High-altitude satellite relative navigation using carrier-phase differential global positioning system techniques

A new carrier-phase differential global positioning system relative navigation estimator has been developed that extends the use of carrier-phase differential global positioning system techniques to spacecraft formations that operate at geostationary altitudes and above. The estimator achieves rapid convergence to the carrier-phase ambiguities and incorporates a cycle slip detection and recovery algorithm. It solves a linearized problem using least-squares square root information processing that does not require spacecraft dynamics models. In this context, integer ambiguities are resolved using an integer least-squares algorithm. The cycle slip algorithm identifies the slip channel by statistical hypothesis testing and estimates the magnitude of the slip. Global positioning system receiver-in-the-loop tests with simulated low-Earth orbit data show nearly instantaneous convergence to the correct integer ambiguities and relative position error magnitudes of less than 3 mm. Truth-model simulations are used to simulate geostationary orbits and high-Earth orbit scenarios. The geostationary orbit scenario produces nearly instantaneous convergence to the ambiguities and error magnitudes of less than 0.1 m. The high-Earth orbit case at a radial distance of 17.8 Earth radii converges in minutes with error magnitudes of less than 3 m. Cycle slips, present in the hardware-in-the-loop simulations, are detected and corrected without significant accuracy degradation.