The polynomial predictive particle filter

We firstly constructed a new dynamic state space model with little exact knowledge of the original state dynamics by using the polynomial predictive filter and state dimension extension. Then a particle filter was used to estimate the extended state, where the sum of the extended particle weights was applied to test whether the filter is convergent or not. Finally the estimate of the original state was obtained by wiping off the components corresponding to the backward time steps. Simulation results demonstrate that, for unknown state dynamics, where the existed particle filter (PF) diverges, the proposed polynomial predictive particle filter (PPPF) still works well.