Analysis of Satellite Ephemeris Error in Differential and Non-differential Navigation with LEO Satellites

Low Earth orbit (LEO) satellite ephemeris error is analyzed for standalone (non-differential) and differential navigation. First, the range residual due to ephemeris error is derived for a standalone stationary receiver making range-type measurements to a LEO satellite, leading to deriving upper and lower bounds to this residual. Second, the derived residual is generalized to a differential framework, comprising two receivers making range-type measurements to the same LEO satellite. The differential range residual is found to be minimized whenever the baseline between the receivers is colinear with the projected line-of-sight (LOS) vectors on the local navigation plane, and maximized in the normal direction. Third, the combined effect of the baseline’s orientation and distance is analyzed, where the distance between the two receivers is shown to have no impact on the differential residual along the direction of minimum error. Finally, experimental results are presented to demonstrate the benefit of differential navigation. A ground vehicle traveled for 486 m in 50 seconds, while aiding its onboard inertial measurement unit (IMU) with differential Doppler measurements from 2 Starlink, 1 Orbcomm, and 1 Iridium LEO satellites, whose erroneous ephemerides were obtained from SGP4, initialized with two-line element (TLE) files. It is shown that differential navigation significantly reduces the effect of LEO ephemerides errors, achieving a two-dimensional (2D) position root-mean squared error (RMSE) of 11.7 m, as compared to 54.4 m for the non-differential scenario.