Stochastic stability of center difference predictive filter

In this paper, based on Stirling'׳s polynomial interpolation formula, the Second-order Central Difference Predictive Filter (CDPF2) is proposed for nonlinear estimation. To facilitate the new method, the algorithm flow of CDPF2 is given first. Then, the theoretical deductions demonstrate that the estimated accuracy of the model error and system state for the CDPF2 is higher than that of the conventional PF. In addition, the stochastic boundedness and the error behavior of CDPF2 is analyzed for general nonlinear systems in a stochastic framework. The theoretical analysis presents that the estimation error will remain bounded and the covariance will remain stable if the system׳s initial estimation error, disturbing noise terms and model error are small enough, which is the core part of the CDPF2 theory. All of the results have been demonstrated by numerical simulations for a nonlinear example system.