Sequential Monte Carlo algorithms for a class of outer measures

Closed-form stochastic filtering equations can be derived in a general setting where probability distributions are replaced by some specific outer measures. In this article, we study how the principles of the sequential Monte Carlo method can be adapted for the purpose of practical implementation of these equations. In particular, we explore how sampling can be used to provide support points for the approximation of these outer measures. This step enables practical algorithms to be derived in the spirit of particle filters. The performance of the obtained algorithms is demonstrated in simulations and their versatility is illustrated through various examples.