Non-linear State Estimation Using Imprecise Samples

In state estimation theory, the general formulation is often done under assumptions of stochastic noise processes obeying well known probability distributions such as the Gaussian family. However, in many practical applications, due to the presence of high non-linearities and unknown noise probability distributions, other methods are required. Methods such as imprecise probabilities and set-membership approaches offer robust alternative solutions to the lack of statistical information. In these frameworks, the solution to the estimation problem is no longer a posterior distribution but either a set of densities or a solution set in the state space. The main objective in this work is to take advantage of both Monte Carlo approaches and set membership methods. A novel approach to non-linear non-Gaussian state estimation problems is presented based on mixtures of imprecise samples which can be seen as unknown probability density functions with known supports. The derivation of a sequential Bayesian procedure and convergence properties of such a representation are provided.