Joint source localization and propagation speed estimation using TDOA with hypothesized propagation speed

Underwater acoustic localization (UWAL) presents a significant challenge in numerous underwater applications. The speed of sound propagation, often treated as an unknown parameter, varies across different underwater environments, necessitating the joint estimation of both the source position and the sound propagation speed. In this study, we model the sound propagation speed as the sum of a hypothesized constant and a residual term, thereby formulating a new optimization problem to determine the source position and the residual speed. To address the rank-deficient issue, we employ a nullspace projection, enabling an coarse estimate of the source position through weighted least squares (WLS). To enhance accuracy, two strategies lead to two methods: the first utilizes perturbation analysis to estimate a correction that reduces error, while the second refines the coarse estimate using the maximum likelihood objective function and Taylor expansion. Performance analysis demonstrates that both proposed methods can achieve the Cramér–Rao lower bound (CRLB) in low-noise conditions. Simulations validate these analytical results and highlight the computational efficiency of the proposed methods.