Efficient approximation of structured covariance under joint Toeplitz and rank constraints

The disturbance (clutter plus noise and jamming) covariance matrix which plays a central role in radar space time adaptive processing (STAP) should be estimated from sample training observations in practice. Traditional maximum likelihood (ML) estimators lead to degraded false alarm and detection performance in the realistic regime of limited training. Therefore constrained ML estimation has received much attention which exploits structure and other properties that a disturbance covariance matrix exhibits. In this paper
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, we derive a new covariance estimator for STAP that jointly considers a Toeplitz structure and a rank constraint on the clutter component. Past work has shown that in the regime of low training, even handling each constraint individually is hard and techniques often resort to slow numerically based solutions. Our proposed solution leverages a recent advance called rank constrained ML estimator (RCML) of structured covariances to build a computationally friendly approximation that involves a cascade of two closed form solutions. Experimental investigation shows that the proposed estimator outperforms state of the art alternatives in the sense of: normalized signal to interference and noise ratio (SINR), and probability of detection versus signal to noise ratio (SNR).