Rank-Constrained Maximum Likelihood Estimation of Structured Covariance Matrices

Abstract

This paper develops and analyzes the performance of a structured covariance matrix estimate for the important practical problem of radar space-time adaptive processing in the face of severely limited training data. Traditional maximum likelihood (ML) estimators are effective when training data are abundant, but they lead to poor estimates, degraded false alarm rates, and detection loss in the realistic regime of limited training. The problem is exacerbated by recent advances, which have led to high-dimensional N of the observations arising from increased antenna elements, as well as higher temporal resolution (P time epochs and finally N = JP). This work addresses the problem by incorporating constraints in the ML estimation problem obtained from the geometry and physics of the airborne phased array radar scenario. In particular, we exploit the structure of the disturbance covariance and, importantly, knowledge of the clutter rank to derive a new rank-constrained maximum likelihood (RCML) estimator of clutter and disturbance covariance. We demonstrate that despite the presence of the challenging rank constraint, the estimation can be transformed to a convex problem and derive closed-form expressions for the estimated covariance matrix. Performance analysis using the knowledge-aided sensor signal processing and expert reasoning data set (where ground truth covariance is made available) shows that the proposed estimator outperforms state-of-the-art alternatives in the sense of a higher normalized signal-to-interference and noise ratio. Crucially, the RCML estimator excels for low training, including the notoriously difficult regime of K ≤ N training samples.