Computationally efficient toeplitz approximation of structured covariance under a rank constraint

Disturbance covariance estimation is a centrally important problem in radar space-time adaptive processing (STAP). Because training is invariably scarce, estimators that exploit inherent structure and physical radar constraints are needed in practice. This paper develops a new computationally efficient estimator that obtains a Toeplitz approximation of the structured interference covariance under a rank constraint. Previous work has shown that exact maximum likelihood (ML) estimation of Toeplitz covariance matrix has no closed-form solution, and most versions of this problem result in iterative estimators that are computationally expensive. Our proposed solution focuses on a computationally efficient approximation and involves a cascade of two closed-form solutions. First, we obtain the rank-constrained ML estimator whose merits have recently been established firmly for radar STAP. The central contribution of this paper is the rank-preserving Toeplitz approximation, which we demonstrate can be modeled as an equality-constrained quadratic program and also admits a closed form. Extensive performance evaluation on both simulated and knowledge-aided sensor signal processing and expert reasoning data confirms that the proposed estimator yields unbeatable performance for radar STAP under the previously stated conditions of rank and Toeplitz constraints.