Sparse and Low Rank Recovery Based Robust DOA Estimation Method

Focusing on the problem of rather large estimation error in the traditional Direction Of Arrival (DOA) estimation algorithm induced by finite subsampling, a robust DOA estimation method based on Sparseand Low Rank Decomposition (SLRD) is proposed in this paper. Following the low-rank matrix decomposition method, the received signal covariance matrix is firstly modeled as the sum of the low-rank noise-free covariance matrix and sparse noise covariance one. After that, the convex optimization problem associated with the signal and noise covariance matrix is constructed on the basis of the low rank recovery theory. Subsequently, a convex model of the estimation error of the sampling covariance matrix can be formulated, and this convex set is explicitly included into the convex optimization problem to improve the estimation performance of signal covariance matrix such that the estimation accuracy and robustness of DOA can be enhanced. Finally, with the obtained optimal noiseless covariance matrix, the DOA estimation can be implemented by employing the Minimum Variance Distortionless Response (MVDR) method. In addition, exploiting the statistical characteristics of the sampling covariance matrix estimation error subjecting to the asymptotic normal distribution, an error parameter factor selection criterion is deduced to reconstruct the noise-free covariance matrix preferably. Compared with the traditional Conventional BeamForming (CBF), Minimum Variance Distortionless Response(MVDR), MUltiple SIgnal Classification (MUSIC) and Sparse and Low-rank Decomposition based Augmented Lagrange Multiplier(SLD-ALM) algorithms, numerical simulations show that the proposed algorithm has higher DOA estimation accuracy and better robustness performance under finite sampling snapshot.