On the use of Empirical Likelihood for non-Gaussian clutter covariance matrix estimation

This paper presents an improved estimation scheme when the clutter distribution is unknown. The Empirical Likelihood (EL) is a recent semi-parametric estimation method which allows to estimate unknown parameters by using information contained in the observed data such as constraints on the parameter of interest as well as an a priori structure. The aim of this paper is twofold. First, the empirical likelihood is briefly introduced and then, some constraints on the unknown parameters are added. To illustrate this situation, we focus on the problem of estimating the clutter covariance matrix when this matrix is assumed to be Toeplitz. Finally, theoretical results are emphasized by several simulations corresponding to real situations: the mixture of a Gaussian (thermal noise) and a non-Gaussian (clutter) noise.