Grid-based Rao-Blackwellisation of particle filtering for switching observation models

This paper is concerned with the problem of estimating both continuous and discrete hidden states of stochastic dynamic systems, called hybrid state space models. Of several hybrid state space models, this paper focuses on switching observation models. In this model, the discrete states are used for indicating one of several observation models, and the continuous and discrete states independently evolve with time but the observations is generated depending on both the states. The contribution of this paper is to propose a Rao-Blackwellised particle filter for this model in conjunction with the grid based filter. Normally, the Kalman filter has been most widely used for Rao-Blackwellisation of particle filters, but in the proposed algorithm the grid-based filter is used to analytically estimate the posterior distribution on the discrete state. In experiments a nonlinear and non-Gaussian benchmark model is used to evaluate the performance of the proposed algorithm. The experimental result with Monte Carlo simulations shows that the proposed algorithm outperforms the basic particle filter, especially when the number of the particles used for estimation is small.