Highly Robust Complex Covariance Estimators With Applications to Sensor Array Processing

Many applications in signal processing require the estimation of mean and covariance matrices of multivariate complex-valued data. Often, the data are non-Gaussian and are corrupted by outliers or impulsive noise. To mitigate this, robust estimators are employed. However, existing robust estimation techniques employed in signal processing, such as
$M$
-estimators, provide limited robustness in the multivariate case. For this reason, this paper introduces the signal processing community to the highly robust class of multivariate estimators called multivariate
$S$
-estimators. The paper extends multivariate
$S$
-estimation theory to the complex-valued domain. The theoretical performances of
$S$
-estimators are explored and compared with
$M$
-estimators through the practical lens of the minimum variance distortionless response (MVDR) beamformer, and the empirical finite-sample performances of the estimators are explored through the practical lens of direction-of-arrival (DOA) estimation using the multiple signal classification (MUSIC) algorithm.