A Joint Robust Estimation and Random Matrix Framework with Application to Array Processing

International audienceAn original interface between robust estimation theory and random matrix theory for the estimation of population covariance matrices is proposed. Consider a random vector x = ANy ∈ CN with y ∈ CM made of M ≥ N independent entries, E[y] = 0, and E[yy*] = IN. It is shown that a class of robust estimators ĈN of CN = ANA*N, obtained from n independent copies of x, is (N, n)-consistent with the traditional sample covariance matrix r̂N in the sense that ∥ĈN - αr̂N∥ → 0 in spectral norm for some α > 0, almost surely, as N, n → ∞ with N/n and M/N bounded. This result, in general not valid in the fixed N regime, is used to propose improved subspace estimation techniques, among which an enhanced direction-of-arrival estimator called robust G-MUSIC