TOA and FOA Based UAV-Assisted Localization for Satellite Navigation Enhancement

This paper addresses the problem of ground node localization in satellite-denied environments by employing unmanned aerial vehicles (UAVs) as mobile beacons. Existing approaches often neglect the joint impact of node prior uncertainty, UAV dynamic errors, and TOA/FOA measurement noise. To this end, we propose a joint localization algorithm, termed SDTL-q, based on maximum likelihood estimation. The method integrates time-of-arrival (TOA), frequency-of-arrival (FOA), UAV motion models, and prior constraints, and is solved using the Gauss-Newton method. A corresponding Cramér-Rao lower bound (CRLB) is derived under coupled error conditions. Simulation results demonstrate that SDTL-q achieves over 30% improvement in positioning accuracy under high-quality priors and maintains approximately 1.8 m accuracy even with degraded priors, indicating strong robustness to prior uncertainty. In addition, analysis of the sampling period reveals the trade-off between measurement frequency and energy efficiency. These findings highlight the applicability of the proposed algorithm in real-world UAV-assisted localization scenarios with imperfect prior information.