Underwater TDOA/FDOA joint localisation method based on cross-ambiguity function

In the underwater sound source localisation systems, the sound wave signal is accompanied by time delay and Doppler shift, where the cross-ambiguity function (CAF) is commonly applied as a method of estimating them. This study proposes a novel method for calculating the exact value of the CAF,based on the theory of curved surface interpolation. Firstly, two optimisation problems with equality and inequality constraints are developed, where the penalty function method is employed to turn the equality constraint problem into an unconstrained problem. Secondly, the time delay and Doppler shift of the CAF solution are processed to obtain the measurement values required for accurate localisation. Furthermore, the authors propose an improved time difference of arrival and frequency difference of arrival (TDOA/FDOA)-based joint localisation algorithm, which changes the structure of traditional localisation equations and eliminates the localisation imprecision caused by neglecting the square term of the noise. The performance of the proposed algorithm is verified by extensive simulations and comparisons with several established methods. Remarkably, the proposed localisation method is confirmed to be noticeably superior and effective for the considered application.