Precise orbit determination for GRACE

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doi: lO.l016/SO273-1177(03)00159-5

PRECISE ORBIT DETERMINATION FOR GRACE Z. Kang’, P. Nagell, and R. Pastor’ ‘Center for Space Research,

University

of Texas, 3925 W. Braker Lane Suite 200, Austin,

TX 787S9, USA

ABSTRACT The twin, co-orbiting GRACE (Gravity Recovery and Climate Experiment) satellites were launched in March 2002. The primary objective of the GRACE mission is to determine the Earth’s gravity field and its temporal variations with unprecedented accuracy. To satisfy this objective as well as other applications (e.g. atmospheric profiling by radio occultation), accurate orbits for GRACE are required. This paper describes several results related to the use of the data collected by the GRACE GPS receiver, high precision accelerometer observations and precise attitude data from star trackers in the application of the GRACE Precise Orbit Determination (POD). The orbit accuracy is assessedusing a number of tests, which include analysis of GPS tracking observation residuals, Satellite Laser Ranging (SLR) residuals, K-Band Ranging (KBR) residuals and external orbit comparisons. The results show that an accuracy of better than 5 cm in each direction for GRACE orbits can be obtained. The relative accuracy of the two GRACE satellites is about 1 cm in position and 10 micrometers per second in velocity. 0 2003 COSPAR. Published

by Elsevier Science Ltd. All rights reserved.

INTRODUCTION GRACE (Gravity Recovery And Climate Experiment) is a joint project between the National Aeronautics and Space Administration (NASA) and the Deutsches Zentrum ftir Luft- und Raumfahrt (DLR). The primary objective of the GRACE mission is to map, with unprecedented accuracy, the long- to medium-wavelength spherical harmonic coefficients of the Earth’s gravity field and to observe its temporal variations (Tapley, B., and C. Reigber, 2002). To satisfy this objective as well as other applications (e.g. atmospheric profiling), accurate orbits for GRACE are required. The twin GRACE satellites were launched in March 2002 into near polar orbits with an initial altitude of 500 km. For the Precise Orbit Determination (POD) and gravity field recovery, both GRACE satellites are equipped with the following key science instruments: a Black-Jack GPS onboard receiver, a SuperSTAR accelerometer, a star tracker, a K-Band Ranging (KBR) system and a laser retro reflector. The Black-Jack receiver is an advanced codeless, dual frequency flight GPS receiver developed by the Jet Propulsion Laboratory (JPL). The SuperSTAR accelerometer, which is manufactured by ONERA, measures the non-gravitational accelerations due to surface forces acting on the spacecraft, such as atmospheric drag and solar radiation pressure. The star tracker measures the precise satellite attitude which is needed to translate the accelerometer data from the instrument reference system to the inertial reference system In addition, the data from the KBR system and laser retro reflector can be used for evaluation of GRACE POD results. This paper describes the POD methodology for GRACE using the high accuracy GPS tracking and accelerometer data, along with the attitude data from the star trackers. The study was performed using the CSR Multi-Satellite Orbit Determination Program MSODP, which is based on a dynamic orbit determination method utilizing the batch processing approach (Rim, 1992). The data used are GRACE level 1B products produced by the NASA JPL. The orbit accuracy is evaluated by analyzing GPS tracking observation residuals, by confirmation of the orbit solution with independent SLR tracking. Adv. Space Res. Vol. 31, No. 8, pp. 1875-1881.2003 8 2003 COSPAR. Published by Elsevier Science Ltd. All rights Printed in Great Britain 0273-l 177/03 $30.00 + 0.00

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STRATEGIES

The use of GPS-SST (Global Positioning System-Satellite to Satellite Tracking) for low-Earth satellite orbit determination is presently considered to be the most powerful method. The main advantage of this system is that it allows continuous and multi-dimensional tracking of low-Earth satellites. Therefore, a number of orbit determination methods have been used to determine the low-Earth satellite orbits using GPS-SST data. One is the traditional dynamic method which relies on physically accurate force models. A second method is the kinematic orbit determination which requires only the geometric information contained in GPS observations. A third one is the reduced dynamic orbit determination which optimally weights the force model and geometric information (Kang et al. 2002). Using the dynamic orbit determination method, we can not only determine the satellite orbits, but also improve the force models such as the Earth’s gravity field model. However, the orbit accuracy depends on the quality of the force models used in the dynamic solution. The orbit quality obtained with the kinematic method depends on the configuration and the measurement noise and the quality of the orbit and clock solutions of the GPS satellites (Kuang et al. 2001). With the reduced dynamic technique, one can balance force model and measurement errors and try to obtain an optimal solution. The differences between the dynamic and reduced dynamic method are smaller when using better force models and solving for many empirical parameters. Usually, not only the satellite orbits are obtained, but also the gravity field model is adjusted. The dynamic orbit determination method for GRACE was selected for this study. As is known, the orbit accuracy depends heavily on the force models used in the dynamic orbit determination, but the forces acting on the low-Earth satellites are currently not modeled precisely enough, including the nonconservative forces. In order to solve this problem, the GRACE mission uses a three-axis accelerometer to measure the non-gravitational accelerations. Two different approaches were used to reduce the effects of force model errors on precise orbit determination. One was to solve for many empirical acceleration parameters; the other was to tune the gravity model using GRACE data. GRACE DATA PROCESSING First, GPS double-differenced (GPS DD) carrier phase measurements were formed using about 40 global IGS stations (Rim et al. 2001). Next, precise orbits for the GRACE were determined using only GPS DD observation by fixing GPS satellite orbits to the IGS solution and solving for many drag coefficients (Cd) and one-cycle-perrevolution (1 cpr) Transverse (T) and Normal (N) empirical parameters. For comparison, precise orbits were also estimated using the combination of GPS DD, accelerometer and attitude observations. Finally, the orbit accuracy was assessedusing the methods outlined in the previous section. For the GRACE POD, the following force models were used: TEG4 (Tapley et al. 2000) and tuned gravity model, solid Earth and ocean tides, DTM density model (Barlier et al. 1978), solar radiation and Earth radiation pressure. The estimated parameters included GRACE initial position and velocity, GPS DD phase ambiguity, zenith delay parameters, drag coefficients, 1 cpr empirical parameters. The nonconservative force models are switched off when accelerometer observations are used in the POD, in which case accelerometer biases were included in the estimation process. POD TEST CASES For the GRACE POD, the GPS data were processed with and without accelerometer data. For the GPS data only case, three different parameterizations were tested to evaluate the effect of the sub-arc length on the GRACE orbit accuracy. Those are: case 1 (3-hour sub-arc Cd and 1 cpr T, N); case 2 (l/Zrevolution sub-arc Cd and 3-hour sub-arc 1 cpr T, N, and case 3 (3-hour sub-arc Cd and l/2 revolution sub-arc 1 cpr T, N). For comparison, two gravity models were used, TEG4 (which includes CHAMP data but not GRACE data) and a gravity model that was tuned with GRACE data. Finally, the comparison’ for GRACE-A satellite with GRACE-B satellite was performed using GPS DD RMS (Root-Mean-Square), SLR residuals and external orbit comparisons.

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Five one-day arcs (May 2 - 6,2002) were processed using GPS observations, in certain cases augmented with accelerometer observations. The GPS data were sampled at a 30-second interval, and a 5-second data interval was used for attitude and accelerometer data. RESULTS AND DISCUSSION The GRACE precise orbit determination using GPS data without and with accelerometer data was carried out based on the method and test cases described above. The orbit accuracy is assessedthrough a number of tests. as mentioned before. Different Sub-arc Length Table 1 summarizes the GRACE-A GPS DD RMS and SLR residuals for different sub-arc lengths. The RMS and residuals decrease as the sub-arc length decreases. The RMS of tit of the GPS DD observations should be about 1 cm according to the claimed noise level of phase observations (0.5 mm). The actual best GPS DD RMS of tit is about 1.1 cm. The difference between this RMS of fit and claimed observation precision is due to the error in the gravity model, GPS orbits etc. In addition, the GPS DD RMS of fit has about the same value for different arcs (1.05 - 1.14 cm). The GPS DD fits are treated as internal tests and are a measure the orbit precision, not the orbit accuracy. Certain types of systemic errors may not be included in those RMS values. As an independent, external evaluation of the GRACE orbit solution, SLR data were processed to compute the residuals by fixing the orbits. The five-day SLR residual is 2.29 cm. Table 2 gives the GRACE-A orbit comparison between CSR and JPL. It can be seen that the orbit differences decrease as the sub-arc length decreases. This means that the orbit accuracy is improved by increasing the number of parameters. Table 1. GRACE-A GPS DD RMS and SLR Residuals

Case 1 2 3

Table 2. GRACE-A Orbit Comparison between CSR and JPL [cm] (different sub-arc length for Cd and empirical parameters) Radial Along-track Cross-track 4.36 7.78 3.65 3.81 4.57 3.59 3.52 3.68 2.80

Position (3D) 9.60 6.95 5.81 -

One of the key science instruments onboard the GRACE satellites is the K-Band Ranging (KBR) system, which measures the dual one-way range change between the twin GRACE satellites with a precision of about 10 micrometers for KBR range and 1 micrometer per second for KBR range rate with a 5-second data interval. The KBR data are used mainly for gravity field recovery. But the KBR data residuals computed by fixing the GRACE POD orbits can be used for evaluating the relative orbit accuracy of the GRACE. Figures 1 and 2 show the KBR range and range rate residuals. It can be seen that the KBR residuals are nearly the same for the different cases. This means that the absolute accuracy of the orbits can be improved by solving for more Cd and empirical parameters, but the relative accuracy is not significantly improved in those tests. The KBR range residual is about 1 cm; the KBR range rate residual is about 10 micrometers per second.

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Fig. 2. GRACE KBR Range Rate RMS Different Gravity Models The orbit accuracy in the dynamic solution depends on the accuracy of the force models. Generally, the orbit accuracy can be improved using the gravity model tuned with satellite data collected by the satellites under study. The TEG4 gravity model has already included the CHAMJ? satellite data and because the CHAMP and GRACE satellites are flying in similar orbits, it is anticipated that the tuned gravity model cannot improve the orbit

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accuracy substantially. The TEG4 gravity field model includes 8Odays of CHAMP data. The tuned gravity model is obtained by processing 14days of GRACE GPS and KBR data. Tables 3 and 4 show the results for different gravity models. The GPS DD RMS of fit shows little improvement. The SLR residual is reduced from 3.64 cm to 2.29cm. For the comparison with external orbits, the results are nearly the same for both gravity models. Table 3. GRACE-A GPS DD RMS and SLR Residuals

Total

Case TEG4 Tuned

1.11

1.10

3.64

2.29

Table 4. GRACE-A Orbit Comparison between CSR and JPL [cm] (different gravity models) Radial Along-track 1 Cross-track 1 3.32 3.72 2.80 3.52 3.68 2.80

383

Position (3D) 5.71 5.81

Combination of GPS Tracking, Accelerometer and Attitude Data The GRACE orbits may be determined using GPS data with and without the accelerometer data, which can replace the non-gravitational accelerations computed using force models in the dynamic orbit determination. The GRACE POD results are included in Tables 5 and 6. It can be seen that the GRACE cross-track component using only GPS data is better than that using GPS, attitude and accelerometer data in this particular case. The reason is that three accelerometer biases (one each axis) have to be estimated using accelerometer data (the accelerometer observations are not absolute values) and the cross-track bias is more difficult to estimate accurately.

AK

1 2 3 4 5 Total

Case GPS GPS+Al-I+ACC

Table 5. GRACE-A GPS DD RMS and SLR Residuals (combination of GPS DD, accelerometer and attitude observations) GPS DD RMS [cm] SLR Residuals [cm. GPS 1 GPS+A-IT+ACC GPS 1 GPS+A’IT+ACC # of data points 1.12 I 1.14 6.70 8.03 5 1.12 1.13 1.82 6.29 103 1.06 1.08 2.01 4.93 108 1.05 1.08 2.56 6.72 94 1.14 1.16 2.34 3.60 13 1.10 1.12 2.29 5.65 383 Table 6. GRACE-A Orbit Comparison between CSR and JPL [cm] (combination of GPS DD, accelerometer and attitude observations) Radial Along-track Cross-track Position (3D) 3.52 3.68 2.80 5.81 3.42 3.59 8.21 9.59 -

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Different Satellites - GRACE-A aud GRACE-B The GRACE has two identical satellites, GRACE-A and GRACE-B which carrier the same science instruments for POD and gravity field recovery. The orbit accuracy should be the same for both satellites. Tables 7 and 8 show the comparison results for the two satellites. It can be seen that the GPS DD RMS, SLR residuals and external comparison are nearly the same. Table 7. GRACE-A GPS DD RMS and SLR Residuals

Case GRACE-A GRACE-B

Table 8. GRACE-A Orbit Comparison between CSR and JPL [cm] (GRACE-A and GRACE-B) Radial Along-track Cross-track 3.52 3.68 2.80 3.93 4.90 2.64

Position (3D) 5.81 6.81

CONCLUSIONS, The precise orbit determination for GRACE has been successfully carried out. Since the gravity model error was the major sources of the orbits errors, a tuned gravity field was obtained by combing GRACE information with TEG4 information for POD. In addition, the Cd drag coefficients and 1 cpr empirical parameters were estimated for reducing the effects of force model errors on the orbit determination. The main conclusions are: l

l

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The orbit accuracy can be improved through estimating more drag and empirical acceleration parameters as well as using the tuned gravity model by dynamic orbit determination. The results are comparable with JPL’s reduced dynamic solution. The orbit accuracy for GRACE-A and GRACE-B is nearly the same based on different orbit quality tests. Based on the internal tests (observation fits), external comparison (SLR residuals, orbit comparison between CSR and JPL), an accuracy of better than 5 cm in each direction has been achieved for GRACE orbits. From KBR residuals, the relative accuracy between the two GRACE satellites is about 1 cm in position and 10 micrometers per second in velocity.

ACKNOWLEDGMENTS The authors would like to extend special thanks to JPL for providing their GRACE orbits for comparison. This research was supported by NASA contract NAS5-97213. REFERENCES Barlier, F., C. Berger, J. Falin, G. Kockarts, and G. Thuillier, Atmospheric Model Based on Satellite Drag Data, Annales de Geophysique, Vol. 34, pp. 9-24, 1978

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Kang, Z., B. Tapley, S. Bettapur, H. Rim, and P. Nagel, Precise Orbit Determination for CHAMP Using Accelerometer Data, AAS-02-212, 12* AASIAIAA Space Flight Mechanics Meeting in San Antonio, 2002. Kuang, D., Y. Bar-Sever, W. Bertiger, S. Desai, B. Haines, B. Iijima, G. Kruizinga, T. Meehan, and L. Romans, Precision Orbit Determination for CHAMP using GPS Data from BlackJack Receiver, Proceeding of the ION National Technical Meeting 2001, Long Beach, California, January 24,200l. Rim, H., TOPEX Orbit Determination Using GPS Tracking System, CSR Report CSR-92-3. Center for Space Research, The University of Texas at Austin, Austin, Texas, 1992. Rim, H., Z. Kang, P. Nagel, S. Yoon, S. Bettadpur, B. Schutz, and B. Tapley, CHAMP Precision Orbit Determination, AAS-01-334, AAS/AIAA Astrodynamics Specialist Conference in QuebecCity. Quebec, Canada ,200l. Tapley, B., D. P. Chambers, M. K. Cheng, M. C. Kim, S. Poole, and J. C. Ries, The TEG4 Earth Gravity Model, 25” European Geophysical Society General Assembly, Nice, France, April 25-29. 2002. Tapley, B., and C. Reigber, Gravity Field Determination from GRACE: Preliminary Results. Weikko A. Heiskanen Symposium in Geodesy, Ohio State University, October l-5, 2002. E-mail address of Z. Kang: [email protected] Manuscript received 28 October 2002; revised 10 March 2003; accepted 14 March 2003