A Bayesian Approach to Adaptive Detection in Nonhomogeneous Environments

• Published in: IEEE transactions on signal processing 2008-01, Vol.56 (1), p.205-217
• Main Authors: Bidon, S., Besson, O., Tourneret, J.-Y.
• Format: Article
• Language: English
• Subjects: Adaptive detection; Adaptive signal detection; Applied sciences; Bayesian analysis; Bayesian methods; Bayesian model; Colored noise; Computer Science; Covariance matrix; covariance matrix estimation; Detection, estimation, filtering, equalization, prediction; Detectors; Engineering Sciences; Exact sciences and technology; heterogeneous environment; Information, signal and communications theory; Matched filters; Mathematical analysis; Mathematical models; Matrices; Matrix methods; maximum a posteriori (MAP) estimation; Maximum likelihood detection; Maximum likelihood estimation; minimum mean square error estimation; Monte Carlo methods; Other; Signal and communications theory; Signal detection; Signal, noise; Studies; Telecommunications and information theory; Testing
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2007.901664

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 matched filter 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 estimate. Two detectors require generating samples distributed according to the joint posterior distribution of primary and secondary data covariance matrices. This is achieved through the use of a Gibbs sampling strategy. Numerical simulations illustrate the performances of these detectors, and compare them with those of the conventional adaptive matched filter.