Position calibration method of seabed array element under asynchronous clocks and unknown sound speed

A position calibration method of the seabed array element is proposed when the clock at the transmitter is asynchronous to the clock at the receiver and the sound speed is unknown. The proposed method augments the sound speed and the time delay bias as the states to be determined. Firstly, a least square estimator is established based on the pseudo-times of arrivals to attain an initial estimate. Then, the estimation bias is calculated with the help of Taylor series expansion, and a bias-compensated algorithm is given to offset the bias of the initial estimate. Simulation results show the position estimation bias of the proposed method is smaller than 0.2 m and the corresponding root mean squared error reaches the Cramer-Rao lower bound. Sea experiments show, in the subsequent long baseline positioning, the average positioning error of the existing methods are larger than 5 m, while the proposed method can perform better with average localization error being 2.97 m.