An efficient orbit integrator/filter for GPS-based precise LEO autonomous navigation

Single-epoch point positioning with GPS is as accurate in low orbit as on the ground: typically 50-100 meters for the GPS standard positioning services (SPS) user. This is achieved at any observation epoch without orbit dynamic information. With sophisticated models and filtering techniques onboard the spacecraft, the orbit accuracy of a low Earth orbiter (LEO) can be improved to 10 meters or better using the civilian broadcast GPS signals. To achieve this accuracy autonomously in real time, a high-performance computing processor onboard the satellite is required to carry out the sophisticated orbit integration and filtering process. In this paper, an efficient orbit integrator/filter is presented that computes the nominal orbit states (the position and velocity) and the state transition equations with numerical methods of integral equation, instead of differential equation usually used in orbit computation. The algorithm can be easily embedded in a flight GPS receiver or an onboard processor. TOPEX/Poseidon orbit data are used to test the algorithm and experimentally demonstrate its efficiency and accuracy as the function of filtering time/data arc, against the GIPSY-OSASIS´s precise orbit solution. The numerical results demonstrate that the proposed numerical method of the integral equation is a precise numerical method for orbit prediction. The designed sequential filter allows use of simple orbit state equation to efficiently correct dynamical model errors and improve the observed orbit RMS error from 50 m to about 6 m (1σ) within 6 hours of tracking/filtering time