckoning sensors. More exactly, the GPS receiver data is not used in the processing to better quantify the contrition of the proposed approach. In practice, the GPS receiver data can be used to account for dead-reckoning sensor errors.
Figure 10 depicts the comparison of the estimated trajectory. In the figure, the RTK result is used as a reference, and the dead-reckoning results with and without the context-dependent weighting are shown. Note that when the context-dependent weighting is not used, the estimated trajectory (in red) is subject to two erroneous turns at the lower left corner and upper right corner, respectively.
Figure 10. Estimated trajectories.
The entropy as a function of time is evaluated and shown in Figure 11. Note that the entropies are relatively low at 240 seconds and 1960 seconds, respectively. These two instants correspond to the moments when the vehicle is at the aforementioned corners. Through the use of entropy-based context-dependent weighting in the dead-reckoning process, the navigation error is significantly reduced, as shown in the estimated trajectory (in blue). Thus, the effectiveness of the proposed scheme is verified.
Figure 11. Entropy as a function of time.
Conclusion
For autonomous vehicle applications, knowledge of the current state (such as position, velocity and attitude) of the host vehicle are needed. For robust and autonomous navigation, many different sensors have been incorporated and fused to form a navigation suite. In fusing different sensor data for better accuracy and integrity, the quality of sensors must be considered. We investigated the use of a scan-matching technique for aided navigation. The context of the environment in terms of the richness of features may affect the quality of the resulting navigation system.
To address the context-dependent issue, we used a context-dependent entropy measure to assess the quality in scan matching. In addition to the increments in translation and rotation, the corresponding quality indices are obtained to better blend the scan-matching result into the navigation system. As a result, anomalous navigation results due to lack of features and improper registration can be better dealt with. The proposed scheme is experimentally verified.
Acknowledgments
The work is supported by the joint NCKU-ARTC research project, Taiwan.
JYH-CHING JUANG received a Ph.D. in electrical engineering from the University of Southern California, Los Angeles. He was with Lockheed Aeronautical System Company, Burbank, before joining the faculty of the Department of Electrical Engineering, National Cheng Kung University, Tainan, Taiwan. His research interests include sensor networks, GNSS signal processing and software-based receivers.
SHANG-LIN YU is an M.S. student in the Department of Electrical Engineering, National Cheng Kung University.
SHUN-HUNG CHEN received a Ph.D. from the Department of Electrical Engineering, National Cheng Kung University. He is with the Electronic Control Technology Group, Research & Development Division, Automotive Research & Testing Center in Taiwan. His research interests include vehicle navigation and autonomous driving.
Using Microwaves and Laser Ranging for Precise Orbit Determination
By Erik Schönemann, Tim A. Springer, Michiel Otten, and Matthias Becker
Though Galileo’s GIOVE-A is a test satellite not necessarily ready for scientific use, orbit analyses with a reduced accuracy can help to identify weaknesses and suggest improvements. This month, the authors share work being carried out to precisely determine the orbit of GIOVE-A using SLR and microwave observations. This preliminary investigation will benefit the procedures to be implemented for the future Galileo constellation.
INNOVATION INSIGHTS by Richard Langley
WE USE THEM FOR LISTENING TO MUSIC, for routine surgeries, for making a point in a presentation, and even for hanging pictures straight. Of course, I’m talking about lasers. Invented in 1960, the laser (an acronym for light amplification by the stimulated emission of radiation) has become ubiquitous in modern society. Every CD and DVD player has one. Many printers use them. But lasers are also used in a wide range of industrial and scientific applications including determining the orbits of satellites through satellite laser ranging (SLR).
In the SLR technique, pulses of laser light from a ground reference station are directed at satellites equipped with an array of corner-cube retroreflectors, which direct the pulses back towards a collocated receiving telescope. By accurately measuring the two-way travel times of the pulses and knowing the location of the station and other operating parameters, the positions of the satellites can be determined. A network of SLR reference stations around the globe is used to monitor the orbits of satellites over time and their variations have been used by scientists to improve our knowledge of the Earth’s gravity field; to study the long term dynamics of the solid Earth, oceans, and atmosphere; and even to verify predictions of the General Theory of Relativity.
The first SLR measurements were obtained from the Beacon Explorer-B satellite, which was launched in October 1964. Since then, dozens of satellites equipped with corner-cube retroreflectors have been launched including a number of radio-navigation satellites. Every GLONASS satellite is equipped with retroreflectors and two GPS satellites have been equipped—SVN35/PRN05 and SVN36/PRN06. The COMPASS-M1 satellite in medium Earth orbit carries retroreflectors, as do both GIOVE-A and –B, the Galileo test satellites.
Precise orbit determination of radio-navigation satellites using SLR has the advantage of being unaffected by any onboard satellite electronics and associated signal biases. Radiometric observations of a satellite’s microwave signals, on the other hand, are influenced by the satellite’s clock, for example, and its effect must be estimated to obtain precise (and accurate) satellite orbits for navigation and positioning. Therefore, a comparison of SLR- and microwave-derived orbits can be very useful for studying the performance of the data measurement and orbit-determination processes of both techniques.
In this month’s column, we take a look at some work being carried out to precisely determine the orbit of the GIOVE-A test satellite using SLR and microwave observations. This preliminary investigation will benefit the procedures to be implemented for the future Galileo constellation.
“Innovation” is a regular column that features discussions about recent 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 at the University of New Brunswick, who welcomes your comments and topic i deas. To contact him, see the “Contributing Editors” section on page 6.
The navigation office of the European Space Operations Centre (ESOC) is engaged in various activities using observations of the Galileo test satellite, GIOVE-A (Galileo In-Orbit Validation Element-A), recorded at the Galileo Experimental Sensor Stations (GESS). The work includes the assessment of the quality and performance of GIOVE satellite observables and the testing and improvement of orbit-determination software. These activities support the long-term goal of advancing the scientific applications of the future Galileo constellation.
Since the launch of GIOVE-A on December 28, 2005, various tests have been carried out to analyze the quality of the new code (pseudorange) and carrier-phase observables derived from tracking the satellite’s microwave signals. All of these tests demonstrate the advantages of the new signal structure compared to that of legacy GPS signals. In general, the reduction of the noise by factor of 4-5 as well as a reduction of the code multipath by approximately a factor of 1.2 (GPS C1C versus GIOVE-A C1B/C1C) could be seen.
As the comparison of observations is done indirectly (GPS and GIOVE-A have different orbits) and the databases used for most analyses published up to now is sparse, a deeper analysis of the signal quality parameters seems appropriate, especially as data quality has a direct impact on the precision of orbit determination. Our analyses, presented in the first half of this article, are based on a broad base of data from most of the stations in the GESS network. Because of the difficulty in accessing the phase multipath directly, we first evaluated the signal strength and the code multipath, which gave the first hint of the multipath behavior. In order to compare GPS and GIOVE-A data directly, only data received from the same elevation angles and azimuths were used. Subsequently, we present an analysis of the phase residuals derived by precise point positioning.
The second part of this article focuses on the precise orbit determination or POD of the GIOVE-A spacecraft. The Navigation Package for Earth Observation Satellites (NAPEOS) software used at the ESOC Navigation Support Office allows microwave (radiometric) and satellite laser ranging (SLR) observations to be used either separately or together. The two methods are different due to different tracking networks and the different sensitivity of the observables to atmospheric effects and in their noise levels. We will present the orbit results focusing on internal orbit consistency checks and SLR validation of the microwave-based orbits.
Data Analysis
We first describe the procedures used for analyzing the microwave data followed by those used for the SLR data.
Microwave Analysis. For the GIOVE-A signal analysis and precise orbit determination we used the RINEX data from all of the GESS stations available from the GIOVE archiving facility (see TABLE 1). All stations are equipped with GPS/Galileo antennas, built by Space Engineering S.p.A. and Galileo Experimental Test Receivers (GETRs), built by Septentrio. The data, containing tracking data of all GPS satellites and the GIOVE-A satellite, is given in the RINEX 3.00 data format with a sampling interval of 1 second. To save on storage space for the long-term analyses, such as orbit determination, the RINEX data is decimated to 30-second samples and Hatanaka-compressed, using a test version of the Hatanaka software for the RINEX 3.00 format.
The signal analyses shown here were carried out using GNU Octave, an open-source program for performing numerical computations similar to Matlab, and different scripts developed by the Institut für Physikalische Geodäsie at the Technische Universität Darmstadt. These analyses cover a selection of the designated Galileo signals recorded by the GESS within the time span from December 16 to 27, 2006. Within this time period, the current GPS signals, as well as the GIOVE-A signals E1 and E5, shown in TABLE 2, were recorded. The table also shows the signal components as well as the RINEX observation-type identifiers, which we use in this article.
The stations used for the analyses show a quite similar level of performance in general. There are stations with different behaviors for single signals, as for example GIEN with a stronger code multipath behavior on C1B and C1A, but no station with a considerably different performance level could be identified. The averaging over the data from all sites reduces the station-dependent effects such as multipath and the atmosphere to a large extent, and gives a good indication of the mean signal performance.
The analyzed phase residuals were taken from the processing carried out for the second part of this article. Hence, they include observation data over an extended period of 149 days and were limited to the GIOVE-A C1C/L1C and C7Q/L7Q signals.
This extended data period is from December 12, 2006 (day of year 346), until May 26, 2007 (day of year 146). During this interval, there is a period where no GIOVE-A data was available due to maintenance of the spacecraft. This gap occurred from February 12 to 28, 2007. So in total we have analyzed 149 days of microwave data. Because there are some differences between the results before and after this gap in February, many of the statistics are given for the first and second part separately. The first part covers December 12, 2006, until February 11, 2007; the second part covers March 1, 2007, until May 26, 2007.
We performed the precise orbit determination using the NAPEOS software, a general-purpose software package for orbit determination, prediction, and control, supporting all phases of an Earth-observation mission in terms of mission preparation and operations.
For the GIOVE-A analysis, the three main NAPEOS programs we used are GnssObs, Bahn, and Multiarc. GnssObs reads, cleans, and decimates the RINEX data and converts the data into the NAPEOS internal tracking-data format. The NAPEOS tracking-data format contains the ionosphere-free linear combination, for both code and phase, of the RINEX observations. For GPS, the ionosphere-free linear combination is based on the combination of C1P and C2P code and L1P and L2P phase measurements. GIOVE-A offers several different observables allowing for many different ionosphere-free observations. For most of the work presented in this article, we have used the ionosphere-free linear combination of the C1C and C7Q and L1C and L7Q observations for code and phase respectively.
The next module, Bahn, performs the parameter estimation. In this step, we use the ionosphere-free code and phase observations at a sampling interval of 5 minutes, and we have applied an elevation angle cut-off of 5 degrees. The data is processed in batches of 24 hours, thus resulting in 1-day-arc solutions. The estimated parameters in these daily solutions are the GIOVE-A state vector (position and velocity), five dynamical orbit parameters from the extended Center for Orbit Determination in Europe (CODE) orbit model, a GIOVE-A clock offset for each epoch, all receiver clock offsets for each epoch, one GPS-GIOVE-A “intersystem bias” parameter per day for each station except for a selected reference station, and the carrier-phase ambiguities (integers not resolved). The station coordinates are estimated but tightly constrained (1 millimeter) to their a priori value. We obtained the a priori station coordinates by combining the full set of daily solutions.
Despite the fact that the 13 GESS stations provide very good global coverage, it is expected that 24-hour solutions will not give the most precise GIOVE-A orbit estimates. To generate longer arc solutions, we have used the Multiarc program. This is a tool that has recently been added to the NAPEOS software package. It allows for a rigorous combination of normal equations, also referred to as normal equation stacking, which are generated by Bahn. During the normal equation combination, the satellite orbit parameters may also be rigorously combined, thus effectively leading to multi-day orbital arcs. For the work presented in this article, we have used Multiarc to generate solutions with arc lengths of 1, 2, 3, 4, and 5 days. We also used Multiarc to compute accurate a priori station coordinates by stacking all available 1-day normal equations.
Satellite Laser Ranging
Besides the 13 GESS stations, GIOVE-A is also tracked by more than 17 different SLR stations around the world. For most periods of the mission, the tracking has been consistent enough to allow for GIOVE-A POD using only the SLR data. As the SLR data is completely independent of the microwave data, the resulting orbit solutions will be to a large extent independent as well and thus can be used to give an indication of the achieved precision of the different microwave solutions.
The orbit determination strategy used for the SLR solutions is very similar to the one used for the microwave orbits with the main difference being the increased arc-length of 7 days. The same satellite parameters are estimated as with the microwave solutions: the GIOVE-A state vector and five dynamical orbit parameters from the extended CODE orbit model. No further parameters need to be estimated and all corrections applied to the SLR data are according to the International Earth Rotation and Reference Systems Service 2003 standards and, for station coordinates, we used those from the rescaled International Terrestrial Reference Frame 2005 solution. As the noise level of the SLR data is very low, the measurements can also be directly used to give an indication of the precision of the radial position components of the different microwave solutions by computing the SLR residuals without using them in the estimation process itself.
Combined Microwave and SLR Analysis. In this step, the SLR data was added to the microwave data in the 24-hour solutions. For the data weighting, we used 100 millimeters for SLR and 1000 millimeters and 10 millimeters for GIOVE-A and GPS code and phase observables respectively. The only change in the analysis strategy in this case was that we now processed the SLR data in 24-hour solutions and not in 7-day batches. All the processing options remained as described in the two previous sections. The resulting 1-day solutions, or rather the associated normal equations, were used in Multiarc to generate combined solutions of different arc lengths.
Microwave Data Quality
We now take a detailed look at the quality of the microwave data in terms of signal-to-noise ratio (SNR), code-tracking noise and multipath, carrier-phase-tracking noise, and carrier-phase residuals.
Signal-to-Noise Ratio. The SNR (or equivalently carrier-to-noise-density ratio, C/N0) is strongly dependent on the satellite transmitter, the signal path through the atmosphere, and the receiver configuration (ground station, antenna, receiver, cable, etc.). Hence the SNR cannot be seen as an absolute value. The SNR is specific to the position, the equipment, and the time. Furthermore, the determination of the SNR values depends on the receiver and the firmware used. As a result, SNR values from different receivers cannot be readily compared. Nevertheless, using only one type of receiver, assuming similar effects on all the different signals at the same epoch, and taking averages over a long time span, we expect the relationships among the signals to be constant. Based on this assumption, we can use the SNR values given in the GESS RINEX files without adjustment.
To compare the GPS with the GIOVE-A SNR values, we ordered the corresponding SNR values of all stations on all days by satellite position into a grid with widths of 5 degrees in azimuth and 5 degrees in elevation angle. For the evaluation, we took the grid cells occupied by both GPS and GIOVE-A values and computed the median over all the cells of equal elevation angle. The median per elevation-angle bin for each signal is shown in FIGURE 1.
FIGURE 1. Signal-to-noise ratio, GPS versus GIOVE-A
As can be seen from the figure, the signal strength of the GIOVE-A C8Q observable ranks best, followed by the GPS C1C, GIOVE-A C7Q, C5I/C5Q, C1A, and C1B/C1C. The weakest signal is found for the GPS C1P/C2P observable, with a maximum signal strength of 40 (receiver-dependent unit, approximately dB-Hz) at the zenith. Comparing the GPS open signals versus GIOVE-A, GPS C1C is considerably stronger than the GIOVE C1B/C1C. According to the GPS and Galileo interface control documents, GIOVE-A C1B/C1A should show up with a stronger signal strength than GPS C1C. The power levels guaranteed on the Earth’s surface are -160 dBW for GPS and -158 dBW for the future Galileo satellite signals except for the BOC(10,5) and BOC(n,m) modeled signals, for which a power level of even -155dBW is guaranteed. But looking at the SNR values shown in Figure 1, we see that the GIOVE-A C1B/C1C is worse by approximately 4 dB than the GPS C1C. But keeping in mind that GIOVE-A is an experimental satellite, an increase of the signal power for the future operational Galileo satellites should improve the signal performance above that shown in this article.
Code-Tracking Noise. For signals containing data and pilot components, as in the case of those from GIOVE-A, the code-tracking noise can easily be computed as the difference between the data and the pilot signal. The advantage of this computation scheme is that both signals are influenced by identical error sources (atmospheric errors, multipath errors, receiver errors, etc.). Based on the assumption of equal uncertainties in the two components, we divided the resulting noise values by the square root of two to specify the noise level of each part according to the laws of error propagation. TABLE 3 shows the code-tracking noise for the two analyzed GIOVE-A codes sorted by elevation angle. The median code-tracking noise is 0.62 meters for C1B/C1C and 0.35 meters for C5I/C5Q, for observations below an elevation angle of 5 degrees. For the C1B and C1C code measurements, the noise median stays below 0.2 meters for an elevation angle above 25 degrees, whereas the median for the C5I and C5Q code measurements for elevation angles above 35 degrees even comes down below 0.1 meters. The results discussed above are consistent with the code-tracking noise values published previously.
Code Multipath. We computed the relative code multipath effects as code minus phase differences assuming the amplitude of phase multipath to be insignificant compared to the amplitude of the code multipath. Ionospheric effects were taken into account by using the phase measurements on two frequencies in the usual way:
In this equation, CMPx is the estimate of the multipath error on the code, Px and Lx are the code and phase measurements of the same frequency, while Ly is the phase measurement used to correct the frequency-dependent ionospheric effect. The constant, , describes the relationship of the ionospheric behavior for the two frequencies.
In order to compare the code multipath level of GPS versus GIOVE-A, we sorted the multipath values using a grid covering the sky with widths of 5 degrees for both elevation angle and azimuth as before. FIGURE 2 shows the median standard deviation of the code multipath values, derived in each grid cell per day and station, versus the elevation angle. No significant difference between GPS C1C and GIOVE-A C1B and C1C, the open code signals on G1/E1, could be found. The code multipath behavior of the GPS precise codes are comparable with the GIOVE-A C5I, C5Q, and C7Q, whereas the C8Q shows the least code multipath effects closely followed by the GIOVE-A C1A, the public regulated service signal.
FIGURE 2. Code multipath, GPS versus GIOVE-A
Carrier-Phase-Tracking Noise Analyses. In the same manner as that carried out with the code, we computed the GIOVE-A carrier-phase-tracking noise as the difference of the two components (pilot minus data). To accommodate the effect of error propagation, the resulting errors were divided by the square root of two. The resulting phase-tracking noise values were sorted by elevation angle and can be found in TABLE 4.
In conformity with the theory that the phase-tracking noise is independent of the modulation scheme, both signals (L1B/L1C and L5I/L5Q) show the same results in units of cycles. Looking at the results in units of distance, GIOVE-A L1B/L1C shows up with a mean phase noise of 0.7 millimeters and L5I/L5Q with 0.9 millimeters. These values confirm those of previous studies.
Carrier-Phase Residuals. Phase residuals contain the phase tracking noise, multipath, as well as all unmodeled remaining errors such as antenna calibration inaccuracy and tropospheric effects. The magnitude of the residuals can be seen as an indicator for the observation and model accuracy as well as for measurement quality.
The following analyses are based on the ionosphere-free linear combination (GPS L1C/L2P, GIOVE-A L1C/L7Q), computed with NAPEOS. The analyses include data of the 13 GESS over a period of 149 days.
To compare the GPS and GIOVE-A residuals, we sorted them into a grid with a width of one degree in both satellite azimuth and elevation angle. Only data in overlapping grid locations were compared to make sure the data was affected in a similar way by multipath or other disturbances.
To properly interpret the results, we should mention that for GIOVE-A, 0.06 percent of the ambiguities (2501) were not fixed correctly whereas for GPS all ambiguities were fixed correctly. Looking at the GIOVE-A observations that were correctly fixed, we find a significantly larger number of rejected observations. The number of rejected observations is less by one third for GPS (6 percent) as for the GIOVE-A (9 percent) data.
Due to the small number of GIOVE-A observations for elevation angles above 86 degrees, the outlier-cleaned mean as well as the standard deviation at this elevation-angle range are not meaningful. For all elevation angles, GIOVE-A residuals show a lower standard deviation than GPS, indicating a superior performance of GIOVE-A signals.
Phase and Code Validation in Processing. Looking at the quality of the code and phase measurements on the different signals, it is conspicuous that GIOVE-A C1A/L1A and C8Q/L8Q rank best, whereas for the current processing of GIOVE-A data, usually the C1C and C7Q signals are used. This leads to the question of which is the best signal combination for GIOVE-A. Hence, we processed 10 days of GIOVE-A data, using different signal combinations. Presently the processing of the C8Q/L8Q signals is not yet implemented in NAPEOS. However, we were able to process the GIOVE-A C1A/L1A – C7Q/L7Q combination. The root-mean-square (RMS) of the code results were reduced by a factor of approximately 1.4 using L1A/C1A compared to L1C/C1C, whereas the RMS of the phase observations showed only a minor improvement. Furthermore, there is a higher number of rejected observations with L1A/C1A. Further analyses have to be carried out to evaluate the potential benefits of the different signal combinations.
Orbit Quality
In this section, we assess the quality of our precise orbit determination solutions. We have three sets of different orbit solutions. Set 1 is made up of the 7-day solutions based solely on SLR observations. Set 2 consists of the solutions based on the microwave observations using 1- to 5-day arcs. Set 3 consists of the solutions based on a joint analysis of the microwave and SLR observations also using 1- to 5-day arcs.
First, we assess the orbit quality by looking at the internal consistency of the solutions. For the two sets using microwave observations, the internal orbit consistency is done using an orbit fit. This will not tell us much about the absolute quality of the solutions but it will indicate the optimal arc length and whether adding the SLR observations to the microwave data improves the orbit estimates.
Secondly, we validate the orbits by determining the SLR residuals. Of course, the solutions that used SLR observations should perform better than the microwave-only solutions. However, the validation of the microwave orbits against the SLR observations will give us a good impression of the absolute accuracy of our orbits.
As a third test, we compare the best orbit (best arc length) of each of the three sets (set 1 only has one arc length) against each other. This should give us another indication of the quality of the orbits.
Internal Orbit Consistency. To determine the internal orbit consistency of the different solutions we make an orbit fit. For this orbit fit test, we used the middle 24 hours of two consecutive solutions and fit one 48-hour arc through these two parts. The satellite orbit was modeled by estimating the satellite state vector and all nine parameters of the extended CODE orbit model. The RMS of this fit gives us an indication of the internal consistency of the orbit estimates. For longer arcs, the RMS of fit should go down because the solutions are not fully independent of each other. So a lower RMS for the longer arc solutions is expected. On the other hand, this means that if the RMS does not go down with increasing arc length that we have reached the limit of our modeling capabilities. Furthermore, comparing the internal orbit consistencies of equal length solutions will tell us which solution has a better internal consistency. The results of this internal orbit consistency check are given in TABLE 5. The table gives the mean of the 2-day RMS over all processed days. The mean is given separately for the first and second part of the observation interval (see above) and also for the total observation interval.
Table 5 shows several interesting results. First of all, it shows that the results of part 2 of the observation interval are significantly better than the results from part 1. The reason for this is unclear since the statistics from the 1-day solutions, such as the residual RMS and number of observations, did not change significantly after the observation gap. The improvement, however, is very significant. The second observation is that the results including the SLR data are significantly better compared to those using only the microwave data. This is true for all arc lengths! As expected, we see a significant improvement of the internal consistency when going from 1-day arcs to 3-day arcs. The 4-day arcs show only a slight improvement compared to the 3-day arcs. The 5-day arcs do not show a significant improvement. This indicates that with the current observations and modeling techniques, the optimal arc length for precise orbit determination seems to be around 3 to 4 days.
SLR Validation. In this section, we look at the SLR residuals obtained from the different orbit solutions. We generated a clean SLR dataset by using the SLR-only orbit to remove any outliers in the SLR observations. The total number of valid SLR normal points for the entire period is 3520 observations from 17 different SLR stations. (A normal point is an average of a number of individual laser returns.) The number of observations for the first part of the observation period is 796 points from 12 stations and for the second part, there were 2724 normal points from 17 stations. For two of the three solutions, the SLR data has been used in the orbit determination process so the residuals will give a too-optimistic indication of the orbit quality.
As can be seen from TABLE 6, the 3-day solution based on the microwave-only data has the lowest SLR residuals and indicates a radial precision of around 100 millimeters. A similar behavior can be seen in the microwave plus SLR solution with the exception of the 1-day solution (and to a smaller extent also the 2-day solution) where the orbit solution is mainly driven by the SLR data, but the quality as can be seen from the internal consistency of the orbit is poor. Interestingly, there is a large improvement in SLR residuals for the microwave plus SLR solution, although the number of SLR data points is only 2 percent of the total tracking data in the combined solution. The values for the SLR-only solution are included in the table to give an indication of the lowest possible SLR residuals one could expect by combining the microwave and SLR data.
Orbit Comparison. To get an indication of the overall orbit quality, the best solutions were compared against each other for the second period of observation. TABLE 7 gives the RMS differences between the SLR only (SLR), 3-day microwave only (micro), and the 3-day microwave and SLR solution (micro+SLR) for the radial, along-track, and cross-track position components as well as the norm (3D).
As expected, the largest difference is between the SLR-only and microwave-only solutions giving a total (norm) orbit difference of 652 millimeters. As a major part of the SLR tracking from GIOVE-A comes from European stations, the quality of the SLR solutions is directly correlated with the ability of the European stations to track GIOVE-A. Bad weather over Europe can lead to data gaps for more than 24 hours, affecting the orbit quality. It is interesting to see the large impact the SLR data has on the combined solution. As mentioned before, the SLR data is only around 2 percent of the total tracking data but has a significant impact on the orbit solution as can be seen from the difference between the microwave-only and microwave-plus-SLR solution.
Based on the analysis presented above, we conclude that the 3-day solution using both microwave and SLR observations has provided the best orbit estimates.
Conclusion
The analyses of the observation data quality (signal quality) confirmed the good results from prior analyses for code multipath behavior and code noise. GPS C1C and the GIOVE-A C1B/C1C show a comparable multipath behavior, whereas the GPS precise codes C1P/C2P are comparable to the GIOVE-A C5I, C5Q, and C7Q. The least code multipath behavior could be found for GIOVE-A C8Q observable, closely followed by the GIOVE-A C1A. Based on this, the combination C1A/L1A – C8Q/L8Q should show the best noise behavior within the data processing scheme.
The results given in this article demonstrate that the 13-station GESS network allows us to determine the orbit of the GIOVE-A satellite quite accurately (~200 millimeters) using only microwave observations. The SLR validation of the microwave orbits gives an RMS of 100 millimeters (one-way range RMS). This result gives an absolute value for the orbital error. Of course, the SLR observations mainly tell us something about the radial orbit errors; the along- and cross-track errors could be much higher. To obtain accurate GIOVE-A orbit estimates, we need to keep the orbits and clocks of the GPS satellites, tracked simultaneously with the GIOVE-A satellite, fixed using the International GNSS Service (IGS) final orbit and clock products. Furthermore, an arc length of 3 days should be used. The microwave-based orbit estimates may be improved by adding the available SLR observations into the orbit-estimation process. Although there are relatively few SLR observations, they do have a significant positive effect on the orbit estimates, improving the internal consistency from 52 to 41 millimeters. Also, the validation of the orbits using the SLR observations shows a significant improvement. However, this is not an independent validation because the same SLR observations were used in the orbit determination.
The results presented in this article, even though based on observations from the GIOVE-A test satellite, can be considered as a first attempt towards establishing an optimal data processing approach for the future Galileo satellite constellation.
Acknowledgments
This article is based on the paper “GIOVE-A Precise Orbit Determination from Microwave and Satellite Laser Ranging Data – First Perspectives for the Galileo Constellation and Its Scientific Use” presented at the 1st Colloquium on the Scientific and Fundamental Aspects of the Galileo Program, held in Toulouse, France, October 1-7, 2007.
ERIK SCHÖNEMANN studied geodesy at the Technische Universität Darmstadt (TUD), Germany, writing his diploma thesis at the University of New South Wales, Sydney, Australia. Since receiving his diploma from TUD in April 2005, he has been working for the Institute of Physical Geodesy at TUD on GNSS station calibration and validation and analyses of GIOVE-A and GIOVE-B data.
TIM SPRINGER received his Ph.D. in physics from the Astronomical Institute of the University of Berne (AIUB) in 1999. He has been a key person in the development of the Center for Orbit Determination in Europe, one of the IGS analysis centers, located at AIUB. Since 2004, he has been working for the Navigation Support Office (NSO) at the European Space Operations Centre (ESOC) of the European Space Agency (ESA) in Darmstadt. In this group, he has led the development of the new ESOC GNSS software, which is used for most GNSS activities at NSO including GIOVE-A and -B analyses.
MICHIEL OTTEN obtained a degree in aerospace engineering from Delft University of Technology in 2001. He has been working for ESOC’s NSO since 2002. His main role within NSO is the precise orbit determination of low Earth-orbiting satellites equipped for SLR, DORIS, and GPS tracking. He is also responsible for ESA’s International DORIS Service Analysis Centre activities.
MATTHIAS BECKER is a full professor of geodesy and director of the Institute of Physical Geodesy, TUD. He received his diploma and Ph.D. in geodesy from TUD in 1979 and 1984, respectively. He is responsible for research and teaching in the fields of physical geodesy and satellite geodesy.
FURTHER READING
• GIOVE-A
“Meet GIOVE-A: Galileo’s First Test Satellite” by E. Rooney, M. Unwin, A. Bradford, P. Davies, G. Gatti, V. Alpe, G. Mandorlo, and M. Malik in GPS World, Vol. 18, No. 5, May 2007, pp. 36–42.
“Galileo Signal Experimentation” by M. Hollreiser, M. Crisci, J.-M. Sleewaegen, J. Giraud, A. Simsky, D. Mertens, T. Burger, and M. Falcone in GPS World, Vol. 18, No. 5, May 2007, pp. 44-50.
• GIOVE Tracking Network
“GIOVE Mission Sensor Station Receiver Performance Characterization: Preliminary Results” by M. Crisci, M. Hollreiser, M. Falcone, M. Spelat, J. Giraud, and S. La Barbera in Proceedings of Navitec 2006, the 3rd ESA Workshop on Satellite Navigation User Equipment Technologies, Noordwijk, The Netherlands, December 11-13, 2006.
• GIOVE Tracking Performance
“Performance Assessment of Galileo Ranging Signals Transmitted by GSTB-V2 Satellites” by A. Simsky, J.-M. Sleewaegen, M. Hollreiser, and M. Crisci in Proceedings of ION GNSS 2006, the 19th International Technical Meeting of the Satellite Division of The Institute of Navigation, Fort Worth, Texas, September 26-29, 2006, pp. 1547–1559.
“Code and Carrier Phase Tracking Performance of a Future Galileo RTK Receiver” by T. Pany, M. Irsigler, B. Eissfeller, and J. Winkel in Proceedings of ENC-GNSS 2002, the European Navigation Conference, Copenhagen, Denmark, May 27-30, 2002.
• Multipath Mitigation in Modernized GNSS
“Comparison of Multipath Mitigation Techniques with Consideration of Future Signal Structures” by M. Irsigler and B. Eissfeller in Proceedings of ION GPS/GNSS 2003, the 16th International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Oregon, September 9-12, 2003, pp. 2584–2592.
• GIOVE Orbit Determination
“Estimation and Prediction of the GIOVE Clocks” by I. Hidalgo, R. Píriz, A. Mozo, G. Tobias, P. Tavella, I. Sesia, G. Cerretto, P. Waller, F. González, and J. Hahn in Proceedings of the 40th Annual Precise Time and Time Interval (PTTI) Meeting, Reston, Virginia, December 1-4, 2008.
• Satellite Laser Ranging
“GIOVE’s Track: Satellite Laser-Ranging Campaigns” by M. Falcone, D. Navarro-Reyes, J. Hahn, M. Otten, R. Piriz, and M. Pearlman in GPS World, Vol. 17, No. 11, November 2006, pp. 34–37.
“The International Laser Ranging Service: Current Status and Future Developments” by W. Gurtner, R. Noomen, and M.R. Pearlman in Advances in Space Research, Vol. 36, No. 3, 2005, pp. 327–332 (doi:10.1016/j.asr.2004.12.012).
“Laser Ranging to GPS Satellites with Centimeter Accuracy” by J.J. Degnan and E.C. Pavlis in GPS World, Vol. 5, No. 9, September 1994, pp. 62–7.
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