In this article we introduce a new Gaussian proposal distribution to be used in conjunction with the sequential Monte Carlo (SMC) method for solving non-linear filtering problem. This proposal incorporates all the information about the to be estimated current state from both the available state and observation processes. This makes it more effective than the commonly used state transition density as a proposal, which ignores the recent observation. The introduced proposal is completely characterized by the exact moments obtained from the dynamical system. This is in contrast with recent works where the moments are approximated either numerically or by linearizing the observation model. Because of its Gaussian nature, it is also very easy to implement. We show further that the newly introduced proposal performs better than other similar proposal functions which also incorporate both state and observations.
|Publisher||Department of Applied Mathematics, University of Twente|