Structured covariance matrix estimation: a parametric approach

The problem of estimating a positive semi-definite Toeplitz covariance matrix consisting of a low rank matrix plus a scaled identity from noisy data arises in many applications. We propose a computationally attractive (noniterative) covariance matrix estimator with certain optimality properties. For example, under suitable assumptions the proposed estimator achieves the Cramer-Rao lower bound on the covariance matrix parameters. The resulting covariance matrix estimate is also guaranteed to possess all of the structural properties of the true covariance matrix. Previous approaches to this problem have either resulted in computationally unattractive iterative solutions or have provided estimates that only satisfy some of the structural relations