Abstract

This paper presents two approaches to derive an asymptotic distri-bution of the robust Adaptive Normalized Matched Filter (ANMF). More precisely, the ANMF has originally been derived under the assumption of Gaussian distributed noise where the variance is dif-ferent between the observation under test and the set of secondary data. We propose in this work to relax the Gaussian hypothe-sis: we analyze the ANMF built with robust estimators, namely the M-estimators and the Tyler’s estimator, under the Complex Elliptically Symmetric (CES) distributions framework. In this con-text, we derive two asymptotic distributions for this robust ANMF. Firstly, we combine the asymptotic properties of the robust esti-mators and the Gaussian-based distribution of the ANMF at finite distance. Secondly, we directly derive the asymptotic distribution of the robust ANMF. Then, Monte-Carlo simulations show the good approximation provided by the proposed methods. Moreover, for a non-asymptotic regime, the simulations provide very promising results.