A system that provides GPS-based navigation/orbit determination capabilities for high-altitude spacecraft. The system uses an existing spacecraft processor and an easy-to-space-qualify minimum-hardware front end to minimize the need for new space-qualified hardware. The system also uses coherent integration to acquire and track the very weak GPS signals at high altitudes. The system also uses diurnal thermal modeling of a spacecraft clock and precision orbit propagation to enable longer coherent integration, a special Kalman filter to allow weak signal tracking by integrated operation of orbit determination and GPS signal tracking, and a segment-by-segment, post-processing, delayed-time approach to allow a low-speed spacecraft processor to provide the software GPS capability.