The purpose of this thesis is to characterize random signals, observed in air and underwater context, by using a statistical approach. In signal processing, the hypothesis of Gaussian model is often used for a statistical study. However, the Gaussian model is not valid when the probability density function of data are characterized by heavy-tailed and skewness phenomena. A family of laws can fit these phenomena: the α-stable distributions. Firstly, the α-stable distribution have been used to estimate generated and real data, extracted from a mono-beam echo-sounder, for seabed sediments classification. The classification is made by using the theory of belief functions, which can take into account the imprecision and uncertainty of data and theirs estimations. The results have been compared to a Bayesian approach. Secondly, in a context a marine surveillance, a statistical study from the α-stable distribution has been made to characterize undesirable echo reflected by a sea surface, called sea clutter, where the sea surface is considered in a bistatic configuration. The sea surface has been firstly generated by the Elfouhaily sea spectrum and the Radar Cross Section (RCS) of the sea surface has been computed by the Physical Optics (PO). The Weibull and distributions have been used and the results compared to the α-stable model. The validity of each model has been evaluated by a Kolmogorov-Smirnov test.
