Inner and outer approximations of probabilistic sets

International audience; This paper proposes a set-membership method to characterize a probabilistic set,i.e., a set enclosing the true value for the parameter vector of a parametric system witha given probability. The approach assumes that all errors are independent and an intervalfor the error is known. To each error interval, a probability to be an outlier is provided.It is shown that characterizing the probabilistic set is a set inversion problem. The maincontribution of the paper is to provide a method to characterize the inner part of theprobabilistic set. As an illustration, an application to the static localization of a mobilerobot is considered.