A Time Difference of Arrival Based Target Motion Analysis for Localization of Underwater Vehicles

We present a non-convex, partially observable solution for underwater vehicle localization, referred to as the time difference of arrival target motion analysis (TD-TMA). TD-TMA is especially suitable for the practical case in which localization ambiguities arise due to a lack of receivers, the effective sound velocity is unknown, and cooperation between the nodes is not available. The method relies on periodic emissions from a target vehicle, which are detected by an observer to yield a series of time difference of arrival (TDoA) measurements. The measurements are arranged in the framework of target motion analysis to obtain a set of localization solutions for the target. Maneuvering of either the target or the observer removes ambiguities and yields a single solution. We formalize TD-TMA as a least squares optimization problem, and solve it in polynomial time. Numerical results show that TD-TMA provides accurate localization performance in terms of both the target's kinematics and positioning, which are close to the posterior Cramér-Rao lower bound. Two sea experiments successfully demonstrate the effectiveness of the solution in real sea environments.