Kinematic Point Positioning of a LEO With Simultaneous Reduced-Dynamic Orbit Estimation

A technique for finding, with sub-decimeter precision, the trajectories of Low Earth Orbit (LEO) spacecraft with GPS receivers on board, has been developed at NASA’s Goddard Space Flight Center (GSFC). This technique has been tested, by computing a 24-hour orbit for the oceanographic satellite JASON-1. With three independent, precise tracking systems: GPS, DORIS, SLR, and at a height of 1300 km, this satellite currently has the bestdetermined orbits of any LEO. The GPS data has been post-processed in precise point-positioning mode (with data from a receiver on board the satellite, and precise orbits and clock corrections from an external source). The clock of the receiver has been eliminated by singledifferencing between GPS satellites. The resulting trajectory agrees to better than 5 cm (3-D RMS) with “truth”: a very precise orbit calculated independently, using well-tested space-geodetic techniques implemented in the GEODYN software used at Goddard SFC. The method presented here is a form of reduced-dynamic orbit determination that is easily incorporated into preexisting, precise kinematic software, because it relies on the use of a linearized orbit dynamics theory with a simple analytical formulation, easily programmed in a computer. A purely kinematic trajectory for the rover is obtained simultaneously with the reduced-dynamic orbit. This method is the product of a study aimed at overcoming the limitations of the kinematic approach when dealing with very fast-moving LEOs, by introducing some easily implemented constraints on the solution. Those limitations are a consequence of the short observing times available for estimating the biases in the ionosphere-free carrierphase combination. The technique has been tested with a modified version of the kinematic “IT” software developed by the first author. This software already has the option to use the same method, in long-baseline differential solutions, to estimate and correct errors in the GPS broadcast ephemerides, to improve results when these less precise orbits are used.