Real-Time Relative Positioning of Spacecraft over Long Baselines

This paper deals with the problem of real-time onboard relative positioning of low-Earth-orbit spacecraft over long baselines using the Global Positioning System. Large intersatellite separations, up to hundreds of kilometers, are of interest to multistatic and bistatic synthetic-aperture radar applications, in which highly accurate relative positioning may be required in spite of the long baseline. To compute the baseline with high accuracy, the integer nature of dualfrequency, double-difference carrier-phase ambiguities can be exploited. However, the large intersatellite separation complicates the integer-ambiguities determination task due to the presence of significant differential ionospheric delays and broadcast ephemeris errors. To overcome this problem, an original approach is proposed, combining an extended Kalman filter with an integer least-square estimator in a closed-loop scheme, capable of fast on-the-fly integer-ambiguities resolution. These integer solutions are then used to compute the relative positions with a singleepoch kinematic least-square algorithm that processes ionospheric-free combinations of debiased carrier-phase measurements. Approach performance and robustness are assessed by using the flight data of the Gravity Recovery and Climate Experiment mission. Results show that the baseline can be computed in real time with decimeter-level accuracy in different operating conditions.