  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.
