GPS-Based Relative Navigation of LEO Formations with Varying Baselines

This paper deals with the GPS-based relative navigation of LEO formations. Specifically, we consider applications characterized by two co-flying satellites with a large and highly variable separation, which are relevant to next generation monostatic/bistatic Synthetic Aperture Radar missions. In these applications, both scientific goals and control needs require the determination of the relative state with high accuracy. To this end, an Extended Kalman Filter is developed that processes double-difference pseudorange and carrier phase measurements on L1 and L2 frequencies. To preserve accuracy and robustness of the integer solution problem against large variations of the baseline, an original approach is developed in which, for each receiver, the Vertical Total Electron Content is included in the filter state. In addition, the double-difference ambiguities are re-estimated by the filter at each time step. A major technical problem of a filter processing double-differences is re-organizing the filter state when the pivot satellite changes. This is solved by an original and effective procedure that speeds up the filter convergence. Once the floating point estimates of the double-difference ambiguities have been produced by the dynamic filter, their integer values are extracted with the Least-Square Ambiguity Decorrelation Adjustment method and processed within a kinematic filter to estimate the relative position with high accuracy. Filter robustness and performance are evaluated by means of Monte Carlo simulations performed on the reference orbital scenario identified within the Italian SABRINA mission study. Results show that the integer ambiguities are always resolved, allowing to achieve a centimeter-level accuracy in all the simulated conditions.