Knowledge-Aided Bayesian Detection in Heterogeneous Environments

• Published in: IEEE signal processing letters 2007-05, Vol.14 (5), p.355-358
• Main Authors: Besson, O., Tourneret, J.-Y., Bidon, S.
• Format: Article
• Language: English
• Subjects: Aerospace electronics; Bayesian analysis; Bayesian detection; Bayesian methods; Clutter; Covariance; Covariance matrix; Detectors; Engineering Sciences; Estimates; heterogenous environments; knowledge-aided processing; Matched filters; Mathematical analysis; Matrices; maximum a posteriori estimation; Radar detection; Signal and Image processing; Signal detection; Testing; Training; Working environment noise
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2006.888088

We address the problem of detecting a signal of interest in the presence of noise with unknown covariance matrix, using a set of training samples. We consider a situation where the environment is not homogeneous, i.e., when the covariance matrices of the primary and the secondary data are different. A knowledge-aided Bayesian framework is proposed, where these covariance matrices are considered as random, and some information about the covariance matrix of the training samples is available. Within this framework, the maximum a priori (MAP) estimate of the primary data covariance matrix is derived. It is shown that it amounts to colored loading of the sample covariance matrix of the secondary data. The MAP estimate is in turn used to yield a Bayesian version of the adaptive matched filter. Numerical simulations illustrate the performance of this detector, and compare it with the conventional adaptive matched filter