Initialization-Free Method for Three Dimensional Source Localization Under Stratification Effect

Three-dimensional (3-D) underwater acoustic localization, considering the stratification effects caused by depth, pressure, and other factors, has attracted significant interest. However, previous research has necessitated initial grazing angles that are difficult to obtain and accurate initial position estimates for iterative algorithms are hard to come by. To address the above problems, in this article, we propose two 3-D target localization methods that eliminate the need for initial location guesses and grazing angles. We first combine the Euclidean distance with the fast horizontal ranging (HR) model derived under stratification effects to construct an equation and transform the localization problem into a constrained weighted least squares problem. Subsequently, two solution methods are proposed: the first is a closed-form method that is computationally attractive, whereas the second is a convex optimization method that requires a small number of sensors and provides robust position estimation. Furthermore, we derive the Cramer-Rao lower bound (CRLB) and analyze the minimum number of sensors required by the proposed method and its computational complexity. Finally, Bellhop underwater acoustic channel and MATLAB simulation experiments were established to verify the advantages and performance of the proposed methods.