Orbital Errors in LEO Satellite Positioning: Modeling, Analysis, and Bayesian Calibration

Abstract

Low-Earth orbit (LEO) satellites offer a promising alternative to global navigation satellite systems for precise positioning. However, their relatively low altitudes make them more susceptible to orbital perturbations, which in turn degrade positioning accuracy. In this work, we study (i) the mechanisms through which orbital errors affect positioning performance and (ii) the fundamental calibration strategies for mitigating low-Earth orbital errors. We first model the satellite orbit and analyze historical two-line element data to characterize the statistical behavior of low-Earth orbital errors. Based on these real-data statistics, we derive the misspecified Cramér-Rao bound to quantify the impact of orbital errors on positioning performance. Subsequently, we develop a Bayesian orbit calibration framework that leverages the learned orbital error statistics as prior information to enhance calibration accuracy. This work sheds light on orbital error modeling, real-data-based evaluation, theoretical impact analysis, and calibration methodologies. Extensive simulations show that stale orbital information can severely degrade positioning performance, whereas learning and incorporating orbital error statistics can effectively enhance orbit calibration and ultimately improve positioning accuracy.