An Efficient Closed-Form Method For Underwater Source Localization With Isogradient Sound Speed Profile

In this paper, we address the underwater localization problem with isogradient sound speed profile (SSP) using time-of-arrival (TOA) measurements. The sound speed is related to the unknown source depth in the isogradient SSP model, which is highly nonlinear. Owing to this nature of the isogradient SSP model, the maximum likelihood (ML) problem for estimating the source position is non-convex such that local convergence may occur without sufficiently good initialization. To address this difficulty, we first approximate the isogradient SSP model, and then propose a closed-form two-step weighted least squares (TSWLS) method for estimating the source position based on the approximate model. The solution method is accurate since the approximate model takes the source depth into consideration, and can be used to solve the ML problem as an initialization. Moreover, the proposed TSWLS solution is simple and computationally attractive since it is in closed form. Simulation results show that the proposed TSWLS solution is sufficiently accurate and can be used as the initial estimate for solving the non-convex ML problem, such that the mean square error (MSE) of the ML solution can reach the Cramér-Rao lower bound (CRLB). Index Terms-Underwater localization, time-of-arrival, isogradient sound speed profile, two-step weighted least squares.