LEO-Based Positioning under Orbital Errors

Low Earth orbit (LEO) satellites hold considerable promise for providing accurate positioning services; however, their low altitudes also induce significant orbital perturbations that can degrade positioning accuracy. We study the LEO-based positioning under orbital errors within a signals-of-opportunity framework based on downlink communication signals. Initially, we present a realistic LEO orbit model that captures Earth's non-sphericity, and combine it with a wideband communication model that captures fast satellite dynamics and multipath propagation. Subsequently, we derive the misspecified Cramér-Rao bound (MCRB) to analyze the impact of the orbit mismatch on positioning accuracy. Finally, we design a two-stage scheme to ensure accurate positioning under orbital errors by first calibrating the satellite orbit and then positioning the user. The MCRB analysis reveals that typical orbital errors can cause kilometer-level position errors. Our simulation results show that this positioning error can be effectively reduced with the proposed orbit calibration method.