A Hybrid Analytical-Machine Learning Approach for LEO Satellite Orbit Prediction

A hybrid analytical-machine learning (ML) framework for improved low Earth orbit (LEO) satellite orbit prediction is developed. The framework assumes the following three stages. (i) LEO satellite first pass: A terrestrial receiver with knowledge of its position produces carrier phase measurements from received LEO satellite signals, enabling it to estimate the time of arrival. The LEO satellite's states are initialized with simplified general perturbations 4 (SGP4)-propagated two-line element (TLE) data, and are subsequently estimated via an extended Kalman filter (EKF) during the period of satellite visibility. (ii) LEO satellite not in view: a nonlinear autoregressive with exogenous inputs (NARX) neural network is trained on the estimated ephemeris and is used to propagate the LEO satellite orbit for the period where the satellite is not in view. (iii) LEO satellite second pass: a terrestrial receiver with no knowledge of its position uses the ML-predicted LEO ephemeris along with its carrier phase measurements from received LEO signals to estimate its own position via an EKF. Experimental results with with signals from an Orbcomm satellite are presented to demonstrate the efficacy of the proposed framework. It is shown that during the satellite's second pass, the ML-predicted ephemeris error is reduced by nearly 90% from that of an SGP4 propagation. In addition, it is shown that if the receiver was to use the SGP4-predicted satellite ephemeris to localize itself, the EKF's initial position error of 2.2 km increases to 6.7 km, while the proposed framework reduces the position error to 448 m.