Filtered Dual-Frequency Carrier-Phase Differential GPS for Relative Navigation of High-Altitude Spacecraft

Abstract

A new dual-frequency carrier-phase difierential GPS relative navigation fllter has been developed for high-altitude spacecraft. This work extends the use of CDGPS techniques to satellite formations operating at altitudes up to 17 Re. The new fllter uses dynamics models for the spacecraft orbits, the receiver clocks, the ionospheric TEC, and the GPS satellite residual position and clock errors. The orbit model includes a 10£10 gravity model, solar radiation pressure, atmospheric drag, and sun and moon perturbations. The process noise driving the orbital dynamics is separated into a common-mode part and much lower intensity difierential-mode part. This separation allows the noise intensities to be tuned independently, leading to a more accurate model of the large process noise efiects that enter the absolute navigation solution and the small efiects that enter the relative navigation solution. Each receiver clock is modeled as a 2-state random walk. The ionospheric TEC is modeled as a flrst-order Markov process. The TEC variables are estimated as an average value and a difierential value between two receivers. The model is tuned to allow the average TEC to have large variations, but to constrain the difierential TEC to small variations. This scheme indicates to the fllter that it can use a difierencing operation between the receivers to remove most of the TEC efiects. The GPS satellite residual position and clock errors are also modeled as a flrst-order Markov process. The fllter tracks un-difierenced carrierphase ambiguities, preserving the information that these quantities are constant, and still utilizes the integer nature of the double-difierenced ambiguities in the relative navigation solution. The fllter successfully navigates in truth-model simulations at high altitudes over relatively short baseline distances with the assumption that the receivers can track the weak GPS side-lobe signals. In these tests, the fllter exhibits excellent carrier-phase ambiguity convergence, correctly estimating the integer part of the biases in the flrst measurement step in a geostationary orbit (GEO) and in 3 thirty-second measurement steps in a highaltitude Earth orbit (HEO) at a radial distance of 17:8 Re. The relative position estimation errors are 5 cm in GEO and 30 cm in HEO. The relative velocity errors are 0:02 mm=s in GEO and 0:4 mm=s in HEO. The absolute velocity estimation errors are 3:5 mm=s in GEO and 40 mm=s in HEO. Additionally, the fllter successfully removes the large TEC efiects caused by a GPS satellite setting behind the Earth.