Performance Evaluation of Navigation Using LEO Satellite Signals with Periodically Transmitted Satellite Positions

Abstract

The navigation performance with low Earth orbit (LEO) satellite signals is evaluated. The navigation framework used to perform this evaluation tightly integrates a vehicle’s inertial navigation system (INS) with Doppler and pseudorange measurements from LEO satellites. The following scenario is considered. A vehicle has access to global navigation satellite system (GNSS) signals and a priori, uncertain information about LEO satellite states. The vehicle navigates by tightly integrating GNSS pseudorange measurements with its onboard INS. During the period when GNSS signals are available, the vehicle tracks the LEO satellites from pseudorange and Doppler measurements, refining estimates about their states. Next, GNSS signals are assumed to be unavailable. The vehicle transitions to a simultaneous tracking and navigation (STAN) mode where it simultaneously tracks the LEO satellites and navigates by integrating pseudorange and Doppler measurements made on the LEO satellites with its onboard INS. The performance of this navigation framework is evaluated for two cases: when the LEO satellites periodically transmit their position and when the do not transmit such information. Simulation results with existing LEO satellite constellations pertaining to Orbcomm and Globalstar as well as the future satellite constellation pertaining to Starlink are presented. It was assumed that the LEO satellites are periodically transmitting their positions. These simulation results consider an unmanned aerial vehicle (UAV) equipped with a tactical-grade inertial measurement unit (IMU) navigating for 81.6 km in 600 seconds, in which GNSS signals were only available for the first 100 seconds. It is demonstrated that the final position error of the INS-Orbcomm-Globalstar system was 93.01 m while the INS-Starlink system was 9.81 m. The position root mean squared error (RMSE) of the INS-Orbcomm-Globalstar system was 58.59 m while the INS-Starlink system was 10.13 m. Experimental results with existing Orbcomm LEO satellites are presented in which only Doppler measurements were made on two available satellites. The experimental results were conducted on a ground vehicle equipped with a tactical-grade IMU that traversed 7.5 km in 258 seconds, in which GNSS signals were only available for the first 30 seconds. It is demonstrated that the final position error of the INS without GNSS signals was 3.73 km and the position RMSE was 1.42 km. On the other hand, the final position error of the INS-Orbcomm system was 233.3 m and the position RMSE was 188.6 m when the position of the satellite was decoded from its transmitted message. If such position was not decoded and was estimated only from the STAN framework, the final position error was 476.3 m and the position RMSE was 195.6 m.