Regularized constrained total least squares localization for underwater acoustic sensor networks using angle-delay-doppler measurements

This paper addresses the challenge of underwater acoustic localization using measurements of angle, time delay and Doppler shift. Poor sensor placement can cause numerical instability in the coefficient matrix, which diminishes localization accuracy. To tackle this, we propose a two-stage localization approach based on the regularized constrained total least squares (RCTLS) method. First, we linearize the time delay and Doppler shift equations using azimuth and elevation angles, and apply a weighted least squares (WLS) method for an initial position estimation. Second, to mitigate the impact of ill-conditioned equations and measurement errors, we employ the RCTLS method for a more robust estimation, thus reducing localization error. Due to the unique characteristics of the underwater communications, the presence of errors in the sound speed and sensor position and velocity, as well as the sensor motion effect during the observation period are considered. We also derive the hybrid Cramer Rao lower bound (CRLB) as a benchmark to evaluate estimation performance. Simulations demonstrate that our method significantly improves localization accuracy compared to conventional approaches.