Rank constrained ML estimation of structured covariance matrices with applications in radar target detection

We consider here the continually important problem of radar target detection in the presence of clutter, noise and jamming. Under complex Gaussian noise statistics, the optimal detection statistic relies on an inversion of the disturbance (clutter + noise and jamming) covariance matrix. The disturbance (and hence clutter) covariance must be estimated in practice from sample, i.e. training observations. Traditional maximum likelihood (ML) estimators are effective when training is abundant but lead to poor estimates and hence high detection error in the realistic regime of limited or small training. The problem is exacerbated by recent advances which have led to high dimensionality N of the observations arising from increased antenna elements (J) as well as higher temporal resolution (P time epochs and finally N = J.P). This work introduces physically inspired constraints into ML estimation. In particular, we exploit both the structure of the disturbance covariance and importantly the knowledge of the clutter rank to yield a new rank constrained maximum likelihood (RCML) estimator of clutter/disturbance covariance. Experimental validation on the KASSPER data set (where ground truth covariance is made available) shows that the proposed estimator vastly outperforms state-of-the art alternatives in the sense of: 1.) higher normalized signal to interference and noise ratio (SINR), and 2.) lower variance of target amplitude estimators that utilize disturbance covariance. Crucially the proposed RCML estimator can excel even for low training including the notoriously difficult regime of K ≤ N training samples.