Ephemeris Error Modeling in Opportunistic LEO Satellite Tracking with Pseudorange and Doppler Measurements

A framework for tracking the ephemerides of low Earth orbit (LEO) satellites is presented. This framework considers a known receiver that tracks the position and velocity states of LEO satellites using pseudorange and Doppler measurements extracted opportunistically from the satellite’s signals. An analytical procedure to estimate the epoch time adjustment to reduce the simplified general perturbation 4 (SGP4)-propagated ephemerides errors is developed. An extended Kalman filter (EKF) is formulated in which the satellite’s argument of latitude is estimated in a closed-loop fashion using pseudorange or Doppler observables, and subsequently, an epoch time adjustment is approximated to reduce the satellite state initialization errors. A simulation study is conducted to validate the proposed framework for a Starlink satellite, where the initialization errors were reduced from 1,880 m when using SGP4 ephemerides to 356 m and 367 m when using pseudorange and Doppler measurements, respectively. Experimental results are presented where the ephemerides of an Orbcomm LEO satellite’s ephemerides are refined: the satellite’s position RMSE is reduced from over 7.1 km with SGP4 open-loop propagation to 242 m after the implementation of the proposed tracking framework. The tracked ephemerides are then used to localize a ground receiver, reducing the initial error from 2.67 km to 211 m. Using the SGP4 ephemerides was shown to increase the localization error to over 5.8 km.