Towards Navigation with Non-Cooperative LEO Satellites: Resolving Ephemeris and Timing Errors

This paper summarizes current state-of-the-art navigation results with non-cooperative low Earth orbit (LEO) satellites with poorly known ephemerides and timing. Experimental results with four LEO constellations (Starlink, OneWeb, Orbcomm, and Iridium) are presented. Six frameworks (F1)–(F6) that estimate LEO ephemerides and timing errors are compared: (F1) open-loop two-line element-initialized simplified general perturbations (TLE+SGP4); (F2) differential TLE+SGP4, where differential measurement corrections are communicated to the navigating receiver from a base station with a known position; (F3) simultaneous tracking and navigation (STAN), where the receiver estimates its own states along with the satellites’ states; (F4) differential STAN; (F5) long baseline ephemeris corrections, where two parameters, sufficient to account for ephemeris errors, are estimated at a reference receiver and communicated over a long baseline to the navigating receiver; and (F6) equivalent timing error compensation, where an epoch time adjustment, accounting for ephemeris spatial and timing errors, is estimated on-board the navigating receiver or at a base station. Five experiments (E1)–(E5) are presented on stationary receivers and ground and aerial vehicles, revealing the tremendous promise of exploiting non-cooperative LEO satellites for accurate positioning, navigation, and timing (PNT), particularly with the incorporation of ephemeris and timing error compensation strategies. In (E1), a ground vehicle, fused Doppler measurements extracted from 2 Starlink, 1 OneWeb, 2 Orbcomm, and 1 Iridium LEO satellites with an industrial-grade inertial measurement unit (IMU) and an altimeter. The vehicle traversed 540 m in 60 seconds, where GNSS signals were only available for the first 48 m. Over the entire period, a three dimensional (3-D) root mean-squared error (RMSE) of 41.3, 7.1, 10.7, 6.8 m was achieved with F1, F2, F3, and F4, respectively. The 3-D final errors were 112.6, 5.4, 19.5, 10.2 m, respectively. (E2) considered a known reference base station located in St. Louis, Missouri, USA, communicating ephemeris corrections for 7 Starlink satellites over a 635 km baseline to an unknown stationary receiver in Columbus, OH, USA. Starting from an initial error of 200 km, a horizontal final error of 8.8 m was achieved with F5. (E3) considered a stationary tracking receiver extracting carrier phase and Doppler measurements from 3 Starlink and 2 OneWeb satellites and consequently estimating each satellite’s equivalent timing error with F6. Starting from a mean 3-D initial error of 11.3 km, mean 3-D final errors of 3.2 and 7.9 m for carrier phase and Doppler, respectively, were achieved. (E4) considered an unmanned aerial vehicle (UAV) with a receiver extracting carrier phase measurements from 2 Orbcomm satellites. The UAV traversed 780 m in 90 seconds, where GNSS signals were unavailable for the last 60 s. The navigation solution employing F1 yielded a 3-D RMSE of 76 m, while F6 achieved 12.3 m. (E5) considered a mobile ground vehicle with a receiver extracting Doppler measurements from 4 Starlink, 1 OneWeb, 2 Orbcomm, and 1 Iridium satellites. The vehicle traversed 1.58 km in 70 seconds, where GNSS signals were unavailable for the last 1.05 km. Over the entire period, the GNSS-only navigation solution yielded a 3-D RMSE of 110 m and a final error of 322 m, while F6 achieved a 3-D RMSE of 4.2 m and a final error of 8.1 m.