Knowledge-aided Bayesian covariance matrix estimation in compound-Gaussian clutter

Abstract

We address the problem of estimating a covariance matrix R using K samples zk whose covariance matrices are kR, where k are random variables. This problem naturally arises in radar applications in the case of compound-Gaussian clutter. In contrast to the conventional approach which consists in considering R as a deterministic quantity, a knowledge-aided (KA) approach is advocated here, where R is assumed to be a random matrix with some prior distribution. The posterior distribution of R is derived. Since it does not lead to a closed-form expression for the minimum mean-square error (MMSE) estimate of R, both R and k are estimated using a Gibbs-sampling strategy. The maximum a posteriori (MAP) estimator ofR is also derived. It is shown that it obeys an implicit equation which can be solved through an iterative procedure, similarly to the case of deterministic ks, except that KA is now introduced in the iterative scheme. The new estimators are shown to improve over conventional estimators, especially in small sample support.