Projection Filter Method Based on State Estimation to Nonlinear Systems

Abstract

For nonlinear systems (NLS), the estimator design is a crucial and important problem. In this paper, projection-filtermethod (PFM) based state estimation approach is proposed to NLS. As the weak solution of stochastic differential model of NLS is denoted by the Kolmogorov's forward equation, this paper presents a new finite-dimensional approximating filter for nonlinear filtering problem. By using the differential geometrical approach to statistical manifold onto which the stochastic partial differential equation of the probability density is projected, a finite-dimensional stochastic ordinary differential equation of the associating parameters is gained. The arithmetic of the projection filter can be predigested in the case of exponential family. Combining with the Bayes rule, the posterior density of the states is obtained By taking an illustrative example, numerical experiment results show that the new state estimator is feasible and has good performance than PF.