On Estimation of Covariance Matrices Modeled as a Sum of Kronecker Products

We address the problem of estimation of covariance matrices expressible as a sum of Kronecker products (KPs). Our goal is to arrive at estimates of the KP component matrices within a maximum-likelihood (ML) framework. Since the exact solution of the ML cost function is non-tractable, we propose a covariance-matching (CM) approach, noting that the estimates obtained from covariance-matching coincide assymptotically with those obtained from ML-estimation [1]. The minimization of the CM cost function is more tractable and can be solved efficiently as it is ’biconvex’ in the components as we describe in Section 1. We look into two variants of the CM approach; in the first case, we consider the unconstrained solution to the CM cost function whereas in the second case, we restrict the estimated KP components be positive-definite (PD).