Covariance Matrix Estimation With Heterogeneous Samples

We consider the problem of estimating the covariance matrix of an observation vector, using heterogeneous training samples, i.e., samples whose covariance matrices are not exactly . More precisely, we assume that the training samples can be clustered into groups, each one containing snapshots sharing the same covariance matrix . Furthermore, a Bayesian approach is proposed in which the matrices are assumed to be random with some prior distribution. We consider two different assumptions for . In a fully Bayesian framework, is assumed to be random with a given prior distribution. Under this assumption, we derive the minimum mean-square error (MMSE) estimator of which is implemented using a Gibbs-sampling strategy. Moreover, a simpler scheme based on a weighted sample covariance matrix (SCM) is also considered. The weights minimizing the mean square error (MSE) of the estimated covariance matrix are derived. Furthermore, we consider estimators based on colored or diagonal loading of the w...

• Type: Journal
• Year: 2008
• Where: TSP
• Authors: Olivier Besson, Stéphanie Bidon, Jean-Yves Tourneret
• Keywords: Covariance Matrix, Prior Distribution, Training Samples, TSP 2008