The dynamics of global positioning system orbits and the determination of precise ephemerides

Abstract

Analytical orbit perturbation theory suggests that the errors in the ephemerides of the Global Positioning System (GPS) satellites should be mostly resonant effects that can be corrected by adjusting a few parameters in a simple empirical acceleration formula, despite the complexity of their causes (mismodeling of gravity, radiation pressure, etc.), at least for arcs free from orbit maneuvers. This theoretical conclusion has been tested with simulations and actual data analyses. For these analyses, data from the Spring 1985 Experiment have been used to calculate improved ephemerides; in turn, these ephemerides have been used in the estimation of the coordinates of stations within the continental United States, previously positioned with very long baseline interferometry (VLBI). The agreement between the VLBI and the GPS results gives a measure of orbit quality. The outcome of this test supports the idea that the errors are mostly of a resonant nature. The principles described here are potentially applicable to the computation of the precise ephemerides of other spacecraft, such as geosynchronous relay satellites and oceanographic satellites, which are usually in highly resonant, nearly circular, repeating orbits.