Robust DOA Estimation Against Outliers via Joint Sparse Representation

Several approaches for estimating the direction of arrival (DOA) are traditionally developed assuming Gaussian noise, making them highly sensitive to outliers. Therefore, when confronted with impulsive noise, the performance of these methods may significantly deteriorate. In this letter, we characterize impulsive noise as Gaussian noise mixed sparse outliers. By exploiting their statistical differences, we propose an innovative DOA estimation technique within the framework of sparse signal recovery (SSR). Unlike common robust loss functions, such as
$\ell _{1}$
and
$\ell _{p}$
norms, we combine the
$\ell _{2}$
-norm with the Minimax Logarithmic Concave function as the loss function. Furthermore, to address the issue of grid mismatch, we utilize an alternating optimization approach to acquire the grid deviations, with the aid of rough DOA estimations and estimated outliers. Simulation results indicate that the proposed technique exhibits robustness against large outliers.