Warm Start Navigation with Non-Cooperative LEO Satellites via Online Ephemeris Error Estimation

A framework enabling warm start navigation with non-cooperative low Earth orbit (LEO) satellites whose ephemerides are poorly known is developed. In this framework, a standalone terrestrial receiver with poor knowledge about its states makes pseudorange and/or Doppler measurements to overhead LEO satellites, simultaneously estimating its own states and the LEO satellites’ orbit and clock errors, in a completely global navigation satellite systems (GNSS)-denied fashion. First, analytical models for temporal and spatial ephemeris errors are presented and their effect on Doppler frequency measurements are shown. Second, a batch weighted nonlinear least-squares filter is formulated to estimate ephemeris and clock errors from pseudorange or Doppler measurements and its performance is evaluated as a function of satellite-to-receiver relative geometry. Third, a new formulation of the marginalized particle filter (MPF) is developed, where the conventional use of the Kalman filter is replaced with a batch least-squares to estimate the linear states. The MPF aims to simultaneously estimate the receiver’s horizontal position along with the LEO satellite ephemeris and clock errors by treating the former as the nonlinear states and the latter as linear states. Fourth, the performance of the proposed MPF is examined and compared to that of an extended Kalman filter (EKF) with Monte Carlo (MC)-based simulations. The proposed approach’s performance is shown to be superior to that of the EKF, with the proposed approach yielding around 7 m in positioning error versus 2 km with the EKF. Experimental results of stationary receiver positioning are presented, demonstrating the efficacy of the MPF with Doppler measurements extracted from 6 Starlink and 7 OneWeb LEO satellites, where the receiver’s position is estimated along with the orbit and clock errors that are inherited from publicly available two-line element (TLE) files. Starting from an initial estimate 1.7 km away, it is shown that using erroneous TLE ephemerides yields a positioning error of 1.37 km, while the proposed online ephemeris estimation with MPF yields an error of 57.6 m. Finally, the LEO ephemeris error correction strategy is shown experimentally via a LEO-aided inertial navigation system (INS), yielding a ground vehicle position root-mean squared error (RMSE) of 21 m over a 1.5 km trajectory.