Partial estimators and application to covariance estimation of gaussian and elliptical distributions

TL;DR

This paper introduces a generic method for constructing partial estimators to improve robustness against outliers in covariance estimation, especially relevant for signal processing applications like RADAR and SONAR detection.

Contribution

The paper proposes a novel generic approach to develop partial estimators from existing estimators, enhancing robustness in covariance estimation for elliptical distributions.

Findings

Partial estimators improve robustness to outliers.

Algorithms demonstrated for Gaussian and elliptical distributions.

Enhanced covariance estimation in signal processing contexts.

Abstract

Robustness to outliers is often a desirable property of statistical estimators. Indeed many well known estimators offer very good optimal performance in theory but are unusable in applied contexts because of their sensitivity to outliers. Of particular interest to the authors is the case of covariance estimators in adaptive matched filtering schemes in signal processing applications such as RADAR and SONAR detection, for which a contamination by outliers of the estimated noise covariance can lead to a great impact on performances, in particular when these outliers are similar to the target signal of the matched filter. This paper presents a generic method for building partial estimators from known estimators, which aim at avoiding these issues; the resulting algorithms are shown for a few chosen cases.