Analysis and Correction of LEO Satellite Propagation Errors with Application to Navigation

The propagation error dynamics of low Earth orbit (LEO) space vehicles (SVs) are analyzed and modeled, leading to an approach to correct these errors. The approach maps a propagation error in the SV's argument of latitude orbital element to an error in the SV's position and velocity states, resolved in the SV's body frame of reference. The effect of an ephemeris epoch time adjustment on LEO SV orbit errors is examined using orbital dynamics. Implementing the epoch time adjustment is demonstrated to significantly decrease open-loop simplified general perturbations (SGP4)-propagated ephemeris errors with (i) real transmitted orbit data from an Orbcomm LEO SV and (ii) SpaceX published accurate orbit data describing four Starlink LEO SVs. Finally, experimental results are presented, evaluating opportunistic unmanned aerial vehicle (UAV) navigation with carrier phase measurements from 2 Orbcomm LEO SVs. The UAV traversed a trajectory of 780 m in 90 seconds. Global navigation satellite system (GNSS) signals were only available to the UAV during the first 30 seconds of the flight duration, during which the proposed ephemeris correction approach was performed, after which GNSS signals were cut off for the remaining 60 seconds, during which the UAV navigated with signals from the 2 LEO SVs. It is shown that using open-loop SGP4-propagated ephemerides for the LEO SVs yields a three-dimensional (3D) UAV position root-mean squared-error (RMSE) of 75.69 m, while incorporating the corrected ephemerides resulted in a position RMSE of 12.28 m.