Carrier-phase differential global positioning system navigation filter for high-altitude spacecraft

A new navigation Kalman filter has been developed which uses carrier-phase differential Global Positioning System techniques in a framework that includes integer ambiguities to estimate the relative states of high-altitude, formation-flying spacecraft. This model-based approach to relative navigation allows spacecraft formations to use carrier-phase techniques above the Global Positioning System constellation. The filter uses dynamics models for the spacecraft orbits, receiver clocks, ionospheric total electron content, and Global Positioning System satellite residual position and clock errors. The process noise driving the orbital dynamics is separated into a common-mode part and lower intensity differential-mode part to better model how disturbances influence formations. The ionospheric total electron content model contains information that allows the filter to decide when to use the dual-frequency measurements to correct for the ionosphere and when to use them to aid in integer ambiguity resolution. The filter tracks undifferenced carrier-phase ambiguities, but still resolves the double-differenced integer ambiguities for use in the relative navigation solution. Monte Carlo simulations are used to evaluate the filter's performance. In geostationary scenarios, the filter's mean relative position error magnitude is 1.2 cm, and its maximum error magnitude is 6 cm. In high-Earth-orbit scenarios at an apogee distance of 18 Earth radii, the filter's mean error magnitude is 11 cm, and its maximum error magnitude is 54 cm. The correct integer ambiguities are resolved in one or two 30 s measurement steps in most cases.