Improved distributed localization of underwater sources using joint time-difference-of-arrival and direction-of-arrival estimation

In distributed localization of underwater targets, joint time-difference-of-arrival and direction-of-arrival measurements provide an effective means for target localization. However, increased measurement errors under low signal-to-noise ratio (SNR) conditions can make the approximation errors introduced by the linear treatment of nonlinear observation equations more pronounced, thereby degrading localization performance. To address these issues, an improved localization method based on joint time-difference-of-arrival and direction-of-arrival estimation is proposed. The method introduces auxiliary variables to transform the nonlinear observation equations into a pseudo-linear form, enabling the construction of a weighted least squares problem for estimating the target location. The initial solution is further refined by imposing a projection constraint derived from the geometric relationship between the target and the reference node, thereby reducing the estimation inconsistency arising from the pseudo-linear formulation. On this basis, iterative optimization is employed to obtain a more accurate estimate, thereby extending the effective SNR range. The method achieves high accuracy under high-SNR conditions while maintaining robustness in low-SNR environments. Theoretical analysis shows that the projection-corrected closed-form estimate can achieve the Cramer–Rao lower bound under small noise conditions. Simulation results and processing of SWellEx-96 experimental data verify the effectiveness of the proposed method.