Robust random matrix theory and applications to radar detection

This article presents recent results obtained from both Random Matrix Theory and Robust Estimation Theory, and applied to radar detection problems. More precisely, to answer the problem of high dimensional data, we focus on a regularized version of the Tyler's covariance matrix estimator (Tyler, 1987; Pascal, Chitour et al., 2008). Thus, it is shown thanks to the statistical analysis of this estimator, i.e. first and second-order behavior in high dimensional regime (N/n -> c is an element of (0, 1] when N, n -> infinity), that an optimal design of a robust detector, namely the adaptive normalized matched filter (ANMF) can be derived. The optimality considered in this paper refers to the maximisation (resp. minimization) of the detection probability (resp. probability of false alarm). Finally, Monte-Carlo simulations are conducted to highlight the improvement brought by the proposed approach compared to classical techniques of the literature.