A Novel Positional Calibration Method for an Underwater Acoustic Beacon Array Based on the Equivalent Virtual Long Baseline Positioning Model

The performance of long baseline (LBL) positioning systems is significantly impacted by the distribution and positional calibration accuracy of underwater acoustic beacon arrays. In previous calibration methods for beacon arrays based on autonomous underwater vehicle (AUV) platforms, the slant range information of each beacon was processed independently, and each beacon was calibrated one at a time. This approach not only decreases the calibration efficiency but also leaves the positional calibration accuracy of each beacon highly susceptible to the navigation trajectory of the AUV. To overcome these limitations, an equivalent virtual LBL (EVLBL) positioning model is introduced in this paper. This model operates by adjusting the positions of each beacon according to the dead reckoning increments computed during the AUV's reception of positioning signals, effectively forming a virtual beacon array. Consequently, the AUV is capable of mitigating LBL positioning errors that arise from its motion by simultaneously receiving positioning signals from all beacons. Additionally, an overall calibration method for beacon arrays based on particle swarm optimization (PSO) is proposed. In this approach, the minimization of the deviation between the EVLBL trajectory and the dead reckoning trajectory is set as the optimization objective, and the coordinates of each beacon are iteratively optimized. The simulation results demonstrate that the proposed EVLBL-based PSO algorithm (EVPSO) significantly enhanced the calibration efficiency and positional accuracy of the beacon array. Compared with conventional methods, the estimation error of the beacon positions was reduced from 6.40 m to within 1.00 m. After compensating for the beacon array positions, the positioning error of the LBL system decreased from approximately 5.00 m (with conventional methods) to around 1.00 m (with EVPSO), demonstrating the effectiveness of the proposed approach.