Highly Robust Complex Covariance Estimators With Applications to Sensor Array Processing

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Date

2023-03-24

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Publisher

IEEE

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.

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Keywords

Signal processing, Estimation, Covariance matrices, Robustness, Probability density function, Electric breakdown, Symmetric matrices, Complex elliptically symmetric distribution, complex-valued S-estimator, covariance and shape matrix estimation, robust estimation of multivariate location and scatter, Sq-estimator

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