Accurate closed-form solution for moving underwater vehicle localization using two-way travel time

Position information is essential for an underwater vehicle that can affect the performance of many other applications. Vehicle motion during the two-way travel time (TWTT) using an acoustic positioning system can affect the localization accuracy of the estimators based on the traditional static model. A new time measurement model for moving vehicle localization is presented, which compensates for the vehicle motion. The Cramér–Rao lower bounds (CRLBs) of the proposed model are derived for two different cases, where the depth of the underwater vehicle is unknown or known. Then, closed-form solutions for the two cases using the proposed model are derived and the solutions are shown analytically to reach the CRLBs. Simulations collaborate the theoretical performance of the proposed estimators and the moving model significantly improves the localization accuracy in comparison with the static model.