Efficient Underwater Acoustical Localization Method Based on TDOA with Sensor Position Errors

Underwater acoustic localization (UWAL) is extremely challenging due to the multipath nature of extreme underwater environments, the sensor position uncertainty caused by unpredictable ocean currents, and the lack of underwater observation data due to sparse array, which all affect localization performance. Addressing these issues, this paper proposes a simple and effective underwater acoustic localization method using the time difference of arrival (TDOA) measurements based on the multipath channel effect of the underwater environment. By introducing the calibration source, localization performance was improved, and the sensor position error was corrected. The Cramér–Rao lower bound (CRLB) was derived, and the proposed method was able to achieve the CRLB with small deviation. Numerical simulations confirm the improved performance of the proposed method, including (1) a 20 dB and 30 dB reduction in the CRLB for far and near source scenarios, respectively, indicating improved accuracy and reliability when estimating unknown sources; (2) better Mean Squared Error (MSE) performance compared to existing methods and an efficiency of over 90% in low noise and above 80% in moderate noise in several scenarios, with a delayed threshold effect; and (3) achieving CRLB performance with only three sensors in a 3D space, even under moderate noise, while existing methods require at least five sensors for comparable performance. Our results demonstrate the efficacy of the proposed method in enhancing the accuracy and efficiency of source localization.