A Bayesian Approach to Adaptive Detection in Nonhomogeneous Environments

Abstract--We consider the adaptive detection of a signal of interest embedded in colored noise, when the environment is nonhomogeneous, i.e., when the training samples used for adaptation do not share the same covariance matrix as the vector under test. A Bayesian framework is proposed where the covariance matrices of the primary and the secondary data are assumed to be random, with some appropriate joint distribution. The prior distributions of these matrices require a rough knowledge about the environment. This provides a flexible, yet simple, knowledge-aided model where the degree of nonhomogeneity can be tuned through some scalar variables. Within this framework, an approximate generalized likelihood ratio test is formulated. Accordingly, two Bayesian versions of the adaptive matchedfilter are presented,where the conventional maximum likelihood estimate of the primary data covariance matrix is replaced either by its minimum mean-square error estimate or by its maximum a posteriori ...

• Type: Journal
• Year: 2008
• Where: TSP
• Authors: Stéphanie Bidon, Olivier Besson, Jean-Yves Tourneret
• Keywords: Covariance, Covariance Matrices, Secondary Data, TSP 2008