Bayesian Covariance Matrix Estimation with Non-Homogeneous Snapshots

We address the problem of estimating the covariance matrix Mp of an observation vector, using K groups of training samples {Zk}Kk=1, of respective size Lk, whose covariance matrices Mk may differ from Mp. A Bayesian model is formulated where we assume that Mp and the matrices Mk are random, with some prior distribution. Within this framework, we derive the minimum mean-square error (MMSE) estimator of Mp which is implemented using a Gibbs-sampling strategy. Moreover, we consider simpler estimators based on a weighted sum of the sample covariance matrices of Zk. We derive an expression for the weights that result in minimum mean square error (MSE), within this class of estimators. Numerical simulations are presented to illustrate the performances of the different estimation schemes.