Bounds for estimation of covariance matrices from heterogeneous samples

Olivier Besson (1) , Stéphanie Bidon (1) , Jean-Yves Tourneret (2)

1 DEOS - Département Electronique, Optronique et Signal
2 IRIT - Institut de recherche en informatique de Toulouse

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.

Mots clés: Bayesian bound; Covariance matrix estimation; Cramér–Rao bound; Heterogeneous environment

Domaines: Traitement du signal et de l'image [eess.SP]

Olivier Besson, Stéphanie Bidon, Jean-Yves Tourneret. Bounds for estimation of covariance matrices from heterogeneous samples. IEEE Transactions on Signal Processing, 2008, 5 (7), pp.3357-3362. ⟨10.1109/TSP.2008.917341⟩. ⟨hal-03610279⟩