Improved LEO PNT Accuracy Enabled by Long Baseline Ephemeris Corrections

A model for the time-varying ephemeris error impact on low Earth orbit (LEO) satellites ranging measurements is derived and parameterized in terms of two parameters. It is shown that for a particular space vehicle (SV) location along the orbit, the ephemeris error has no impact on the extracted pseudorange measurements. This enables the disambiguation of timing and ephemeris errors at a stationary reference receiver. The two parameters can be estimated by the reference and communicated asynchronously to an unknown receiver listening to the same LEO SVs to correct for ephemeris ranging errors, leading to improved positioning, navigation, and timing (PNT) accuracy. A simulation study is presented to evaluate the efficacy of the correction approach. The study considered an unmanned aerial vehicle (UAV) traveling a 30.5 km trajectory in 600 seconds in Columbus, Ohio, USA, without global navigation satellite system (GNSS) signals. The UAV was assumed to be equipped with a tactical-grade inertial measurement unit (IMU), an altimeter, and a LEO receiver. Starting with an initial estimate of its own states from a GNSS receiver, the UAV navigated by fusing altimeter measurements in a loosely coupled fashion via an extended Kalman filter (EKF) to aid the onboard IMU, while LEO observables from 2 Orbcomm, 1 Iridium NEXT, 22 OneWeb, and 100 Starlink SVs were fused to aid the IMU in a tightly-coupled fashion. Four LEO-aided IMU navigation frameworks are compared: (i) using erroneous LEO ephemerides from simplified general perturbations (SGP4), initialized with two-line element (TLE); (ii) using corrected ephemerides, after receiving the two parameters from the reference receiver; (iii) using erroneous ephemerides from TLE+SGP4 along with differential measurements from the reference receiver; and (iv) using corrected ephemerides, after receiving the two parameters, along with differential measurements from the reference receiver. Assuming the reference receiver was placed in Columbus at a mean baseline distance of 13.9 km from the UAV, the three-dimensional (3-D) position root-mean squared error (RMSE) by the four frameworks was 477 m, 7.12 m, 8.39 m, and 1.51 m, respectively. Next, the UAV was simulated to navigate in Baltimore, Maryland, USA, at a mean baseline distance of 577 km from the reference receiver. Here, two frameworks were compared: (i) using all visible LEO SVs over Baltimore, regardless of their visibility over Columbus, with LEO ephemerides obtained from TLE+SGP4 and (ii) using only LEO SVs over Baltimore whose ephemerides were corrected by the reference receiver in Columbus. The 3-D position RMSE of the two frameworks were 490 m and 17.9 m, respectively, demonstrating the applicability of the proposed approach over long baselines.