Positioning Using LEO Satellite Communication Signals Under Orbital Errors

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 LEO-based positioning under orbital errors within a signal-of-opportunity framework. First, we introduce a LEO orbit model that accounts for Earth's non-sphericity and derive a wideband communication model that captures fast- and slow-time Doppler effects and multipath propagation. Subsequently, we perform a misspecified Cram\'er-Rao bound (MCRB) analysis to evaluate the impact of orbital errors on positioning performance. Then, we propose a two-stage positioning method starting with a (i) MCRB-based weighted orbit calibration, followed by (ii) least-squares user positioning using the corrected orbit. The MCRB analysis indicates that orbital errors can induce kilometer-level position biases. Extensive simulations show that the proposed estimator can considerably enhance the positioning accuracy relative to the orbit-mismatched baseline, yielding errors on the order of a few meters.