Machine Learning-Driven Long-Term Ephemeris Error Correction for Improved LEO PNT

Joe Saroufim, Paul El-Kouba, Samer Hayek, and Zaher M. Kassas

Abstract:	A machine learning (ML) framework for long-term low Earth orbit (LEO) satellite ephemeris error correction is presented. The framework consists of a time delay neural network (TDNN) which predicts the dynamics of the ephemeris error components in the satellite’s perifocal frame with respect to the corresponding argument of latitude and the duration of propagation. First, the model is trained to capture the errors exhibited by the simplified general perturbations 4 (SGP4) orbit propagator relative to the high precision orbit propagator (HPOP) over a 6-hour period for 300 Starlink LEO satellites. Next, this ML framework is integrated with an ephemeris error compensation scheme, wherein a reference receiver estimates two ephemeris parameters for each satellite. These parameters are utilized by the ML framework to forecast error behavior at a later time, enabling ephemeris error corrections at another receiver over a very long baseline, leading to an accurate navigation solution. The efficacy of the proposed approach is validated via a numerical simulation study. The study considered an unmanned aerial vehicle (UAV) traveling a 26.41 km trajectory in 480 seconds in Quebec City, Quebec, Canada, without global navigation satellite system (GNSS) signals. The UAV navigated by fusing altimeter measurements in a loosely coupled fashion via an extended Kalman filter (EKF) with its onboard tactical-grade inertial measurement unit (IMU), while LEO observables from Starlink LEO satellites were fused to aid the IMU in a tightly-coupled fashion. A total of 67 Starlink LEO satellites flew overhead the UAV throughout its trajectory, with the number of used Starlink LEO satellites at any point in time ranging between 5 and 10. The UAV received the proposed corrections from a reference receiver in Seattle, Washington, USA, amounting to a 3,790 km baseline. The proposed framework reduced the three-dimensional position root mean squared error (RMSE) from 1,007 m (utilizing SGP4-propagated ephemerides) to 21.02 m (utilizing the proposed ML framework).
Published in:	Proceedings of the 38th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2025) September 8 - 12, 2025 Hilton Baltimore Inner Harbor Baltimore, Maryland
Pages:	974 - 982
Cite this article:	Saroufim, Joe, El-Kouba, Paul, Hayek, Samer, Kassas, Zaher M., "Machine Learning-Driven Long-Term Ephemeris Error Correction for Improved LEO PNT," Proceedings of the 38th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2025), Baltimore, Maryland, September 2025, pp. 974-982. https://doi.org/10.33012/2025.20470
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