Differential LEO Navigation under Asynchronous Satellite Clocks: Architecture and Performance Bounds

Low Earth Orbit (LEO) communication satellites have emerged as a promising source of signals of opportunity for resilient positioning, navigation, and timing (PNT) in GNSS-challenged environments. Unlike GNSS constellations, however, commercial LEO systems are not globally synchronized, and independent satellite clock biases and drifts severely degrade kinematic estimation and induce statistical inconsistency when not explicitly managed. This paper proposes a base-station-aided differential navigation architecture that explicitly mitigates independent LEO satellite clock biases and drifts without inflating the state vector of the mobile rover. A fixed base station continuously tracks time-varying per-satellite clock states and transmits them as measurement-domain corrections, along with their rigorously propagated uncertainties, to a compact, 8-state rover Extended Kalman Filter (EKF). To support this architecture, we introduce a robust visibility management scheme to seamlessly handle the frequent entry and exit of LEO satellites. Furthermore, we derive the Recursive Bayesian Cramer-Rao Bound (RBCRB) directly linked to the channel-domain signal model to establish fundamental theoretical performance limits. The proposed methodology is validated using real-world urban vehicular data combined with high-fidelity LEO constellation simulations. Results demonstrate that the differential framework completely eliminates the statistical inconsistency endemic to single-receiver baselines. Crucially, the rover's posterior estimation uncertainty perfectly tracks the theoretical RBCRB limits across all kinematic and clock states, ensuring highly reliable PNT even during periods of severe geometric degradation.