Influence functions for array covariance matrix estimators

An influence function (IF) measures the effects of infinitesimal perturbations on the estimator. In this paper, we study the influence functions of sensor array covariance matrix estimators. We derive general results concerning the IF of any affine equivariant (pseudo-)covariance matrix estimator and its eigenvectors and eigenvalues under complex elliptically symmetric model distributions. The complex Gaussian distribution, for example, is a prominent member in this class of distributions. We also derive the IF of the regular covariance matrix estimator and that of the M-functional of covariance. The knowledge of the IF of the covariance matrix estimator allows us to obtain directly the IF of the associated eigenvector and eigenvalue functionals. Consequently, the robustness and sensitivity properties of signal processing algorithms using the eigenvalue decomposition may be established.