Robust autocovariance estimation based on sign and rank correlation coefficients

Abstract

This paper addresses the problem of estimating autocorrelation coefficients in the presence of outliers. Tools for characterizing the robustness are developed as well. Autocorrelation coefficients are obtained recursively by computing partial correlation (PARCOR) coefficients first. In order to achieve robustness, product-moment correlation coefficients are replaced by correlations computed using rank and sign correlation coefficients. Transformations relating rank and sign correlations and conventional correlations are exploited in the process. Finally, robust estimates of autocorrelation coefficients are obtained. They are used to construct an autocovariance matrix. Examples of the performance of the method are given by using a matrix constructed from autocorrelation coefficients and MUSIC subspace frequency estimator. The influence of outliers on conventional estimators and the robustness of the proposed method are illustrated in simulations as well.