Set-membership filtering using random samples

Set-membership filtering aims to determine the set of feasible states when the system dynamics and received measurements are corrupted by bounded noise having unknown statistics. In this paper, randomly generated particles are used to approximate the feasible state set, and the theory of random sets in continuous spaces is used to prove stochastic, set-theoretic convergence as the number of particles increases. Two novel modifications are proposed, which generate random samples that are more evenly distributed over the feasible state set compared to the naive application of the particle filter. The key insight behind both modifications is that for set-membership problems, the particle weights do not need to be selected according to the probability law of the underlying system, but should be designed to achieve even coverage over the entire feasible set. Simulation results in a nonlinear batch reaction problem confirm the superior performance of the proposed modifications.