Trajectory Optimization in Single and Dual-UAV Bearing-Only Target Localization

Abstract: Bearing-only target localization is a fundamental problem in optical measurement and finds extensive applications in unmanned aerial vehicle (UAV) technology. Effective trajectory planning establishes favorable observation geometries, thereby enhancing the target localization accuracy of bearing-only UAV systems. This paper proposes an trajectory optimization method for unmanned aerial vehicles (UAVs) in bearing-only target localization scenarios. By leveraging the Fisher Information Matrix (FIM), the proposed approach dynamically integrates the geometric configuration and vehicle maneuverability into the optimization framework. Specifically, we introduce a spectrally-weighted FIM objective function that provides better gradient dynamics near degenerate configurations, enabling the planner to rapidly escape from poor observation conditions. For dual-UAV scenarios, an intersection angle sine term is introduced to optimize triangulation geometry by improving the sight-line intersection angle, thereby preventing trajectory aggregation. Furthermore, we propose an improved Particle Swarm Optimization (PSO) algorithm with motion model constraints and particle normalization to ensure the physical feasibility of the trajectory and enhance the compatibility with the objective functions. Simulation results demonstrate that the proposed method reduces the median localization error by 99.21% compared to conventional FIM-based approaches in single-UAV scenarios, and achieves a 69.70% improvement for dual-UAV configurations, exhibits superior performance in long-duration bearing-only target localization of maneuverability targets at extended ranges.