GRACE-A Satellite Research Articles

Atmospheric Density Inversion Based on Swarm-C Satellite Accelerometer

We used the Swarm-C accelerometer data to invert the orbital atmospheric density in this study. First, the Swarm-C satellite mission data were obtained from the ESA’s public data platform, and preliminary data error correction was performed. This paper refers to the calibration method of GRACE-A satellite accelerometer data. It adds linear temperature correction on the original basis. Moreover, this study’s accelerometer data correction results were compared with the data correction results published by the ESA. In order to explore the influence of light radiation on the accelerometer, we established a geometric model of Swarm-C to simulate the physical shape of the satellite surface. The light radiation pressure model and the shadow area judgment model were established, the change in the light radiation acceleration during the transition process of the satellite from the umbra area to the penumbra area and then to the shadowless area was studied, and the state transition during the transition process was analyzed. Finally, the atmospheric drag coefficient was calculated based on the Sentman model. Atmospheric density inversion calculations were performed using the above data. We show the spatial distribution of atmospheric density at a fixed latitude, testing our results during geomagnetic storms. We compared the density results with existing research data, demonstrating the effectiveness of our approach.

Adaptive Kalman Filter for Real-Time Precise Orbit Determination of Low Earth Orbit Satellites Based on Pseudorange and Epoch-Differenced Carrier-Phase Measurements

Real-time precise orbit determination (POD) of low earth orbiters (LEOs) is crucial for orbit maintenance as well as autonomous operation for space missions. The Global Positioning System (GPS) has become the dominant technique for real-time precise orbit determination (POD) of LEOs. However, the observation conditions of near-earth space are more critical than those on the ground. Real-time POD accuracy can be seriously affected when the observation environment suffers from strong space events, i.e., a heavy solar storm. In this study, we proposed a reliable adaptive Kalman filter based on pseudorange and epoch-differenced carrier-phase measurements. This approach uses the epoch-differenced carrier phase to eliminate the ambiguities and thus reduces the significant number of unknown parameters. Real calculations demonstrate that four to five observed GPS satellites is sufficient to solve reliable position parameters. Furthermore, with accurate pseudorange and epoch-differenced carrier-phase-based reference orbits, orbital dynamic disturbance can be detected precisely and reliably with an adaptive Kalman filter. Analyses of Swarm-A POD show that sub-meter level real-time orbit solutions can be obtained when the observation conditions are good. For poor observation conditions such as the GRACE-A satellite on 8 September 2017, when fewer than five GPS satellites were observed for 14% of the observation time, 1–2 m orbital accuracy can still be achieved with the proposed approach.

The influence of tesseral harmonic $J_{22}$ term on the TLE orbit error of low polar orbit satellite

By expanding the perturbation function of tesseral harmonic $J_{22}$ term of the earth’s non spherical gravitation, it is found that there is a term $\cos 2\Omega _{e}$ related to the rotation of the earth. The period of the term is half a day, and the coefficient includes the factor $\sin ^{2}i$ related to the orbital inclination angle. For the low polar orbit satellite with orbit inclination close to $90^{\circ }$ , $J_{22}$ term has a great impact on the orbit accuracy, which will reach the order of kilometers. Based on the measured orbit data (historical TLEs and GPS precise ephemeris) of the polar satellite GRACE-A/B, the influence of the tesseral harmonic $J_{22}$ term on TLE orbit error is further verified. It is found that the system bias caused by ignoring $J_{22}$ term exists in TLE orbit data for LEO, which shows a periodic change of 180 degrees with the geographic longitude in the in-track direction. In addition, the accuracy of TLE orbit in the northern hemisphere is significantly higher than that in the southern hemisphere, which is related to the distribution of SSN observation network. For GRACE-A satellite, the maximum system bias of TLE orbit can reach close to 1.5 km near the equator of the earth, and 8 km after a 7-day prediction period.

Impact of GPS receiver antenna GRAPHIC residual variations on single-frequency orbit determination of LEO satellites

Single-frequency (SF) precise orbit determination (POD) using space-borne Global Positioning System (GPS) measurements is a prerequisite for the success of many low-cost small/micro low Earth orbit (LEO) satellite missions. The first-order ionospheric effects are usually eliminated by group and phase ionospheric correction (GRAPHIC) combinations. GPS receiver antenna GRAPHIC residual variations (GRVs) are important systematic error sources in SF orbit determination. Azimuth and elevation dependent GRVs are estimated and obtained based on the GRAPHIC combination residuals in an in-flight calibration. One month of data from GRACE-A, GRACE-B, CHAMP and HY-2A satellites is used to assess the potential of receiver antenna GRVs in SF orbit determination. It is the first time to study the impact of receiver antenna GRVs on SF orbit determination for different LEO satellites, which exhibit different altitudes and data qualities. The impact of receiver antenna GRVs on SF orbit determination is significant. The use of in-flight determined receiver antenna GRVs leads to a better consistency between SF and dual-frequency POD solutions. The improvements are more obvious for GRACE-A and CHAMP satellites, whose receiver antenna GRV patterns demonstrate clear characteristics of systematic deviations. After correcting the receiver antenna GRVs, the root-mean-square of satellite laser ranging validation residuals are 3.11 cm, 2.31 cm, 2.86 cm and 5.29 cm for GRACE-A, GRACE-B, CHAMP and HY-2A satellites, respectively, which are reduced by 11.1%, 4.6%, 14.6% and 4.7%, respectively. At last, a set of a priori GDV corrections of GPS transmitter antennas are used in SF orbit determination and its effects on receiver antenna GRVs estimation and SF orbit determination are analyzed. Applying these corrections can slightly improve the SF orbit quality of GRACE-A satellite.

Estimation of SLR station coordinates by means of SLR measurements to kinematic orbit of LEO satellites

Generally, the dynamical model is used to estimate coordinates of satellite laser ranging (SLR) stations. In this paper, we put forward a kinematic method to estimate the coordinates of SLR stations by using global navigation satellite system (GNSS) technique onboard a low Earth orbiting (LEO) satellite. We applied it to the processing of SLR and GNSS observations of the GRACE-A satellite from January to December 2012. We found that the LEO satellite as a space-based connection between SLR and GNSS techniques allowed the precise estimation of SLR site positions with the agreement level of 2–3 cm with respective to SLRF2014. The SLR network can be attached to the IGS network at the centimeter level. The results show that the proposed method is feasible for determining the coordinates of SLR stations as an idea for the satellite-based integration of different space geodetic techniques.

A shadow function model based on perspective projection and atmospheric effect for satellites in eclipse

Accurate Solar Radiation Pressure (SRP) modelling is critical for correctly describing the dynamics of satellites. A shadow function is a unitless quantity varying between 0 and 1 to scale the solar radiation flux at a satellite’s location during eclipses. Errors in modelling shadow function lead to inaccuracy in SRP that degrades the orbit quality. Shadow function modelling requires solutions to a geometrical problem (Earth’s oblateness) and a physical problem (atmospheric effects). This study presents a new shadow function model (PPM_atm) which uses a perspective projection based approach to solve the geometrical problem rigorously and a linear function to describe the reduction of solar radiation flux due to atmospheric effects. GRACE (Gravity Recovery And Climate Experiment) satellites carry accelerometers that record variations of non-conservative forces, which reveal the variations of shadow function during eclipses. In this study, the PPM_atm is validated using accelerometer observations of the GRACE-A satellite. Test results show that the PPM_atm is closer to the variations in accelerometer observations than the widely used SECM (Spherical Earth Conical Model). Taking the accelerometer observations derived shadow function as the “truth”, the relative error in PPM_atm is −0.79% while the SECM 11.07%. The influence of the PPM_atm is also shown in orbit prediction for Galileo satellites. Compared with the SECM, the PPM_atm can reduce the radial orbit error RMS by 5.6 cm over a 7-day prediction. The impacts of the errors in shadow function modelling on the orbit remain to be systematic and should be mitigated in long-term orbit prediction.

Comparison of precise orbit determination methods of zero-difference kinematic, dynamic and reduced-dynamic of GRACE-A satellite using SHORDE software

Abstract Zero-difference kinematic, dynamic and reduced-dynamic precise orbit determination (POD) are three methods to obtain the precise orbits of Low Earth Orbit satellites (LEOs) by using the on-board GPS observations. Comparing the differences between those methods have great significance to establish the mathematical model and is usefull for us to select a suitable method to determine the orbit of the satellite. Based on the zero-difference GPS carrier-phase measurements, Shanghai Astronomical Observatory (SHAO) has improved the early version of SHORDE and then developed it as an integrated software system, which can perform the POD of LEOs by using the above three methods. In order to introduce the function of the software, we take the Gravity Recovery And Climate Experiment (GRACE) on-board GPS observations in January 2008 as example, then we compute the corresponding orbits of GRACE by using the SHORDE software. In order to evaluate the accuracy, we compare the orbits with the precise orbits provided by Jet Propulsion Laboratory (JPL). The results show that: (1) If we use the dynamic POD method, and the force models are used to represent the non-conservative forces, the average accuracy of the GRACE orbit is 2.40cm, 3.91cm, 2.34cm and 5.17cm in radial (R), along-track (T), cross-track (N) and 3D directions respectively; If we use the accelerometer observation instead of non-conservative perturbation model, the average accuracy of the orbit is 1.82cm, 2.51cm, 3.48cm and 4.68cm in R, T, N and 3D directions respectively. The result shows that if we use accelerometer observation instead of the non-conservative perturbation model, the accuracy of orbit is better. (2) When we use the reduced-dynamic POD method to get the orbits, the average accuracy of the orbit is 0.80cm, 1.36cm, 2.38cm and 2.87cm in R, T, N and 3D directions respectively. This method is carried out by setting up the pseudo-stochastic pulses to absorb the errors of atmospheric drag and other perturbations. (3) If we use the kinematic POD method, the accuracy of the GRACE orbit is 2.92cm, 2.48cm, 2.76cm and 4.75cm in R, T, N and 3D directions respectively. In conclusion, it can be seen that the POD of GRACE satellite is practicable by using different strategies and methods. The orbit solution is well and stable, they all can obtain the GRACE orbits with centimeter-level precision.

Precise orbit and baseline determination for maneuvering low earth orbiters

Orbital maneuvers are usually performed as needed for low earth orbiters to maintain a predefined trajectory or formation-flying configuration. To avoid unexpected discontinuities and to connect pre- and post-maneuver arcs with a minimal set of parameters, a maneuver has to be considered in the routine GPS-based orbit determinations. We propose a maneuver handling method in a reduced-dynamic scheme. With the proper thrust modeling and numerical integration strategy, the effects caused by orbital maneuver can be largely eliminated. The performance for both single-satellite precise orbit determination (POD) and inter-satellite precise baseline determination (PBD) is demonstrated using selected data sets from the Gravity Recovery and Climate Experiment (GRACE) mission. For the POD results, the orbit determination residuals indicate that the orbit with maneuver modeling is well fit to the GPS observations. The external orbit validation shows that the GRACE-B orbits obtained from our approach match the DLR reference orbits better than 3 cm (3D RMS), which is comparable to the result of the maneuver-free GRACE-A satellite. For the PBD results, on average 87 % of double-difference phase ambiguities can be resolved to integers and an RMS of the K-band ranging system residuals of better than 0.7 mm can be achieved, even though the orbital maneuver was performed on the spacecraft. Furthermore, the actual maneuver performance derived from the POD and PBD results provides rigorous feedback on the thruster system, which is not only beneficial for current maneuver assessment but also for future maneuver plans.

Precise Orbit Determination of GRACE-A Satellite with Kinematic GPS PPP

Precise Point Positioning (PPP) has been widely used in navigation and orbit determination applications as we can obtain precise Global Positioning System (GPS) satellite orbit and clock products. Kinematic PPP, which is based on the GPS measurements only from the spaceborne GPS receiver, has some advantages for a simple precise orbit determination (POD). In this study, we developed kinematic PPP technique to estimate the orbits of GRACE-A satellite. The comparison of the mean position between the JPL's orbit product and our results showed the orbit differences 0.18 cm, 0.54 cm, and 0.98 cm in the Radial, in Along-track, and Cross-track direction respectively. In addition, we obtained the root mean square (rms) values of 4.06 cm, 3.90 cm, and 3.23 cm in the satellite coordinate components relative to the known coordinates.

Quality assessment of FORMOSAT-3/COSMIC and GRACE GPS observables: analysis of multipath, ionospheric delay and phase residual in orbit determination

The precise orbit determination antennas of F3/C and GRACE-A satellites are from the same manufacturer, but are installed in different configurations. The current orbit accuracy of F3/C is 3 cm at arcs with good GPS data, compared to 1 cm of GRACE, which has a larger ratio of usable GPS data. This paper compares the qualities of GPS observables from F3/C and GRACE. Using selected satellites and time spans, the following average values for the satellite F3/C and satellite A of GRACE are obtained: multipath effect on the pseudorange P1, 0.78 and 0.38 m; multipath effect on the pseudorange P2, 1.03 and 0.69 m; occurrence frequency of cycle slip, 1/29 and 1/84; standard error of unit weight, 4 and 1 cm; dynamic–kinematic orbit difference, 10 and 2 cm. For gravity determination using F3/C GPS data, a careful selection of GPS data is critical. With six satellites in orbit, F3/C’s large amount of GPS data will make up the deficiency in data quality.

GPS Radio Occultation: Results from CHAMP, GRACE and FORMOSAT-3/COSMIC

The Taiwan/US FORMOSAT-3/COS MIC (FORMOsa SATellite mission - 3/Constellation Observing System for Meteorology, Ionosphere and Climate) satellite constellation was success fully launched on 14 April 2006. It is expected to leverage the use of the GPS (Global Positioning System) radio occultation data for atmospheric and ionospheric research to improve global weather forecasts and aid climate change related studies. FORMOSAT-3/COSMIC, together with the European MetOp, German CHAMP and US/Ger man GRACE-A satellites, form a 9 satellite constellation for precise atmospheric sounding on a global scale. This satellite constellation is expected to provide about 3500 occultation measurements daily. Recent results and the status of the CHAMP and GRACE-A orbit and occultation data analysis are reviewed and complemented with a review of initial results from FORMOSAT-3/COSMIC at GFZ. The significantly in creased potential of the CHAMP, GRACE-A and FORMOSAT-3/COSMIC constellation for atmospheric studies, compared to single satellite missions, is demonstrated for selected applications such as global monitoring of water vapor distributions, tropopause parameters and ionospheric irregularities.

Performance of GPS-based accelerometry: CHAMP and GRACE

Extensive recovery experiments based on GPS satellite-to-satellite tracking data from the CHAMP and GRACE-A satellites show that the performance of GPS-based accelerometry is comparable for both satellites. Several different quality measures like the recovery error, correlation and the contribution measure are used to assess the performance of GPS-based accelerometry and these quality measures indicate that the best performance is obtained in along-track direction. In cross-track direction the performance is slightly worse and due to correlations between the accelerations and the initial conditions in cross-track direction, a bias in this direction seems hardly observable. Unfortunately, GPS-based accelerometry is hardly sensitive in radial direction, due to correlations between the accelerations in the radial direction and the initial conditions in radial and along-track direction. It is shown that predominantly the longer wavelengths are well determined and high-frequency accelerations, caused by e.g. geomagnetic storms, are not well recovered.