APF-Driven Lightweight UAV Swarm Trajectory Optimization in GNSS-Denied Air–Terrestrial Navigation

To enable autonomous route planning for UAV swarms in dynamic air–terrestrial cooperative navigation scenarios within GNSS-denied environments, this paper proposes a lightweight framework based on the Artificial Potential Field (APF) method. In the considered architecture, UAVs act as mobile transit navigation nodes that relay positioning information from sparse ground anchors to terrestrial users. For TOA-based cooperative positioning, the instantaneous geometric configuration of the UAV swarm significantly affects the overall system accuracy. Therefore, the impact of UAV positions on the end-to-end navigation performance is rigorously analyzed, yielding a comprehensive Dilution of Precision (DOP) matrix for the entire air–terrestrial system. By applying the Schur complement, the global performance metric is decomposed, resulting in a scalar evaluation function that directly reflects the geometric quality of the configuration. In practical scenarios involving dynamic and heterogeneous users, real-time trajectory adaptation of the UAV swarm is essential to continuously optimize user positioning accuracy. To this end, an APF-based autonomous joint route planning approach is developed. The potential field is constructed directly from the derived geometric evaluation model, where its negative gradient generates virtual forces that autonomously guide the UAV swarm. This elegantly bridges high-level navigation performance optimization with low-level motion control of the swarm. The simulation results show a 76.1% improvement in the average comprehensive GDOP for users compared to the baseline of hovering UAVs, validating the effectiveness and real-time capability of the proposed lightweight framework.