Author :
Besson, Olivier ; Bidon, Stéphanie ; Tourneret, Jean-Yves
Abstract :
This correspondence derives lower bounds on the mean-square error (MSE) for the estimation of a covariance matrix mbi Mp, using samples mbi Zk,k=1,...,K, whose covariance matrices mbi Mk are randomly distributed around mbi Mp. This framework can be encountered e.g., in a radar system operating in a nonhomogeneous environment, when it is desired to estimate the covariance matrix of a range cell under test, using training samples from adjacent cells, and the noise is nonhomogeneous between the cells. We consider two different assumptions for mbi Mp. First, we assume that mbi Mp is a deterministic and unknown matrix, and we derive the Cramer-Rao bound for its estimation. In a second step, we assume that mbi Mp is a random matrix, with some prior distribution, and we derive the Bayesian bound under this hypothesis.
Keywords :
covariance matrices; mean square error methods; Bayesian bound; Cramer-Rao bound; covariance matrices; deterministic matrix; heterogeneous samples; lower bounds; mean-square error; random matrix; range cell under test; unknown matrix; Array signal processing; Bayesian methods; Covariance matrix; Data models; Maximum likelihood estimation; Radar detection; State estimation; Statistical analysis; System testing; Working environment noise; Bayesian bound; CramÉr–Rao bound; covariance matrix estimation; heterogeneous environment;
