Detection in non gaussian environment: various approaches and use of mixture models

Most of the signal processing methods, especially in detection/estimation theory, are based on a Gaussian noise probability density function (PDF). As real noises are not usually Gaussian, a good performance can not be obtained by assuming a Gaussian probability density. This paper can be viewed as a survey of some alternatives when the noise is known to be non-Gaussian, and even non-stationnary or imperfectly known . The emphasis is on a noise PDF modeled as a mixture, this PDF being sum of two or more elementary density functions. This representation, used in minimax robustness and adaptive methods, is particularly suitable for impulsive noise model and for the case of uncertainties on the noise PDF . Some applications in underwater acoustics are given.Les bruits réels ne suivent que rarement la loi gaussienne; de bonnes performances ne peuvent être obtenues qu'en s'affranchissant de l'hypothèse gaussienne. On expose quelques méthodes de prise en compte du décalage entre la loi réelle et la loi gaussienne. On insiste sur l'importance de la représentation de la loi du bruit par un modèle de mixture, la densité de probabilité étant la somme de deux ou plusieurs densités élémentaire