Simultaneous LEO Satellite Tracking and Differential LEO-Aided IMU Navigation

A navigation framework with differential measurements from low Earth orbit (LEO) satellite signals of opportunity is presented. This framework comprises a navigating rover with unknown states and one or more base stations with known position(s). The framework fuses differenced pseudorange or Doppler measurements from the rover and base station(s) to LEO satellites with unkown states, in an extended Kalman filter (EKF)-based tightly-coupled LEO-aided inertial navigation system (INS), while estimating the rover's states simultaneously with the LEO satellites' states. Simulations are conducted to analyze the navigation performance due to including a varying number of differential base stations. The simulations considered an aerial vehicle equipped with a tactical-grade inertial measurement unit (IMU), an altimeter, a GNSS receiver, and a LEO receiver making pseudorange and Doppler measurements to 14 Starlink LEO satellites. The vehicle-mounted receiver clock was assumed to be an oven-controlled crystal oscillator (OCXO), while the satellites were equipped with chip-scale atomic clocks (CSACs). The aerial vehicle navigated for 28 km in 300 seconds, the last 23 km of which are without GNSS. It is shown that despite relying on two-line element (TLE) files for the LEO ephemerides, which suffer from errors on the order of kilometers, the differential framework could achieve submeter-level accuracy when using pseudo range measurements. With 3 bases, the vehicle's three-dimensional (3-D) position root mean-squared error (RMSE) drops dramatically, reaching a position RMSE of 28 cm when using pseudorange measurements and 1.94 m when using Doppler. Experimental results are presented for an unmanned aerial vehicle (UAV) navigating for 2.28 km in 120 seconds, while utilizing differential carrier phase measurements from 2 Orbcomm LEO satellites. It is shown that using TLE+SGP4 for the LEO satellites' ephemerides yields a 3-D position RMSE of 419 m, while the differential framework reduces it to 12.79 m.