A TDOA sequence estimation method of underwater sound source based on hidden Markov model

To address the time difference of arrival (TDOA) estimation problem in the passive positioning system with wideband underwater motion sound sources and distributed hydrophones, a hidden Markov model-based (HMM) TDOA sequence estimation method is proposed in this paper. The method estimates the TDOA with multi-frame output of cross-correlated signals received on hydrophones. The transfer equation of the TDOA is established as a first-order hidden Markov process by analyzing the motion characteristics of the moving sound source and delays obtained from different hydrophones. Dynamic assignment of the HMM parameters is proposed to address the inconsistent change rate of the TDOA. We then achieve an HMM expression of the TDOA sequence by fitting the transfer equation and dynamic assignment of parameters into the HMM. Then, the Viterbi algorithm (VA) is applied to distinguish the optimal sequence of the TDOA among ambiguous estimations. To deal with the problem of data loss or unreliable issues caused by interferences, a data prediction algorithm which could produce possible time delays is added to VA to avoid the impact of outliers on the estimation results. By utilizing multi-frame processing, the proposed method reduces the signal-to-noise ratio (SNR) requirement of single frames since it does not require accurate estimations of TDOA for each frame. Moreover, the method adapts to a lower SNR, which has significant advantages in terms of whole sequence estimation compared with common methods. The results from the simulations and lake experiments validated the proposed TDOA sequence estimation method.