Ephemeris Tracking and Error Propagation Analysis of LEO Satellites With Application to Opportunistic Navigation

A comprehensive study is performed for low Earth orbit (LEO) space vehicles (SVs) tracking by a receiver opportunistically extracting navigation observables from their downlink radio frequency signals. First, a framework to characterize the LEO SVs orbital motion process noise covariance is developed. Second, the tracking performance via an extended Kalman filter (EKF) is analyzed via comprehensive Monte Carlo simulations for three different sets of observables: 1) pseudorange, 2) Doppler, and 3) fused pseudorange and Doppler measurements. Third, experimental results are presented demonstrating the efficacy of the opportunistic tracking framework in refining the ephemeris of a LEO SV from two-line element (TLE) files. The initial position and velocity errors of over 7.1 km and 7.3 m/s, respectively, of an Orbcomm LEO SV were reduced to 698.7 m and 1.8 m/s, respectively, in just over 6 min of tracking with carrier phase navigation observables, extracted opportunistically. Fourth, the error propagation from the LEO SVs state space to the measurement space and from the measurement space to the receiver's state space is analyzed in the context of stationary receiver localization. Bounds on the magnitude of pseudorange and Doppler residuals are first derived, and the magnitude of the receiver's estimation error is then characterized as a function of errors in the LEO SVs state space. Fifth, experimental results are presented of a stationary receiver tracking an Orbcomm LEO SV by fusing carrier phase observables via an EKF. The tracked LEO ephemeris is then used to localize another stationary receiver, showing a reduction in the receiver's initial horizontal error from 13,476 m to 343 m after just over 6 min. In contrast, it is shown that if the SGP4-propagated ephemeris was used in the EKF to localize the receiver, the error is reduced to 6,852 m, but the filter becomes inconsistent.