This talk introduces a state estimation algorithm where a set-membership approach is used together with particle filtering techniques to provide the posterior density of the states and the outer bounds of the feasible state space region. The algorithm is first introduced for a one-dimensional linear problem, and is compared to the exact Bayesian estimation. It is then extended to multi-dimensional systems, exploiting ellipsoidal outer approximations of the feasible state sets. The algorithm is to be applied for linear dynamic systems, but it is shown how it can be extended for nonlinear applications. Some convergence properties are issued and several linear and nonlinear examples are provided.
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