Multi-UAV Cooperative Localization with PSO-Based Configuration Optimization for Bridge Inspection in GNSS-Denied Environment

Health monitoring of bridge structures imposes stringent requirements on high-precision navigation for inspection equipment, particularly in complex environments such as under-bridge areas where GNSS signals are obstructed, leading to significant positioning errors due to signal blockage or multipath effects. This paper proposes a collaborative navigation framework based on multiple unmanned aerial vehicles (UAVs), integrating one inspection UAV with a cluster of reference UAVs for auxiliary positioning to achieve real-time localization and trajectory optimization during bridge inspections. The framework employs the Gauss-Newton method for position estimation and utilizes the Particle Swarm Optimization (PSO) algorithm to dynamically adjust the spatial configuration of auxiliary UAVs, minimizing the Geometric Dilution of Precision (GDOP), ensuring trajectory smoothness, and avoiding bridge occlusions. Simulation results demonstrate that the proposed method effectively reduces the three-dimensional positioning error of the inspection UAV (mean error $<0.5 ~\mathrm{m}$). To validate the effectiveness of the proposed framework, comparative experiments were conducted against a collaborative Least Squares (UWB-LS) positioning algorithm based on Ultra-Wideband (UWB) technology. The results demonstrate that the proposed method achieves an average positioning error of approximately $0.1-0.5$ meters, significantly outperforming the UWB-LS algorithm, which yields errors of $\mathbf{0. 5 - 1. 5}$ meters. validating the feasibility and superiority of multi-UAV collaborative navigation in bridge inspection scenarios.