Deep-Sea Target Localization with Entropy Reduction: Sound Ray Bending Correction Based on TOA Time Series Analysis and Joint TOA-AOA Fusion

Unlike terrestrial environments, the inhomogeneity distribution of underwater sound speed poses significant challenges for underwater ranging and target localization. In the presence of sound ray bending and sensor node position errors in underwater acoustic sensor networks (UASNs), this paper proposes a joint TOA-AOA deep-sea target localization framework based on sound ray bending correction. From the perspective of information theory and time series analysis, the TOA measurements are time series signals carrying target position information, and the entropy-based analysis quantifies the fundamental limit on localization uncertainty. First, based on the TOA time series measurements and combined with the acoustic propagation characteristics of the deep sea, a sound ray bending correction method is adopted to improve the accuracy of slant range measurement. To enhance target localization accuracy, this paper proposes a two-step WLS closed-form solution based on TOA-AOA. To further reduce localization bias, a maximum likelihood estimation (MLE) method based on the Gauss-Newton is also derived. Subsequently, the paper derives and analyzes the Cramér-Rao lower bound (CRLB) for target localization, proving theoretically that jointly using TOA-AOA can improve localization accuracy. Simulations verify the performance of the proposed methods. The slant range estimation method based on sound ray bending correction effectively improves range measurement accuracy. The proposed closed-form solution enhances target localization accuracy, achieving the CRLB accuracy. The Gauss-Newton MLE solution can attain the CRLB accuracy under certain localization geometries and further reduces localization bias.