Highly Robust Complex Covariance Estimators With Applications to Sensor Array Processing

Abstract

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.INDEX TERMS Complex elliptically symmetric distribution, complex-valued S-estimator, covariance and shape matrix estimation, robust estimation of multivariate location and scatter, Sq-estimator.

Polarization-Space Modulation with Reconfigurable Intelligent Surfaces, Robust Estimation and Quaternion Neural Networks

“…The breakdown point is defined as the minimum fraction of contamination that an estimator cannot handle [27]. The multivariate version of the Huber M-estimator of location has a breakdown point of 1/(n + 1), where n is the dimension of the data space [19]; this is due to the fact that a regression M-estimator can handle vertical outliers but breaks down in the presence of a single leverage point. Therefore, generalized M-estimators (GM-estimators) are needed to handle the latter.…”

“…( 9). For more information on the robust estimation of scatter in signal processing, see Mili and Fishbone [19].…”

“…Quaternions have also been previously proposed to be utilized in various kinds of wireless communication system [15][16][17][18]. Robust estimation methods are seldom used in wireless communication system models, or in digital signal processing applications in general [19], hence we have previously proposed to use the Huber Mestimator as an equalizer in a robust low-latency and highly reliable communications system that employs high-dimensional analog error correction codes using 1-dimensional Riemannian manifolds [20,21].…”