On Resampling for Bayesian Filters in Discrete State Spaces

Bayesian filtering is one of the most important frameworks for applications such as activity recognition and situation recognition. Current applications involving human behaviour models of large (possibly infinite) discrete state spaces imposes challenges to current inference algorithms. In these complex models approximate solutions are inevitable, in particular Sequential Monte Carlo methods are of great interest. We investigate a key component of the particle filter - the resampling step - for semi-Markov models with discrete states. Particle filters and resampling strategies have only been investigated in detail for continuous models. However, efficient inference for models of human behaviour with discrete states requires methods tailored for discrete state spaces.