Ephemeris and Timing Error Disambiguation Enabling Precise LEO PNT

The ephemeris and timing errors of low Earth orbit (LEO) satellites are modeled, leading to an approach to disambiguate these errors from pseudorange-type measurements. First, a model is derived describing the ephemeris error's impact on ranging measurements from LEO space vehicles (SVs) with imprecise ephemerides. A simulation study is presented comparing the impact of ephemeris error on ranging error for 5 LEO constellations (Statlink, OneWeb, Orbcomm, Iridium, and Globalstar) and 5 medium Earth orbit (MEO) constellations (GPS, GLONASS, Galileo, BeiDou-3, and O3B). Second, it is shown that for a particular SV position, the ephemeris error has no effect on range measurements. Next, the ephemeris and timing errors are parametrized by the three-dimensional (3-D) ephemeris error magnitude and its direction angle from the in-track axis. This parametrization is exploited in a proposed algorithm to disambiguate the ephemeris and timing error from the LEO SVs' pseudorange measurements at a reference receiver. The two parameters can be communicated to any unknown receiver listening to the same LEO SVs to correct for ephemerides ranging error, leading to improved positioning, navigation, and timing (PNT) precision. Monte Carlo simulation results are presented demonstrating the efficacy of the proposed algorithm. The simulations considered a reference receiver tracking via pseudorange measurements 22 Starlink and 4 OneWeb LEO SVs with poorly known ephemerides (obtained from two-line element (TLE) files, propagated with SGP4). The proposed algorithm reduced the 3-D position error of all SVs from a few kilometers to less than 120 m. The parameters were communicated to an unknown receiver to correct the LEO ephemerides, after which the receiver estimated its position by fusing its LEO pseudoranges via an extended Kalman filter (EKF), resulting in a horizontal position error of 0.91 m, as compared to 213 m utilizing TLE+SGP4 ephemerides. Two sets of experimental results are presented where the ephemeris correction method was applied to carrier phase measurements: (i) ephemeris parameters were estimated at a reference receiver from 3 Starlink and 7 OneWeb LEO SVs, and used to localize the same receiver, achieving a horizontal final position error of 0.85 m, compared to 7 km utilizing TLE+SGP4 ephemerides; and (ii) the two parameters of 7 Starlink SVs were estimated and communicated from St. Louis, Missouri, to an unknown receiver in Columbus, Ohio, over a baseline distance of 635 km, achieving a horizontal final position error of 8.78 m, compared to 2.41 km utilizing TLE+SGP4 ephemerides.