DOA Estimation of Acoustic Source Signals Exploiting Hyperbolic Exponential Norm for Sparse Linear Arrays

Recently, the rank approximation has been highly effective in the matrix rank minimization problem, whose purpose is to recover potential elements from the observation matrix and maintain a low-rank structure by applying rank constraints. In light of this, we propose a flexible non-convex rank approximation named hyperbolic exponential norm (HEN) in this paper. Then, a high-precision HEN-based direction-of-arrival (DOA) estimation algorithm of acoustic source signals is developed for sparse linear arrays (SLAs). Specifically, we first interpolate the virtual co-array signals by employing the virtual co-array interpolation approach and apply Toeplitz matrix reconstruction to the interpolated signals. Then, a matrix rank minimization problem is formulated based on HEN to complete the missing entries in the reconstructed Toeplitz covariance matrix. Finally, the MUSIC algorithm is directly applied to the completed covariance matrix, which provides the estimated DOAs. The findings from numerical simulations demonstrate that the HEN algorithm not only behaves excellently with regard to angular resolution but also is capable of both overdetermined and underdetermined estimation and presents excellent DOA estimation performance. In addition, the HEN algorithm exhibits favorable computational complexity and yields higher accuracy estimation performance under various scenarios over competing algorithms. The results of the underwater acoustic experiment demonstrate that the HEN algorithm is considerably effective for application in the real-world environment and presents a more reliable performance in comparison with the competing algorithms.