Particle filtering for multivariate state-space models

We propose and investigate a particle filtering method for multivariate state-space models. In the literature, the most studied state-space model is the linear Gaussian model, which includes known matrices and known noise covariance matrices. In our work, we drop the assumption of knowing these matrices, which produces a nonlinear model. In tracking the dynamic states, we propose to integrate out all the static unknowns and therefore, we sample particles only from the space of the dynamic states. In computing the particle weights, again, we only use the sampled states. The sampling distribution of the states is a multivariate Student t distribution, and the computation of the weights is based on another multivariate Student t distribution. The performance of the proposed method is examined by computer simulations.