Satellite Relative Navigation Using Carrier-Phase Differential GPS with Integer Ambiguities

Abstract

A new satellite relative navigation estimator has been developed using carrier-phase differential GPS (CDGPS) methods. This work is an initial step in an effort to extend the use of CDGPS techniques to spacecraft formations that operate at geostationary altitudes and above. The new estimator allows long baselines, achieves faster convergence to carrier-phase double-differenced integer ambiguities than other algorithms, and incorporates robust cycle slip detection and recovery. The algorithm is built up from an improved carrier-phase measurement model that fully accounts for how integer ambiguities can be obtained. To calculate the relative position solution, it uses real-time kinematic methods that do not rely on models of the spacecraft relative dynamics. It linearizes the nonlinear code and double-differenced carrier-phase measurements about the code solutions for the two spacecraft. This linearization allows long baseline distances without significant linearization errors. The inclusion of code measurements as well as carrier-phase measurements in the solution algorithm limits the ambiguity search volume to within the code solution error. This search volume is further reduced by applying an integer condition to the candidate ambiguities. The small search volume promotes rapid and reliable convergence to the correct biases. The linearized problem is solved with a least-squares, square-root information estimator, which is numerically stable and appropriate for use with computationally efficient linear methods, like the LAMBDA method, that decorrelate and estimate integer ambiguities. Tests with real and simulated terrestrial data validate both the method and the simulation environment. GPS receiver-in-the-loop tests with simulated 1 km baseline, LEO formation data show nearly instantaneous convergence to the correct integer ambiguities and relative position error magnitudes of less than 3 mm. In truth model simulations that fully simulate receiver output for a 100 km baseline, LEO formation, the estimator shows slower convergence, but relative position errors of less than 0.1 m. The different ionospheric effects over the long baseline and the GPS ephemeris errors explain the slow convergence. Carrier-phase measurement cycle slips are detected and corrected with a cycle slip recovery algorithm that performs hypothesis testing to identify which channel slipped and that estimates the number of cycles slipped on that channel. Operating on the hardware-in-the-loop data, the estimator detects and recovers from carrier-phase slips without significant degradation to the relative position solution.