DOA Estimation in Impulsive Noise via Low-Rank Matrix Approximation and Weakly Convex Optimization

Conventional direction-of-arrival (DOA) estimators are vulnerable to impulsive noise. In this paper, to tackle this issue, a class of weakly convex-inducing penalties is introduced for robust DOA estimation via low-rank matrix approximation, where ℓ_2,1-norm is adopted as the metric for suppressing the outliers. Two iterative algorithms are developed to construct the noise-free data matrix. To avoid determining the number of sources, the DOAs are estimated by exploiting the special joint diagonalization structure of the constructed signal covariance matrix. Compared with several existing algorithms, the proposed methods enjoy faster computation, similar DOA estimation performance against impulsive noise and requiring no a priori information of the source number. Numerical experiments are included to demonstrate the outlier-resistance of our solutions.