Modélisation du fouillis non gaussien en utilisant les systèmes fractionnaires.

Abstract

The objectives of this thesis are axed around two problems concerning modeling and estimation in radar systems precisely in maritime radar clutter. First, we will start by a description of radar systems and their functions and also discuss sea clutter, its modeling and the most commonly used distributions in marine radar systems. Next, in the first problem we present a radar sea clutter model derived from the fractional differentiation of the compound Gaussian distribution with an inverse Gamma texture. We start with mathematical calculations on the PDF of a generalized Pareto distribution to obtain a new distribution and the cumulative distributed function (CDF) with fractional order. We estimate the distribution parameters suggested by the Nelder-Mead algorithm to optimize the shape parameter, the scale parameter and the order of the fractional derivative. We use the IPIX database, where the latter uses three resolutions 3m, 15m and 30m, then compare the results obtained by fitting the curve of the proposed statistical model to the real data. In the second problem, we present another sea clutter distribution model which is a mixture of two or three distributions. We suggest a mixture of two and three Weibull distributions and then we estimate their parameters by the Nelder-Mead algorithm and use the IPIX database. Then, the obtained results are compared by fitting the curve of the proposed statistical model to the real data. All the parameters of the proposed models are summarized in Tables. for the generalized Pareto fractional model, we compare the MSE of the proposed model with that of the generalized Pareto distribution and for a mixture of two and three Weibull distributions, we compare the MSE for this mixture with that of the Weibull distribution. It is shown the proposed models fit better the real data.