On the practical merits of rank constrained ML estimator of structured covariance matrices

Estimation of the disturbance or interference covariance matrix plays a central role on radar target detection in the presence of clutter, noise and jammer. The disturbance covariance matrix should be inferred from training sample observations in practice. Traditional maximum likelihood (ML) estimators lead degraded false alarm and detection performance in the realistic regime of limited training. For this reason, informed estimators have been actively researched. Recently, a new estimator [1] that explicitly incorporates rank information of the clutter subspace was proposed. This paper reports significant new analytical and experimental investigations on the rank-constrained maximum likelihood (RCML) estimator. First, we show that the RCML estimation problem formulated in [1] has a closed form. Next, we perform new and rigorous experimental evaluation in the form of reporting: 1.) probability of detection versus signal to noise ratio (SNR), and 2.) SINR performance under heterogeneous (target corrupted) training data. In each case, we compare against widely used existing estimators and show that exploiting the rank information has significant practical merits in robust estimation.