Real-Time Sub-cm Differential Orbit Determination of Two Low-Earth Orbiters With GPS Bias Fixing

An effective technique for real-time differential orbit determination of two low Earth orbiters with GPS bias fixing is formulated. With this technique, only moderatequality GPS orbit and clock states (e.g., as available in real-time from the NASA Global Differential GPS System with 10‐20 cm accuracy) are needed to seed the process. The onboard, real-time orbital states of user satellites (few meters in accuracy) are used for orbit initialization and integration. An extended Kalman filter is constructed for the estimation of the differential orbit between the two satellites as well as a reference orbit, together with their associating dynamics parameters. The technique assumes that the two satellites are separated by a moderately long baseline (hundreds of km or less), and that they are of roughly similar shape. The differential dynamics, therefore, can be tightly constrained, strengthening the orbit determination. Without explicit differencing of GPS data, double-differenced phase biases are formed by a special transformation matrix. Integervalued fixing of these biases is then performed, greatly improving the orbit estimation. A 9-day demonstration with the two GRACE spacecraft (with baselines of ~200 km) indicates that ~80% of the double-differenced phase biases can be successfully fixed, and the differential orbit can be determined to ~7 mm 1D RMS as compared to direct measurements of the micron-precision, onboard Kband ranging sub-system.