GPS-based precise relative orbit determination for LEO satellites using GPS double-differenced carrier phases

The GPS-based precise relative orbit determination for Low-Earth Orbiting (LEO) satellites is very important for formation flying missions to satisfy the relative orbit accuracy requirements. Current methods need either reference stations or reference orbits. That isn’t convenient, particularly for real-time processing. Based on this motivation, we investigated the GPS-based precise relative orbit determination without any reference stations or reference orbits. Additionally, ambiguity resolution is important for the precise relative orbit determination. Therefore, we also studied the impacts of ambiguity resolution on the precise relative orbit determination. Lastly, the effects of the arc length were also investigated. The precise relative orbit determination can be achieved by using the Carrier Phase Differential GPS (CDGPS) method. Usually, good absolute orbit accuracy for formation flying satellites can be obtained using high-low double-differenced (DD) carrier-phases formed by two GPS satellites, one ground station and one LEO satellite. The good relative orbit accuracy can be obtained by using high-high DD carrier-phases formed by two GPS satellites and two LEO satellites. If both high-low and high-high GPS DD observations are used for LEO POD, the orbit accuracy should be both absolutely and relatively good. For some formation flying satellite missions, the absolute orbit accuracy requirements are not as stringent as the relative requirements. In this paper, we describe our resent advances in GPS-based precise relative orbit determination for formation flying LEO satellites. The current approaches for precise relative orbit determination of two formation flying satellites using GPS DD observations are: one-step and two-step methods. In the one-step method, the reference and second satellite orbits are determined using both high-low and high-high GPS DD observations. In the two-step method, the reference satellite orbits are first determined using only high-low GPS DD observations; then the second satellite orbits are determined using only high-high GPS DD observations by fixing the reference satellite orbits which are estimated in the first step. Both of the methods need either reference stations or reference orbits. Both absolute and relative orbit accuracy can be achieved in this manner. For our study, we used the observations of the GRACE (Gravity Recovery and Climate Experiment) satellites. The purpose of this paper was to investigate how well the relative orbits of the twin GRACE satellites can be determined using only high-high GPS DD observations. To achieve this goal, the challenge was to not only produce the relative orbit, but also to assess both absolute and relative orbit accuracy. The orbit accuracy was assessed using a number of tests, including analysis of orbit fits, orbit comparisons, Satellite Laser Ranging (SLR) residuals and K-Band Ranging (KBR) residuals. The precise relative orbit determination for the GRACE satellites was carried out using the GRACE data from January 1 to 31, 2008. The four different test cases were: 1. hihi (24h): hihi GPS DD observations for 24-hour arc length without ambiguity resolution 2. hihif (6h): hihi GPS DD observations for 6-hour are length with ambiguity resolution 3. hihif (12h): hihi GPS DD observations for 12-hour are length with ambiguity resolution 4. hihif (24h): hihi GPS DD observations for 24-hour are length with ambiguity resolution The preliminary results show that improved orbit accuracy from 5 to 2 mm for the GRACE satellites is achieved through the ambiguity resolution. There are some differences for different arc lengths. The relative accuracy increase with the arc length. The residuals for 24-hour arc length are relatively stable. The residuals for 6-hour and 12 hour arc lengths vary over the month. In our final paper, the method and models used for the precise relative orbit determination will be described, the effects of the arc lengths, ambiguity resolution will be analyzed, and the relative orbit accuracy will be assessed.