Maximum <i>a posteriori</i> underwater acoustic source localization based on time differences of arrival accounting for refraction

Traditional underwater acoustic source localization methods based on time differences of arrival (TDOA) in the presence of refraction first estimate the source depth and range to each hydrophone and then estimate the horizontal location of the source. The accuracy of these methods is compromised by errors in range estimation. To address this, we propose a three-dimensional source localization method that utilizes TDOA measurements between direct and surface-reflected arrivals at N(N ≥3) hydrophones, taking into account refraction effects. By utilizing multipath signals reflected off the sea surface, the method considers hydrophone position errors, TDOA measurement inaccuracies, and sound-speed variations to perform a Bayesian maximum a posteriori estimation of source localization. Compared with the traditional two-step source localization methods, the proposed method directly estimates the source depth and horizontal location jointly, eliminating the need to estimate ranges between the source and hydrophones. Simulation studies analyzing and comparing the localization performance of the proposed method with that of a two-step source localization method demonstrate the effectiveness of the proposed method. This could lead to more reliable localization of underwater sources, crucial for various applications, such as marine research, underwater navigation, and environmental monitoring.