Underwater target time difference of arrival estimation using low-rank decomposition based generalized cross correlation.

The estimation of time difference of arrival (TDOA) between two sonars is a critical aspect in the context of underwater acoustic localization systems. Different from radar and satellite localization which use electromagnetic waves and suffer from extreme attenuation in seawater, acoustic waves are the only effective long-distance propagation medium in marine environments, so underwater acoustic technique is irreplaceable for underwater target detection and tracking. In passive localization, utilizing a pair of sonars to measure TDOA provides a fundamental and geometrically constrained method to estimate a target's position. However, it is observed that the accuracy of TDOA estimates is significantly declined in scenarios characterized by low signal-to-noise ratio. In this study, we introduce a robust TDOA estimation method based on sub-band extraction. The core idea is to extract sub-bands from the generalized cross correlation phase transform spectrum using a frequency sliding window technique; this sub-band is defined as the frequency components that contributes to the target TDOA or noise. Notably, the extracted sub-band matrix is confirmed to possess a rank-one property, which allows for the application of a low-rank decomposition framework named GoDec+ to derive robust TDOA estimates. Additionally, we demonstrate the performance of our proposed method through numerical simulations and by comparing the results with empirical data obtained from the South China Sea experiments, conducted by Harbin Engineering University in July 2023, the latter involving a controlled acoustic source and two fixed horizontal hydrophone arrays in a deep-water environment.