Detection in non-Gaussian environment.

Summary The radar echoes coming from the various reflections of the emitted signal on the elements of the environment (the clutter) have long been modeled by Gaussian vectors. The optimal detection procedure was then summarized in the implementation of the classical matched filter. With the technological evolution of radar systems, the real nature of the clutter has been shown to be no longer Gaussian. Although the optimality of the matched filter is challenged in such cases, TFAC (Constant False Alarm Rate) techniques have been proposed for this detector, in order to adapt the detection threshold value to the multiple local variations of the clutter. In spite of their diversity, these techniques proved to be neither robust nor optimal in these situations. From the modeling of the clutter by complex non-Gaussian processes, such as Spherically Invariant Random Processes (SIRP), optimal coherent detection structures have been determined. These models include many non-Gaussian laws, such as the K-distribution or the Weibull law, and are recognized in the literature to model in a relevant way many experimental situations. In order to identify the law of their characteristic component which is the texture, without any statistical preconception on the model, we propose, in this thesis, to approach the problem by a Bayesian approach. Two new methods of estimating the law of the texture are proposed: the first is a parametric method, based on a Padé approximation of the moment generating function, and the second is a Monte Carlo estimation. These estimates are performed on reference clutter data and lead to two new optimal detection strategies, respectively named PEOD (Padé Estimated Optimum Detector) and BORD (Bayesian Optimum Radar Detector). The asymptotic expression of the BORD (convergence in law), called the "Asymptotic BORD", is established as well as its law. This last result gives access to the optimal theoretical performance of the Asymptotic BORD which also applies to the BORD in the case where the correlation matrix of the data is non-singular. The detection performances of the BORD and the Asymptotic BORD are evaluated on experimental soil clutter data. The results obtained validate both the relevance of the SIRP model for the clutter and the optimality and adaptability of the BORD to any type of environment.