Mitigating Ephemeris Uncertainty in LEO Geolocation: An Uncertainty-Aware Weighted Least Squares Method via Dual-Satellite Cumulative TDOA/FDOA Fusion

Accurate and robust localization of non-cooperative emitters is a cornerstone capability for modern low Earth orbit. To mitigate localization degradation caused by satellite ephemeris errors, this paper proposes a multi-epoch dual-satellite geolocation method that jointly exploits time difference-of-arrival (TDOA) and frequency-difference-of-arrival (FDOA) measurements, incorporating these uncertainties into the weighted least-squares estimation. We introduce a two-dimensional geodetic parameterization method to decouple estimation variables, effectively resolving the poor observability and improving numerical stability. The localization problem is formulated within a nonlinear least-squares framework, and solved via the Levenberg-Marquardt algorithm with adaptive damping adjustment. Furthermore, an uncertainty-aware weighting scheme is incorporated to mitigate satellite ephemeris errors, while a hybrid Cramér–Rao lower bound (CRLB) is derived to theoretically characterize the combined impact of measurement noise and ephemeris uncertainty. Simulation results demonstrate that the proposed method achieves superior positioning accuracy and convergence robustness compared to conventional approaches, approaching the theoretical performance bound under multi-epoch conditions. This work provides a reliable and high-precision solution for next-generation satellite-based passive positioning.