Robust Covariance Matrix Estimation in Heterogeneous Low Rank Context

This paper addresses the problem of robust covariance matrix (CM) estimation in the context of a disturbance composed of a low rank (LR) heterogeneous clutter plus an additive white Gaussian noise. The LR clutter is modeled by a spherically invariant random vector with assumed high clutter-to-noise ratio. In such a context, adaptive process should require less training samples than classical methods to reach equivalent performance as in a "full rank" clutter configuration. The main issue is that classical robust estimators of the CM cannot be computed in the undersampled configuration. To overcome this issue, the current approach is based on regularization methods. Nevertheless, most of these solutions are enforcing the estimate to be well conditioned, while in our context, it should be LR structured. This paper, therefore, addresses this issue and derives an algorithm to compute the maximum likelihood estimator of the CM for the considered disturbance model. Several relaxations and robust generalizations of the result are discussed. Performance is finally illustrated on numerical simulations and on a space time adaptive processing for airborne radar application.