Particle Filters Revisited

Particle filters are often explained by either heuristics arguments or complex mathematics. Present day particle filters rely on various methods such as importance sampling, resampling method and resampling strategy. Moreover, there are different derivations for discrete and continuous time dynamic models. In this paper we offer a new simple derivation which works both in the discrete and continuous case, and which avoid importance sampling and resampling. The resulting algorithm has a performance as good as the standard MATLAB particle filter.