Position Calibration of Shallow-Sea Hydrophone Arrays in Reverberant Environments

To address the problem of shallow-sea hydrophone calibration, this paper proposes a shallow-sea hydrophone calibration algorithm for the horizontal and depth directions, respectively. In the horizontal direction, a calibration method combining an improved Particle Swarm Optimization (PSO) algorithm and the Time Difference Of Arrival (TDOA) algorithm is proposed. In the depth direction, a depth calibration formula using the time delay difference between Non-Line-of-Sight (NLOS) waves and Line-of-Sight (LOS) waves is put forward. By combining this with the proposed PSO algorithm, the PSO NLOS–LOS depth correction algorithm is obtained. The specific position of the hydrophone is determined by combining the algorithms for horizontal direction and depth. The advantages of the proposed algorithms are verified through simulations and experiments. Simulations show that in the horizontal direction, the proposed algorithm can reduce the average calibration error under different hydrophone array radii to 0.8690 m. In the depth direction, the specific propagation delay is unknown. Compared with the traditional depth calculation method, which requires the specific propagation delay to be known, the algorithm proposed in this paper can reduce the impact on depth calculation caused by delay deviation due to sound ray refraction; in addition, it provides stronger robustness and more accurate depth calibration in shallow sea environments. The new method shows significant improvement in the depth calculation process compared with the traditional algorithm, especially in terms of fault tolerance for errors in the horizontal direction. Experiments show that by combining the calibration algorithms proposed in this paper, the positioning accuracy of the hydrophone array is significantly improved and the average positioning error of the hydrophone array is reduced to within 12 m.