Exact Moment Matching for Efficient Importance Functions in SMC Methods

In this article we introduce a new proposal distribution to be used in conjunction with the sequential Monte Carlo (SMC) method of solving non-linear filtering problem. The proposal distribution incorporates all the information about the to be estimated current state form both the available state and observation processes. This makes it more effective than the state transition density which is more commonly used but ignores the recent observation. Because of its Gaussian nature it is also very easy to implement. We show further that the introduced proposal performs better than other similar importance functions which also incorporate both state and observations.