A bayesian approach to adaptive detection in nonhomogeneous environments

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

Knowledge-aided STAP in heterogeneous clutter using a hierarchical bayesian algorithm

This paper addresses the problem of estimating the covariance matrix of a primary vector from heterogeneous samples and some prior knowledge, under the framework of knowledge-aided space-time adaptive processing (KA-STAP). More precisely, a Gaussian scenario is considered where the covariance matrix of the secondary data may differ from the one of interest. Additionally, some knowledge on the primary data is supposed to be available and summarized into a prior matrix. Two KA-estimation schemes are presented in a Bayesian framework whereby the minimum mean square error (MMSE) estimates are derived. The first scheme is an extension of a previous work and takes into account the non-homogeneity via an original relation. {In search of simplicity and to reduce the computational load, a second estimation scheme, less complex, is proposed and omits the fact that the environment may be heterogeneous.} Along the estimation process, not only the covariance matrix is estimated but also some parameters representing the degree of \emph{a priori} and/or the degree of heterogeneity. Performance of the two approaches are then compared using STAP synthetic data. STAP filter shapes are analyzed and also compared with a colored loading technique

Estimation et détection en milieu non-homogène, application au traitement spatio-temporel adaptatif

Pour un radar aéroporté, la détection de cibles nécessite, de par la nature du fouillis de sol, la mise en place d'un filtre spatio-temporel adaptatif (STAP). Les détecteurs basés sur l'hypothèse d'un milieu homogène sont souvent mis à mal dans un environnement réel, où les caractéristiques du fouillis peuvent varier significativement en distance et en angle. Diverses stratégies existent pour contrer les effets délétères de l'hétérogénéité. La thèse propose d'approfondir deux de ces stratégies. Plus précisément, un nouveau modèle d'environnement est présenté dans un contexte Bayésien : il intègre à la fois une relation originale d'hétérogénéité et de la connaissance a priori. De nouveaux estimateurs de la matrice de covariance du bruit ainsi que de nouveaux détecteurs sont calculés à partir de ce modèle. Ils sont étudiés de manière théorique et par simulations numériques. Les résultats obtenus montrent que le modèle proposé permet d'intégrer de manière intelligente l'information a priori dans le processus de détection. ABSTRACT : Space-time adaptive processing is required in future airborne radar systems to improve the detection of targets embedded in clutter. Performance of detectors based on the assumption of a homogeneous environment can be severely degraded in practical applications. Indeed real world clutter can vary significantly in both angle and range. So far, different strategies have been proposed to overcome the deleterious effect of heterogeneity. This dissertation proposes to study two of these strategies. More precisely a new data model is introduced in a Bayesian framework ; it allows to incorporate both an original relation of heterogeneity and a priori knowledge. New estimation and detection schemes are derived according to the model ; their performances are also studied theoretically and through numerical simulations. Results show that the proposed model and algorithms allow to incorporate in an appropriate way a priori information in the detection schem