LEO Satellite Orbit Prediction via Closed-Loop Machine Learning With Application to Opportunistic Navigation

A framework for low Earth orbit (LEO) satellite orbit prediction via closed-loop machine learning is proposed. The framework’s efficacy is demonstrated by improved navigation of a ground vehicle, navigating with “noncooperative” LEO satellite signals of opportunity, while using the neural network (NN)-predicted satellite ephemerides, compared with using the simplified general perturbations 4 (SGP4) orbit propagator. The framework, termed LEO-NNPON (LEO with NN prediction for opportunistic navigation), assumes the following three stages. First, LEO satellite first pass (tracking): a terrestrial receiver with knowledge of its position extracts measurements (pseudorange, carrier phase, and/or Doppler) from received LEO satellites’ signals, enabling it to estimate the time of arrival. The LEO satellites’ states are initialized with SGP4-propagated two-line element (TLE) data, and are subsequently estimated via an extended Kalman filter (EKF) during the period of satellite visibility. Second, LEO satellite not in view (prediction): a nonlinear autoregressive with exogenous inputs NN is trained on the estimated ephemerides and is used to propagate the LEO satellites’ orbit for the period during which the satellite is not in view. Third, LEO satellite second pass (navigation): a ground-based navigator (e.g., vehicle), equipped with a LEO receiver, extracts navigation observables (pseudorange, carrier phase, and/or Doppler) from the LEO satellite’s downlink signals. These navigation observables are used to aid the navigator-mounted inertial measurement unit (IMU) in a tightly coupled fashion (e.g., via an EKF). The LEO satellite states are obtained from the NN-predicted ephemerides. Experimental results of a ground vehicle equipped with an industrial-grade IMU navigating for 4.05 km with signals from two Orbcomm satellites are presented. Three vehicle navigation frameworks are compared, all initialized with a global navigation satellite system (GNSS)-aided-inertial navigation system (INS) position and velocity solution: first, unaided INS, second, LEO-aided INS, which uses SGP4-propagated LEO ephemerides, and third, LEO-aided INS with LEO-NNPON. The 3D position root-mean-squared error of the unaided INS was 1,865 m, whereas the LEO-aided INS with SGP4 was 175.5 m. The LEO-aided INS with LEO-NNPON was 18.3 m, demonstrating the efficacy of the proposed framework.