Robust Information Geometry State Estimator for Single-LEO and Ground Station Hybrid Positioning

Although low Earth orbit (LEO) satellites provide a crucial supplement in global navigation satellite system (GNSS)-denied environments, sparse coverage during early-stage constellation deployment often results in single-satellite visibility. The resulting observational rank deficiency forces conventional methods to rely on a “time-for-space” strategy, whose latency fails to satisfy the real-time positioning requirements of long-range unmanned aerial vehicle (UAV) clusters. To address this issue, this paper proposes a real-time positioning framework integrating a single LEO satellite, dual ground stations, and UAV cluster topology, incorporating Riemannian information geometry to enhance accuracy. First, a high-reliability positioning model is established to augment the spatial observation dimensions of a single satellite while leveraging cluster topology to ensure continuous positioning for a subset of UAVs under external measurement source unavailability. Second, a robust information geometry state estimator (RIGSE) with general applicability is developed to improve nonlinear estimation performance. Furthermore, the inherent position ambiguity of external measurement sources is mapped into the measurement domain to enable refined noise covariance modeling. The proposed method enables single-epoch instantaneous positioning for UAV clusters without multi-epoch measurements. Comprehensive simulations with multiple error sources demonstrate that the proposed method exhibits robust performance in GNSS-denied environments. Under this method, RIGSE achieves a converged positioning root mean square error of 4.05 m, representing a 19.48% reduction compared with the extended Kalman filter under the same configuration.