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

We address the problem of estimating a covariance matrix R using K samples z_k whose covariance matrices are τ_kR, where τ_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 τ_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 τ_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.