LEO PNT Frameworks for Non-Cooperative Satellites With Poorly Known Ephemerides: Open-Loop SGP4, Tracking, and Differential

Four frameworks for low Earth orbit (LEO) positioning, navigation, and timing (PNT) with pseudorange or Doppler measurements from noncooperative satellites with poorly known ephemerides are developed. The first utilizes publicly available ephemerides information from two-line element files, propagated in an open-loop fashion via the simplified general perturbations 4 (SGP4) model. The second utilizes the simultaneous tracking and navigation (STAN) framework, in which the LEO space vehicles' (SVs') position and velocity are simultaneously estimated with the rover's states along with the clock error difference between the rover and LEO SVs. The third is a differential framework, which utilizes measurements made by a base station with a known position. Here, the rover estimates its states along with its clock error difference with that of the base, while the LEO SVs' states are obtained from SGP4. The fourth is differential STAN (DSTAN)—a hybrid of the second and third frameworks. Simulation results are presented comparing frameworks' performance. An aerial vehicle, equipped with a tactical-grade inertial measurement unit (IMU), an altimeter, and global navigation satellite system (GNSS) and LEO receivers, navigates for 28 km, the last 23 km of which are without GNSS signals. The efficacy of the frameworks is compared with various combinations of LEO constellations (Starlink, OneWeb, Iridium NEXT, Orbcomm, and Globalstar), revealing that (1) using more SVs with SGP4 exacerbates PNT errors; (2) submeter-level accuracy is achievable with DSTAN with pseudorange measurements; (3) meter-level accuracy is achievable with pseudorange or Doppler measurements with STAN; and (4) differential SGP4 could be effective in reducing the effect of ephemerides error on PNT, but ceases to be effective with a large number of SVs. Experimental results are presented of a ground vehicle navigating with LEO Doppler measurements via the four frameworks. The vehicle was equipped with an industrial-grade IMU, an altimeter, and GNSS and LEO receivers. The vehicle navigated for 540 m, the last 492 m of which were without GNSS, while receiving signals from two Starlink, one OneWeb, one Iridium NEXT, and two Orbcomm LEO SVs, achieving a 3D position root-mean-squared error (RMSE) of 41.3, 10.7, 7.1, and 6.8 m.