Innovation: Orbit determination of LEO satellites with real-time corrections

April 24, 2017 - By André Hauschild, Javier Tegedor, Oliver Montenbruck, Hans Visser and Markus Markgraf

Precision on Board

INNOVATION INSIGHTS with Richard Langley

SATELLITES. I have been fascinated by them ever since I was a child. My interest in satellites and space in general led me on my career path, which began with an undergraduate degree in physics at the University of Waterloo. Although it was an applied physics program and I did work terms at Atomic Energy of Canada, I was more interested in astronomy than nuclear physics and took all the astronomy courses I could. That, in turn, led me to pursue a Ph.D. in experimental space science doing research in the application of very long baseline (radio) interferometry (VLBI) to geodesy. As a postdoctoral fellow at MIT, I worked on ranging data from the U.S. and Soviet laser reflectors placed on the surface of Earth’s natural satellite — the moon.

I continued my interest in VLBI and lunar laser ranging for a while after I arrived at the University of New Brunswick in 1981 but I quickly got involved with satellite Doppler positioning and that was when I heard my first satellite signals through the speaker of a Canadian Marconi CMA-722B Doppler receiver. At that time, Doppler positioning was being quickly supplanted by GPS and so my interest naturally migrated to the new system. GPS and the other global navigation satellite systems have been a consuming interest ever since.

That interest includes helping to develop techniques for precision positioning and navigation — ones that minimize as much as possible the effect of various sources of error that plague GPS measurements. One such technique is precise point positioning or PPP, which uses primarily precise carrier-phase measurements along with an accurate model of those measurements to obtain position accuracies down to the centimeter level.

Although often carried out with recorded data, PPP with real-time GPS orbit and clock correction streams has become an established technique for land, air and sea applications. However, the use of real-time corrections for precise positioning of satellites has not been attempted yet although a number of low-Earth-orbit (LEO) satellite missions could benefit from such a capability. Future satellites with altimeter and radio-occultation payloads may require real-time precise-orbit determination to enable onboard processing of science data for forecasting or now-casting of meteorology data, open-loop instrument operation of radar payloads, or quick-look onboard science data generation. Precise real-time orbit information could also be used for maintaining the formations of closely-spaced satellite constellations.

In this month’s column, our authors discuss the results of realistic simulations they have carried out to precisely position a LEO satellite using a source of real-time GPS corrections actually transmitted by a network of geostationary satellites. Even accounting for data outages, 3D positioning accuracies better than a decimeter have been obtained. Precision on board? Not right now but likely coming real soon.

Precise point positioning (PPP) with real-time orbit and clock correction streams has become an established technique over the past decade. Several free as well as commercial sources of precise correction streams are available through the internet or via a satellite link to geostationary satellites.

Many applications exist for land, air and sea applications, but use of real-time corrections for precise positioning has not extended into orbit yet, although a number of low Earth orbit (LEO) satellite missions have a demand for precise orbit determination (POD). Mission requirements often allow for a relatively high latency for the availability of the precise orbit products, thus ground-based, near-real-time processing is sufficient. However, future satellites with altimeter and radio-occultation payloads may require real-time POD to enable onboard processing of science data for short-term forecasting or now-casting of meteorology data, open-loop instrument operations of radar payloads, or quick-look onboard science data generation. Also, precise real-time orbit information may be used for constellation maintenance of satellite formations. Despite early technology readiness demonstrations by the Jet Propulsion Laboratory carried out one decade ago to transmit real-time corrections via geostationary relay satellites to LEO spacecraft, this technique has so far not been implemented and used in a space mission.

POD accuracy of a few decimeters or less with real-time corrections has been demonstrated repeatedly by various groups. For these studies, it was assumed that the required real-time precise orbit and clock products are continuously available on board the LEO satellite. Even though a network of several distributed geostationary Earth orbit (GEO) relay satellites may achieve seamless coverage in the equatorial region, gaps at high latitude close to the North and South Poles may occur. The extent of these gaps depends on the gain pattern of the transmitting antenna of the GEO relay satellite. Likewise, the availability of corrections depends on the LEO orbit characteristics, the gain pattern and mounting of the receiving antenna and the attitude profile of the LEO satellite. Most Earth observation and altimeter missions are launched into polar orbits to achieve global coverage. Up-to-date real-time corrections may therefore not be available for POD processing over the polar regions, which are typically also affected by reduced GNSS satellite visibility. As a result, the positioning performance will be degraded during this part of the orbit.

To study the effects of interrupted availability of precise correction data, we simulated real-time POD using real flight data of the Swarm-C satellite, a representative LEO satellite orbiting Earth at an altitude of about 440 kilometers in a polar orbit with approximately 87° inclination. The satellite was launched into orbit in Nov. 2013 and is part of a three-satellite constellation of identical spacecraft with the mission objective to study Earth’s magnetic field and the electric field in the atmosphere (see FIGURE 1). The orbital period is 93 minutes. The satellite is equipped with a dual-frequency GPS receiver and two zenith-pointing POD antennas. The receiver provides dual-frequency GPS observations of up to eight satellites simultaneously. For the analysis, we selected a test data period of Feb. 1–15, 2016.

FIGURE 1. Close-up view of the Swarm-C satellite with Swarm-A and -B in the background (artist’s impression). The satellites’ booms point in the anti-flight direction. Two GPS antennas are located on the top side of each satellite’s structure (Credit: ESA-AOES-Medialab).

We processed the GPS observations using a high-performance navigation filter together with precise real-time orbit and clock corrections provided by Fugro, a Dutch multi-national company that provides a multi-GNSS real-time PPP service tailored for maritime applications. The complete processing emulates real-time onboard POD and only uses information available up to the current epoch being processed. This information includes GNSS observations and ephemerides as well as satellite attitude information and predicted Earth orientation parameters.

We assessed POD accuracy by comparing the results of the real-time POD filter to a reference orbit, which was generated with a least-squares reduced-dynamics POD and precise post-processed GPS orbit and clock products. Correction data gaps over the polar regions were realistically simulated. During such gaps, an onboard POD filter cannot use the most recent corrections and may have to use outdated orbit and clock correction information for several minutes. We investigated the impact of outages of different durations on the positioning accuracy.

REAL-TIME ORBIT AND CLOCK PRODUCT

Fugro’s G4 reference station network consists of 45 geodetic receivers distributed worldwide, which deliver real-time multi-constellation GNSS observations and ephemerides to the processing centers located in Norway and Germany. Precise orbit and clocks are then computed in real time for all constellations and broadcast to the users via seven L-band geostationary satellites. GNSS orbits are computed using a batch process with hourly updates, and clocks are estimated at a 1-Hz rate in real time. G4 supports GPS, GLONASS and BeiDou. Galileo corrections will be made available to customers as soon as Galileo enters initial operational capability. The broadcast coverage ensures that the majority of users can receive corrections simultaneously through two independent satellite beams, thus ensuring redundancy and increased availability for critical operations at sea (see FIGURE 2).

FIGURE 2. Fugro’s G4 global GNSS station network for real-time orbit and clock generation. Colored dots at the equator show the positions of the geostationary relay satellites. Colored circles indicate the GEO access areas.

Additionally, uncalibrated phase delays (UPDs) for GPS are also estimated and broadcast in real time, which allows integer carrier-phase ambiguity resolution for PPP users requiring higher levels of accuracy. Typical real-time GPS orbit accuracy is 3–4 centimeters root-mean-square (rms) when compared with International GNSS Service final products. GPS clock accuracy is generally better than 0.1 nanoseconds (standard deviation). The accuracy of these products guarantees that end-user position accuracy is a few centimeters in real time. One of the objectives of our study is to determine whether the same level of accuracy can be achieved for real-time LEO POD.

ONBOARD NAVIGATION FOR LEO POD

The precise real-time orbit- and clock-products are used in a Kalman-filter-based real-time navigation algorithm, which has been developed for use in onboard navigation systems for LEO satellites. The algorithm is capable of processing single- or dual-frequency measurements and can be used with pseudoranges only or with both pseudorange and carrier-phase measurements. In the configuration used for this study, the filter processes dual-frequency pseudorange and carrier-phase GPS observations. The state vector comprises 12 + n states: satellite position and velocity vectors, receiver time offset, scaling coefficients for atmospheric drag and solar radiation pressure, empirical accelerations in radial-, along- and cross-track directions, and n carrier-phase ambiguities, one for each satellite tracked. The prediction model of the satellite’s trajectory considers accelerations due to Earth’s gravity field, luni-solar perturbations, drag, solar-radiation pressure, thrust and empirical accelerations.

Although the data is processed post facto in this study, the algorithm emulates a true real-time process by only using past and current observations in the data cleaning and quality control. Furthermore, the limited resources of a satellite onboard processor are taken into account by using only a reduced gravity field model of 70 × 70 terms and fixed Earth-orientation parameters. When processing dual-frequency pseudorange and carrier-phase measurements, typical 3D rms positioning errors are about 50 centimeters with GPS broadcast ephemerides and approximately 10 centimeters with precise orbit and clock products. The algorithm has flight heritage through the use in the Phoenix eXtended Navigation System (XNS) on board the PROBA2 PRoject for OnBoard Autonomy satellite.

The results of the real-time navigation algorithm were compared against reference orbit solutions generated with a precise reduced-dynamics POD, which is based on a least-squares fit using the final orbit products of the Center for Orbit Determination in Europe (CODE). Independent validation through satellite-laser-ranging measurements suggests an accuracy of the reference solution of a few centimeters.

POD WITH CORRECTIONS

For the precise real-time POD analysis, the navigation filter uses orbit and clock corrections together with GPS broadcast data. To assess the best possible real-time POD performance, the GPS observations from Swarm-C are processed with continuously available corrections. To take into account the latency in the clock correction generation process, the corrections are processed in the filter with an assumed delay of 10 seconds. The results for the 3D orbit errors are shown in FIGURE 3.

FIGURE 3. 3D orbit errors of the real-time navigation filter with continuous precise orbit and clock corrections based on Fugro’s products. The errors are plotted over argument of latitude u, where the northern-most point on the orbit corresponds to u = +90° and the southern-most point is u = −90°. 3D rms orbit errors are 6.8 centimeters.

The position errors of the two weeks of data are plotted vs. argument of latitude u, which is the sum of a satellite’s true anomaly and argument of perigee. As a result, the equator crossings of the satellite correspond to u = 0° and u = 180°. As the satellite proceeds along its orbit, it moves from left to right through the plot. The northern-most point on the orbit is reached at u = +90°, the southern-most point is u = −90°. The results show that a 3D rms LEO orbit accuracy of 6.8 centimeters can be achieved with the Fugro real-time orbits and clocks.

In addition, orbit and clock corrections are also generated based on the precise final orbits and clocks from CODE, which are used for the generation of the reference orbit solution. These corrections are also processed in the real-time navigation filter with the same settings as Fugro’s product. Comparison to the reference solution yields 3D rms orbit errors of 6.0 centimeters. This result demonstrates that the use of the real-time orbits and clocks only leads to a small degradation in the orbit accuracy compared to the use of post-processed GPS products.

EFFECTS OF CORRECTION DATA GAPS

The analysis in the previous section has shown that the use of real-time corrections enables high orbit accuracy when the corrections are continuously available. However, in an on-orbit scenario, the demodulator, which keeps track of GEO satellites and delivers corrections to the navigation filter, may not be able to track them continuously for various reasons. Even though dedicated GEO satellite networks for space-borne applications, like NASA’s Tracking and Data Relay Satellite System (TDRSS) or the European Data Relay Satellite (EDRS) system, potentially offer a seamless service volume for LEO users anywhere on the globe, this may not be feasible with a GEO network originally intended for ground-based users. These satellites typically have a more focused beam, which potentially hinders reliable data transmission in polar regions. This situation is depicted in FIGURE 4, which shows the approximate access areas of the GEO satellite network used to transmit Fugro’s corrections. It also depicts the ground track of two orbital revolutions of the Swarm-C satellite, which leaves the access areas at latitudes beyond approximately 80° N/S.

FIGURE 4. Coverage area of the GEO satellite network for orbit- and clock-correction dissemination (colored circles) and Swarm-C satellite ground track (black). Dotted lines indicate the assumed coverage area limits at 66° N/S and 75° N/S.

Even if the beamwidth of a GEO satellite’s antenna allows for a continuous link at high latitudes, the receiving satellite demodulator on board the LEO spacecraft will have to switch signal reception to another GEO satellite when the tracked satellite drops out of the field of view. These switches typically happen in polar regions. The acquisition of the new GEO signal is not a trivial task, as it is done under unfavorable conditions at the edge of the service area and requires, for example, correct prediction of the expected Doppler shift due to relative motion the GEO and LEO satellites. Thus, interruptions in the correction data streams are likely to occur and the extent of these interruptions depends on how the switching mechanism is implemented in the demodulator and how fast the acquisition of the new GEO satellite’s signal takes place.

It is worth mentioning in this context that GEO signal reception depends not only on the transmitting antenna gain pattern, but also on the gain pattern of the receiving antenna on the LEO satellite, the antenna placement on the satellite structure as well as its attitude profile. Experience has shown that satellite design constraints may prevent the antenna from being placed in the most favorable position. Operational constraints can force the satellite not to be oriented in the preferred way for GNSS and GEO signal reception. Instead, priority must often be given to the optimal orientation of body-fixed solar panels for maximum power generation or the pointing of payload sensors, such as optical instruments, to certain target directions.

To study the impact of correction data outage on the LEO POD, we defined reduced-coverage areas. The first scenario limits the reception of correction data beyond latitudes of 66° N/S. In the case of Swarm-C at approximately 440-kilometers altitude, the outage intervals over the North and South Poles extend to 13 minutes at maximum. In the second case, the corrections are received up to 75° N/S, which corresponds to a maximum outage of 8 minutes, twice per orbit. The smaller coverage area serves as a worst-case scenario, whereas the larger service area is more representative of the expected on-orbit performance.

Prediction of Orbit- and Clock-Corrections. When up-to-date corrections are no longer available due to an outage in the GEO satellite link, the last received set of corrections must be extrapolated. Up to a certain prediction interval, this method still provides more precise orbit and clock information than the broadcast ephemerides and thus yields better positioning results. The prediction of orbit and clock information is therefore crucial to bridge correction outages and still maintain a precise positioning solution. The following analysis assesses the errors introduced by only extrapolating the orbit and clock corrections. In addition to these errors, the modeling of the observations is also affected by the absolute errors in the real-time orbit and clock product.

The satellite clock offsets are estimated based on predicted orbits. Therefore, the radial, along-track and cross-track components of the orbit corrections can be computed so that prediction errors over a predefined time interval are minimized. Taking advantage of this, the prediction errors are typically less than 1 centimeter even for extrapolation times of 12 minutes and therefore have negligible effect on the POD.

In the case of the satellite clock offset, corrections are only available up to the present epoch. Thus, the extrapolation is done based on a fit through the past hour of data.

The results for the rms clock extrapolation errors over interpolation intervals of 0–15 minutes are displayed in FIGURE 5.

FIGURE 5. Clock extrapolation errors (rms) for different GPS block types for a linear clock extrapolation polynomial fitted through one hour of data. The results reflect the GPS constellation on Feb. 1, 2016. The largest errors are obtained for the two Block-IIF satellites SVN 38 (PRN 08) and SVN 65 (PRN 24) operated on cesium clocks (light-blue diamonds) and the rubidium clock of Block IIR-A satellite SVN 45 (PRN 21) (red diamonds).

The errors have been computed for clock data of Feb. 1, 2016, for each GPS satellite independently and are color-coded depending on the satellite type. It becomes obvious that the newest generation of Block IIF satellites with their rubidium atomic clocks yield the smallest extrapolation errors. After 15 minutes, the most stable clock has an rms error of approximately 0.10 nanoseconds and the least stable Block IIF rubidium clock does not exceed extrapolation errors of 0.15 nanoseconds. It is interesting to note that two Block IIF satellites are operated on cesium atomic clocks, which are significantly less stable than the rubidium ones. Their maximum rms clock extrapolation error (plotted in light blue) amounts to approximately 0.45 nanoseconds and 0.60 nanoseconds at the longest time interval of 15 minutes. The satellites of the GPS Block IIR (both the earlier IIR-As and the later IIR-Bs, which have a different transmitting antenna panel) and the IIR-M generations are equipped with less stable atomic clocks, which exhibit extrapolation errors of 0.15–0.25 nanoseconds. The Block IIR-A satellite SVN 45 plotted in red exhibits a clearly reduced stability, possibly an indication of degraded performance of its operational rubidium clock. The clock extrapolation error amounts to 0.40 nanoseconds at 15 minutes.

POD with Real-Time Correction Data Gaps. For the simulation of GEO-link outages in the real-time POD, the navigation filter starts extrapolating the orbit and clock corrections when the LEO satellite exceeds the latitude threshold. The 3D rms orbit errors are shown in FIGURE 6.

FIGURE 6. 3D orbit errors of real-time navigation filter results plotted over argument of latitude u, where the northern-most and southern-most point on the orbit correspond to u = +90° and u = −90°, respectively. Corrections are available between 66° S and 66° N (Figure 6a) and 75° S and 75° N (Figure 6b). The orange color indicates outage periods of the GEO-link when extrapolated corrections are used. 3D rms errors are 8.5 centimeters (Figure 6a) and 7.5 centimeters (Figure 6b).

The top plot depicts the conservative threshold of 66° N/S and the bottom plot refers to the threshold of 75° N/S. The orange color marks the time periods during which the corrections are extrapolated. It becomes obvious that the position solution degrades for increasing extrapolation intervals. In the case of the conservative latitude threshold, the maximum 3D position error is 38 centimeters and the rms error is 8.5 centimeters. For the latitude threshold of 75° N/S, the maximum error reduces to 33 centimeters and the rms to 7.5 centimeters. The plot also shows that the largest orbit errors typically do not appear at the end of the extrapolation interval, but shortly afterwards. The reason for this effect is that the systematic extrapolation errors in the clock corrections cause the filter state to diverge. When up-to-date corrections become available again, the filter requires a certain time to recover and converge back.

The degradation of the orbit accuracy is not only affected by the errors due to the clock extrapolation alone; the reduced GPS satellite visibility and unfavorable geometry over the North and South Poles also has an impact on the orbit determination performance. The resulting higher dilution of precision or DOP further amplifies the errors in the modeling of the GPS clock offset. Also, with only eight tracking channels available, the onboard receiver cannot track all visible satellites, leading to reduced measurement redundancy. Additional degradation of orbit accuracy is also caused when observations of GPS satellites are rejected in the data screening process due to the errors introduced by the extrapolation of corrections. Nevertheless, even for the conservative latitude thresholds for orbit and clock corrections, a 3D rms POD accuracy of less than 10 centimeters can be achieved with sufficient margin. This is an important result, since sub-decimeter POD accuracy is a key mission requirement for many space missions, such as radio occultation satellites.

To assess the effects of the absolute orbit and clock errors in the real-time orbit and clock product on the POD, we repeated the same processing procedure with corrections generated based on the CODE final products. In this case, the POD with the conservative latitude threshold of 66° N/S yields 7.2 centimeter 3D rms orbit errors, and the threshold of 75° N/S leads to 3D rms errors of 6.5 centimeters. These results confirm that the use of the real-time product leads to only a small degradation of the POD performance. The results for the orbit determination with continuous and limited availability of corrections are summarized in TABLE 1. In addition, a real-time POD with uncorrected broadcast ephemerides (BCEs) yields an accuracy of 36.4 centimeters.

Table 1. Overview of 3D rms orbit errors (in centimeters) for real-time POD based on different orbit and clock products and different latitude limits for the availability of precise corrections. The age of data (AoD) indicates the extrapolation interval of the corrections.

SUMMARY AND CONCLUSIONS

Onboard orbit determination simulations for the Swarm-C satellite with real-world flight data and precise real-time orbit and clock products from Fugro have achieved sub-decimeter 3D rms orbit errors. When the GPS orbit and clock corrections are continuously available, 6.8 centimeters 3D rms can be achieved. With conservative assumptions for correction data gaps at latitudes beyond 66° N/S, the 3D rms errors are still just 8.5 centimeters. This result fulfills the accuracy requirements of, for example, radio occultation missions with sufficient margin. This is an important result, as it allows us to shift the POD process from the ground into the spacecraft for future missions and thus provide a precise orbit solution without delay, with possible implications for onboard processing of science data, now-casting of meteorology data, or open-loop instrument operation of radar payloads.

Even though a small degradation of the POD accuracy is noticeable in the case of correction data gaps, the dissemination of precise orbit and clock corrections for LEO users is a competitive approach to a global centimeter-level augmentation service using high-rate data channels in the navigation signal itself. This service is presently only offered by the Quasi-Zenith Satellite System (QZSS) on the Michibiki L-band Experiment (LEX) signal and is limited to regional users.

The extrapolation error of the GPS satellite clock corrections has been identified as the main contributor to the error budget. The introduction of additional precise atomic clocks into the GPS constellation in the course of the GPS Block III deployment or the use of the Galileo satellites with their ultra-stable passive hydrogen masers in a multi-GNSS POD promise further improvements. Also, the use of Fugro’s uncalibrated phase delays to fix integer ambiguities in the POD would also lead to improved orbit results.

Having demonstrated the overall fitness of the concept, the development of an onboard real-time POD demonstrator will be the next step. This hardware unit requires a space-enabled dual-frequency GNSS receiver with a geodetic choke-ring antenna, an onboard processing unit for the navigation filter, and a demodulator unit with a suitable antenna, to receive and demodulate the corrections and provide them for the use in the POD.

ACKNOWLEDGMENTS

This article is based on the paper “Precise Onboard Orbit Determination for LEO Satellites with Real-Time Orbit and Clock Corrections” presented at ION GNSS+ 2016, the 29th International Technical Meeting of the Satellite Division of The Institute of Navigation, held Sept. 12–16, 2016, in Portland, Oregon.

The European Space Agency is acknowledged for the provision of Swarm-C GPS measurements. The Center for Orbit Determination in Europe is acknowledged for providing their precise GPS orbit and 5-second high-rate clock products for the POD reference solution.

ANDRÉ HAUSCHILD is a member of the scientific staff of the GNSS Technology and Navigation Group at DLR’s German Space Operations Center (GSOC), Oberpfaffenhofen, near Munich.

JAVIER TEGEDOR works as a GNSS scientist for Fugro Satellite Positioning AS in Oslo, Norway, focusing on the enhancement of Fugro’s high-accuracy positioning services and solutions.

OLIVER MONTENBRUCK is head of the GNSS Technology and Navigation Group at DLR/GSOC.

HANS VISSER works for Fugro-Intersite BV in the Netherlands monitoring the Fugro network.

MARKUS MARKGRAF is a senior research engineer in the GNSS Technology and Navigation Group at DLR/GSOC.

Innovation: Orbit determination of LEO satellites with real-time corrections