Underwater Acoustic Source Localization by TOA With Indeterminate Isogradient Sound Speed Profile

In practical underwater environments, the uncertain and varying propagation speed of an acoustic signal makes time-based localization of an acoustic source challenging. In this paper, we utilize the isogradient sound speed profile (SSP) model with random model parameters to address the underwater source localization problem using time-of-arrival (TOA) measurements. To better reflect the real-world environments, the SSP we used is indeterminate where its model parameters have unknown random deviations from the nominal values. We propose a two-step method for locating an underwater acoustic source for this highly nonlinear challenging problem. In the first step, we propose an approximation to the TOA model that takes the sound speed dependence on the source depth into consideration, and formulate a non-convex constrained weighted least squares (CWLS) problem to obtain an initial source position estimate. In the second step, we expand the original TOA model by the second-order Taylor series at the initial estimate, and then create a different non-convex CWLS problem to obtain a refined solution. Both CWLS problems are solved by applying the semidefinite relaxation technique. Moreover, the proposed method is extended to the case where the source is not time synchronized with the sensors. Furthermore, we derive the Cramér-Rao lower bound (CRLB) for this particular localization problem and show by mean squared error (MSE) analysis that the proposed method is capable of achieving the CRLB performance under small Gaussian errors in the measurements and SSP model parameters. Simulation results confirm the effectiveness of the proposed method in achieving good localization performance.