Asymptotic properties of robust complex covariance matrix estimates

Abstract—In many statistical signal processing applications, the estimation of nuisance parameters and parameters of interest is strongly linked to the resulting performance. Generally, these ap-plications deal with complex data. This paper focuses on covari-ance matrix estimation problems in non-Gaussian environments, and particularly the-estimators in the context of elliptical dis-tributions. First, this paper extends to the complex case the re-sults of Tyler in [D. Tyler, “Robustness and Efficiency Properties of Scatter Matrices, ” Biometrika, vol. 70, no. 2, p. 411, 1983]. More precisely, the asymptotic distribution of these estimators as well as the asymptotic distribution of any homogeneous function of de-gree 0 of the-estimates are derived. On the other hand, we show the improvement of such results on two applications: directions of arrival (DOA) estimation using the MUltiple SIgnal Classifica-tion (MUSIC) algorithm and adaptive radar detection based on the Adaptive Normalized Matched Filter (ANMF) test. Index Terms—Complex-estimators, covariance matrix esti-mation, elliptical distributions, robust estimation. I