Sparse representation based direction-of-arrival estimation using circular acoustic vector sensor arrays

Direction-of-arrival (DOA) estimation using circular array has been attracted significant attention in passive sonar system. Recently, the DOA estimation techniques face some challenges such as the small angle spacing of the incident signals, high correlation or coherence between signals, the considerable ambient noise, etc. To solve these problems, this paper proposes a sparse representation (SR) algorithm to estimate the DOAs of signals in the isotropic ambient noise by using the circular arrays composed of acoustic vector sensors (CAVSA). By exploiting the correlation characteristic of the acoustic pressure and particle velocity, two cross-covariance matrices between the acoustic pressure and x-, y-axes particle velocity are first constructed to eliminate the isotropic ambient noise. Then they are stacked to form an augmented cross-covariance matrix, which fully utilizes the direction information of the x- and y-axes particle velocity components. It is observed an interesting fact that when the number of snapshots is limited, the augmented cross-covariance matrix can be divided into the auto-correlation terms of each signal and the cross-correlation terms of any two incident signals coming from different directions. Based on this, the virtual overcomplete and the extra bases between the acoustic pressure and particle velocity are constructed by Khatri-Rao and Kronecker products, respectively. Finally, the SR-based DOA estimation algorithm is derived via the SR of the augmented cross-covariance vector. Simulation and experimental results demonstrate that the proposed method outperforms some existing DOA estimation methods in terms of the spatial spectrum, the estimation accuracy, and the angular resolution.