GPS-based Precise Orbit Determination Research Articles

GPS-Based Precise Orbit Determination of LEO Satellites Using Space-Based Double-Differenced Observations

One of the important GPS applications in space is precise orbit determination (POD) of Low-Earth Orbit (LEO) satellites. Thousands of LEO satellites are currently in orbit. One of the challenges is how to efficiently and precisely determine the orbits to satisfy the relative and absolute accuracy needs of missions. Currently, GPS-based POD of LEO satellites can be performed using either un-differenced (UD) or ground-based double-differenced (DD) observations. The UD POD needs both precise GPS satellite orbits and clocks; the DD POD needs not only the precise orbits, but also global ground reference receivers. Therefore, the GPS-based LEO POD is based on either global ground stations or precise GNSS clocks, which are not convenient for near real-time or real-time data processing. The GPS orbits can be precisely predicted in certain time; the clocks are not. For some formation flying satellite missions (two or more LEO satellites), the absolute orbit accuracy requirements are not as stringent as the relative requirements. The problem is how to perform LEO POD without global station data and precise GPS clocks in near real-time or real-time to achieve the mission orbit accuracy requirement. Based on this motivation, we investigated the GPS-based LEO POD using space-based DD observations without using global ground station GPS data and precise GPS clock products. For this study, we processed the real GPS observations from two LEO satellites. The absolute and relative orbit accuracy is assessed using several tests, including analysis of the orbit fits, external orbit comparisons, Satellite Laser Ranging (SLR) and K-band Ranging (KBR) residuals.

Precise orbit determination and precision comparison for FY3C and FY3D with receiver antenna GPS and BDS PCV using spaceborne BDS and GPS observation data

The FY3C and FY3D satellites were equipped with global navigation satellite occultation detector (GNOS) receivers that received both GPS and BDS-2 signals. For further improving precise orbit determination (POD) precisions, we estimated receiver GPS and BDS signal phase center variations (PCV) models with 2° and 5° resolutions and set the different weights for GPS and BDS-2 observations in the combined POD. The BDS-based POD precision using BDS-2 satellite antenna phase center offset (PCO) values from the China Satellite Navigation Office (CSNO) are not as accurate as those obtained from the International GNSS Service (IGS) Multi-GNSS experiments project (MGEX). The estimated receiver GPS and BDS PCV models with 2° and 5° resolutions were estimated from the GPS phase residuals of GPS-based POD and BDS phase residuals of combined POD, respectively. In most cases, the POD precisions using the estimated PCVs with 2° resolution are superior to those with 5° resolution. The precisions of the BDS-based POD and combined POD were both improved by introducing the receiver BDS PCV models. The weighting for GPS and BDS-2 observations can further improve the precision of the combined POD. The tested results of selected weights are better than those with equal weight in the combined POD. The experiment results show that orbital precisions of FY3C are worse than those of FY3D.

Research on the Impact of BDS-2/3 Receiver ISB on LEO Satellite POD

In recent years, the multi-GNSS positioning application is becoming more and more popular, same to the low Earth orbit (LEO) satellite precise orbit determination (POD) based on the onboard multi-GNSS measurements. The third-generation Beidou navigation satellite system (BDS-3) provides a new option to obtain the LEO satellite orbit solutions. However, the receiver intersystem bias (ISB) of different GNSS is unavoidable in multi-GNSS data processing. This paper’s main goal is absorption of the impact of the ISB between BDS-3 and BDS-2 on the LEO satellite POD. Taking GPS-based POD solutions for the reference orbit, this paper evaluates the orbit accuracy of BDS-2-based POD, BDS-3-based POD, BDS-2 and BDS-3 combined PODs with/without ISB. The BDS-3-based POD accuracy is 6.57 cm in the 3D direction, a 56% improvement over BDS-2-based POD. When the ISB between BDS-3 and BDS-2 is estimated, the BDS-2/3 combined POD accuracy of 5.37 cm in the 3D direction is better than that without ISB, which is a 64% improvement over BDS-2-based POD and 18% improvement over BDS-3-based POD. For GPS and BDS-2/3 combined POD, the GPS and BDS-3 joint POD solutions have the smallest RMS differences in overlapping consistency and smallest RMS differences compared to GPS-based POD. This study indicates that estimating the BDS-2/3 receiver ISB in BDS-2/3 joint POD could improve the orbit accuracy, and the GPS and BDS-3 joint POD solution is better than another combined POD. This paper will provide meaningful references for the LEO satellite multi-GNSS-based POD.

COST-G gravity field models for precise orbit determination of Low Earth Orbiting Satellites

Accurate time-variable Earth’s gravity field information is important for precise orbit determination (POD) of low Earth orbiters (LEO). In particular the POD of altimeter satellites benefits from accurate modelling of the time-variable gravity field. The Combination Service for Time-variable Gravity Fields (COST-G) provides monthly gravity fields based on a combination of GRACE/GRACE-FO derived monthly gravity field solutions from different analysis centers. These monthly solutions are available with a latency of 2–3 months. The monthly GRACE-FO gravity fields from June 2018 to June 2021 serve as base for a fitted signal model (FSM) of time-variable gravity that enables a few months prediction and therefore application in operational LEO POD. The combined monthly solutions themselves, as well as several variants of the FSM are used for GPS-based POD of Copernicus Sentinel-2 and −3 satellites flying at altitudes of 786km and 814,5km, respectively. The orbit results show a significant improvement when using both, the COST-G monthly and the new COST-G FSM gravity field models compared to results using existing long-term static gravity field models, including seasonal and trend estimates, as well. RMS values of the GPS carrier phase residuals are reduced up to 20%, orbit overlaps between 30–50%. Orbit validations performed by Satellite Laser Ranging (SLR) also show that SLR residuals are reduced by about 10%. The COST-G FSMs show a similar performance as the monthly gravity fields. The LEO POD in particular benefits from the more realistic mass trend estimates in river basins with strong non-periodic inter-annual variations compared to the predicted trends of outdated long-term gravity fields. The FSM thus complements the monthly gravity fields as a new COST-G product. It is foreseen to update the COST-G FSM quarterly.

Dynamic GPS-based LEO orbit determination with 1 cm precision using the Bernese GNSS Software

The Astronomical Institute of the University of Bern (AIUB) has been performing GPS-based Precise Orbit Determination (POD) for a large variety of Low Earth Orbit (LEO) satellites since two decades. Traditionally, LEO orbits have been generated by a reduced-dynamic POD strategy using the Bernese GNSS Software, replacing an explicit modeling of non-gravitational forces by dedicated empirical orbit parametrizations. This LEO POD strategy can be advanced by two main developments: on the one hand, use is made of the GNSS Observation-Specific Bias (OSB) and clock products provided by the Center for Orbit Determination in Europe (CODE), allowing for the resolution of single-receiver GNSS carrier-phase ambiguities. On the other hand, the main focus of this article, a refined satellite non-gravitational force modeling strategy is constructed to reduce the amount of empirical parameters used to compensate for force modeling deficiencies. LEO POD is first performed for Sentinel-3, a satellite formation currently consists of two identical satellites −3A and −3B, which experience a similar in-flight environment and allow for direct POD performance comparisons. A third satellite Swarm-C, which flies at a lower altitude and has a more sophisticated surface geometry, is selected to validate the robustness of the new POD strategy. As a result, both the internal consistency checks and external orbit validations suggest superior orbit quality obtained for the three satellites for a time span of 1.5 years (7 June, 2018 to 31 December, 2019). The ambiguity resolution adds strong constraints to the orbits and the satellite non-gravitational force modeling leads to more tightly constrained (towards zero) pseudo-stochastic empirical parameters. The final orbit solutions agree with external orbit solutions and independent satellite laser ranging measurements at levels of sub-cm, indicating approximately 20% improvement w.r.t. the nominal reduced-dynamic orbit solutions. This suggests potential benefits to the space geodesy community that always pursues best-possible satellite orbits.

Precise Orbit Determination of the China Seismo-Electromagnetic Satellite (CSES) Using Onboard GPS and BDS Observations

The Global Navigation Satellite System (GNSS) occultation receiver onboard the China Seismo-Electromagnetic Satellite (CSES) can provide dual-frequency observations for both GPS and BDS-2 satellites. In this study, the data quality and orbit determination performance of the CSES are assessed. Severe data loss of about 30% is observed in GPS P2/L2 data, resulting in only 11% of epochs possessing six to eight useful GPS satellites. Due to fewer channels being allocated for BDS signals, less than 5% of epochs have more than three useful BDS satellites. Precise orbit determination (POD) of CSES is firstly carried out using GPS data. The results indicate that the orbit overlap differences improved from 3.65 cm to 2.8 cm in 3D root mean square (RMS) by antenna phase center correction. CSES orbits are then derived from the BDS only, and combined GPS and BDS data. BDS-based POD indicates that adding BDS geostationary Earth orbit (GEO) satellites could dramatically degrade the orbit accuracy. When excluding BDS GEO satellites, the orbit overlap differences of BDS-based and combined POD are 23.68 cm and 2.73 cm in 3D, respectively, while the differences compared with GPS-based POD are 14.83 cm and 1.05 cm, respectively. The results suggest that the obtained orbit can satisfy centimeter-level requirements. Given that large GPS tracking losses occurred and few channels are allocated for BDS signals, it is expected that POD performance can be further improved by increasing the number of dual-frequency observations.

GRACE-FO precise orbit determination and gravity recovery

The gravity recovery and climate experiment follow-on (GRACE-FO) satellites, launched in May of 2018, are equipped with geodetic quality GPS receivers for precise orbit determination (POD) and gravity recovery. The primary objective of the GRACE-FO mission is to map the time-variable and mean gravity field of the Earth. To achieve this goal, both GRACE-FO satellites are additionally equipped with a K-band ranging (KBR) system, accelerometers and star trackers. Data processing strategies, data weighting approaches and impacts of observation types and rates are investigated in order to determine the most efficient approach for processing GRACE-FO multi-type data for precise orbit determination and gravity recovery. Two GPS observation types, un-differenced (UD) and double-differenced (DD) observations in general can be used for GPS-based POD and gravity recovery. The GRACE-FO KBR observations are mainly used for gravity recovery, but they can be also used for POD to improve the relative orbit accuracy. The main purpose of this paper is to study the impacts of the DD, UD and KBR observations on GRACE-FO POD and gravity recovery. The precise orbit accuracy is assessed using several tests, which include analysis of orbital fits, satellite laser ranging residuals, KBR range residuals and orbit comparisons. The gravity recovery is validated by comparing different gravity solutions through coefficient-wise comparison, degree difference variances and water height variations over the whole Earth and selected area and river basins.

GRACE accelerometer calibration by high precision non-gravitational force modeling

The precise modeling and knowledge of non-gravitational forces acting on satellites is of big interest to many scientific tasks and missions. Since 2002, the twin GRACE satellites have measured these forces in a low Earth orbit with highly precise accelerometers, for about 15 years. Besides the significance for the GRACE mission, these measurement data allow the evaluation of modeling approaches and the improvement of force models. Unfortunately, before any scientific usage, the accelerometer measurements need to be calibrated, namely scale factor and bias have to be regularly estimated.In this study we demonstrate an accelerometer calibration approach, solely based on high precision non-gravitational force modeling without any use of empirically or stochastically estimated parameters, using our in-house developed satellite simulation tool XHPS. The aim of this work is twofold, first we use the accelerometer data and the residuals resulting from the calibration to quantitatively analyze and validate different non-gravitational force model approaches. In a second step, we compare the calibration results to three different calibration methods from different authors, based on gravity field recovery, GPS-based precise orbit determination, and based on modeled accelerations.We consider atmospheric drag forces and winds, as well as radiation forces due to solar radiation pressure, albedo, Earth infrared and thermal radiation (TRP) of the satellite itself. For TRP, we investigate different transient temperature calculation approaches for the satellite surfaces with absorbed power from the aforementioned radiation sources. A detailed finite element model of the satellite is utilized for every force, considering orientation, material properties and shadowing conditions for each element.For cross-track and radial direction, which are mainly affected by the radiative forces, our calibration residuals are quite small when drag is not super dominant (1–3 nm/s2 for total accelerations around ±50 nm/s2). For these directions the calibration seems to perform better than the other compared methods, where some bigger differences were found. For the drag dominated along-track direction it is vice versa, here our method is not sensitive enough because the difference between modeled and measured drag is bigger (e.g. residuals around 10 nm/s2 for total accelerations around ±70 nm/s2 for low solar activity). In along-track direction the orbit determination based methods are more sensitive and produce more reliable results. Results for the complete GRACE mission time span from 2003 to 2017 are shown, covering different seasonal environmental conditions.

Self-consistent treatment of tidal variations in the geocenter for precise orbit determination

We show that the current levels of accuracy being achieved for the precise orbit determination (POD) of low-Earth orbiters demonstrate the need for the self-consistent treatment of tidal variations in the geocenter. Our study uses as an example the POD of the OSTM/Jason-2 satellite altimeter mission based upon Global Positioning System (GPS) tracking data. Current GPS-based POD solutions are demonstrating root-mean-square (RMS) radial orbit accuracy and precision of \({<}1\) cm and 1 mm, respectively. Meanwhile, we show that the RMS of three-dimensional tidal geocenter variations is \({<}6\) mm, but can be as large as 15 mm, with the largest component along the Earth’s spin axis. Our results demonstrate that GPS-based POD of Earth orbiters is best performed using GPS satellite orbit positions that are defined in a reference frame whose origin is at the center of mass of the entire Earth system, including the ocean tides. Errors in the GPS-based POD solutions for OSTM/Jason-2 of \({<}4\) mm (3D RMS) and \({<}2\) mm (radial RMS) are introduced when tidal geocenter variations are not treated consistently. Nevertheless, inconsistent treatment is measurable in the OSTM/Jason-2 POD solutions and manifests through degraded post-fit tracking data residuals, orbit precision, and relative orbit accuracy. For the latter metric, sea surface height crossover variance is higher by \(6~\hbox {mm}^{2}\) when tidal geocenter variations are treated inconsistently.

GPS-based precise orbit determination of Low Earth Orbiters with limited resources

The combination of GPS measurements and high-fidelity dynamic models via a Kalman filter/smoother, known as the reduced dynamic technique, allows 3D positioning of Low Earth Orbiters to the sub-decimeter level. Such accuracies can only be achieved if the GPS data are nearly continuous, post-processed and a dual-frequency receiver is utilized. The focus of this study is to quantitatively analyze the degradations in position accuracy in the presence of various limitations or constraints, which can be brought on by mission hardware limitations, for example, on micro- or nanosatellites. The constraints explored in this study are as follows: the use of single-frequency data only; real-time processing; limited dynamic modeling due to computing capabilities; and non-continuous GPS receiver operation due to power limits. The experiments are conducted with 6-h data arcs for 7 separate days using data from the CHAllenging Mini-Satellite Payload. A 3D root mean square (rms) error of 15 cm is observed in the best-case solution, in which dual-frequency data are post-processed with all available data. Various levels of accuracy degradations are observed as constraints are placed on this best-case solution. The 3D rms error of the post-processed, single-frequency solution is 68 cm and 1.3 m for the real-time, dual-frequency solution. In very challenging environments, for example, with the receiver on for only 10 min of a 90-min orbit, the 3D rms increases to 350 m.

Final commissioning of the PRISMA GPS navigation system

The primary relative navigation system of the PRISMA technology demonstration mission is based on GPS. The PRISMA satellites have been launched in June 2010 and, since their separation in August, have been successfully conducting a multitude of autonomous formation flying and on-orbit servicing experiments. The onboard navigation system relies on GPS measurements to provide in real-time accurate absolute and relative navigation. The output of the GPS-based navigation system is used to feed the numerous on-board feedback controllers and the safety monitoring and collision avoidance functions. As a consequence the navigation system has to provide the utmost accuracy to the experimental payloads and, at the same time, be robust and reliable to support fault detection isolation and recovery tasks. The commissioning of the GPS navigation system is therefore a crucial milestone for the mission. It has to be ensured that the onboard navigation solution is always reliable even in the presence of hardware anomalies and that the navigation performance satisfies the mission requirements. The performance assessment is done using precise orbit products generated by a ground facility for GPS-based precise orbit determination which needs, in turn, to be also commissioned. The paper summarizes the commissioning activities performed to validate both precise orbit products and onboard navigation and presents key flight results to illustrate the overall system performance.

Precise Near-Real-Time Sea Surface Height Measurements from the Jason-1 and Jason-2/OSTM Missions

Precise measurements of sea surface height from the Jason-1 and Jason-2/Ocean Surface Topography Mission satellite altimeter missions are being generated within seven and four hours, respectively, of real time by applying high accuracy orbit altitudes to their near-real-time altimetry products. The near-real-time orbit altitudes have respective accuracies of <2 and <1 cm (RMS), and the corresponding sea surface height measurements have accuracies of <4.0 and <3.5 cm, respectively. These near-real-time orbit solutions are computed using GPS-based precise orbit determination for Jason-2, and Jason-1/Jason-2 sea surface height crossover differences for Jason-1.

TerraSAR-X Precise Trajectory Estimation and Quality Assessment

Since the launch of TerraSAR-X on June 15, 2007, the required precise orbit products have been provided by the German Space Operations Center to support operational spaceborne synthetic aperture radar (SAR) and interferometric SAR image processing. The TerraSAR-X precise trajectory is reconstructed solely based on the Global Positioning System (GPS) measurements from a geodetic-grade dual-frequency Integrated Geodetic and Occultation Receiver (IGOR) onboard the spacecraft. The GPS-based precise orbit determination (POD) strategy used in the estimation of the precise TerraSAR-X orbit and its performance will be fully described in this paper. Five-month statistics from the internal and external orbit assessment indicate a root-mean-squared 3-D orbit accuracy of better than 10 and 20 cm for the precise science orbit and precise rapid orbit (PRO) products, respectively. The POD performance of the backup single-frequency MosaicGNSS receiver to support operational PRO product generation in case of IGOR tracking failure or interruptions is described as well.

Impact of GPS satellite antenna offsets on GPS-based precise orbit determination

Since the successful demonstration of GPS-based Precise Orbit Determination (POD) on TOPEX/Poseidon in 1992, GPS-based POD for Low-Earth Orbiters (LEO) such as the CHAMP and GRACE satellites has become a popular method. The orbit accuracy of GPS-based POD has been improved from 3 cm to 1 cm in the radial direction. In order to achieve higher-accuracy results, it is necessary to understand and try to reduce the impact of various error sources on the orbits. One of them is the GPS satellite antenna offset. Currently, most GPS data processing institutions are using relative GPS satellite antenna offsets, and there are big differences (meter level) between the antenna offsets. In addition, accurate antenna offset values can be only estimated from processing GPS data currently with an accuracy of cm to dm levels. In this paper, we studied the impact of GPS satellite antenna offsets on GPS-based POD using the different offsets. The results show that the antenna offsets have large effects (a few cm) on the GPS onboard receiver antenna estimation and relatively small effects (about one cm) on the satellite orbit accuracy.

DORIS satellite antenna maps derived from long-term residuals time series

Abstract Recent studies have shown that phase pattern models for the Jason-1 GPS antenna significantly benefit GPS-based precise orbit determination (POD) for the satellite. We have used a similar technique to derive DORIS receiver antenna maps, using all available DORIS tracking data over long time periods (from 1993.0 to 2004.0). We demonstrate that the derived correction models are satellite specific. For a given satellite, year-to-year estimations show clear systematic patterns. Some of these systematic patterns are attributable to the derivative of the multi-path effects in the direction of the satellite velocity. For early SPOT data, the patterns can be explained by an offset in the TAI time tagging (typically 8 μs). In a second step, we have applied the SPOT2 antenna correction models in precise orbit determination and in the positioning of ground beacons. Preliminary results on DORIS/SPOT2 show that application of the DORIS antenna maps lead to a slight improvement of the derived POD and geodetic results (typically less than 5%).

One-Centimeter Orbit Determination for Jason-1: New GPS-Based Strategies

The U.S./French Jason-1 satellite is carrying a state-of-the-art GPS receiver to support precise orbit determination (POD) requirements. The performance of the Jason-1 “BlackJack” GPS receiver was strongly reflected in early POD results from the mission, enabling radial accuracies of 1–2 cm soon after the satellite's 2001 launch. We have made further advances in the GPS-based POD for Jason-1, most notably in describing the phase center variations of the on-board GPS antenna. We have also adopted new geopotential models from the Gravity Recovery and Climate Experiment (GRACE). The new strategies have enabled us to better exploit the unique contributions of the BlackJack GPS tracking data in the POD process. Results of both internal and external (e.g., laser ranging) comparisons indicate that orbit accuracies of 1 cm (radial RMS) are being achieved for Jason-1 using GPS data alone.

GPS-based precise orbit determination of the very low Earth-orbiting gravity mission GOCE

A prerequisite for the success of future gravity missions like the European Gravity field and steady-state Ocean Circulation Explorer (GOCE) is a precise orbit determination (POD). A detailed simulation study has been carried out to assess the achievable orbit accuracy based on satellite-to-satellite tracking (SST) by the US global positioning system (GPS) and in conjunction the implications for gravity field determination. An orbit accuracy at the few centimeter level seems possible, sufficient to support the GOCE gravity mission and in particular its gravity gradiometer.

A History of GPS Sounding

The roots of GPS sounding go back to the first days of interplanetary flight. In the early 1960’s teams from Stanford University and the Jet Propulsion Laboratory exploited radio links between Earth and the Mariner 3 and 4 spacecraft to probe the atmosphere and other properties of Mars. Radio science has since been a staple of planetary exploration. Before the advent of GPS, application of radio occultation to Earth was deemed impractical, and it was not immediately evident that even GPS could be usefully adapted. Techniques devised for geodesy in the 1980’s, including “codeless” carrier reconstruction, clock elimination by double differencing, GPS-based precise orbit determination, and compact, low-cost receivers, set the stage. JPL submitted the first GPS occultation proposal to NASA in 1988. Though that “GPS Geoscience Instrument” did not fly, it established the concept and led soon to the GPS/MET experiment, conceived by the University Corporation for Atmospheric Research and sponsored by the US National Science Foundation. The remarkable success of GPSIMET has led NASA to mount follow-on experiments on five international missions, launching between 1999 and 2001. Those will refine the systems and techniques of GPS sounding, setting the stage for COSMIC-the first operational GPS occultation constellation.