Distribution function tracking filter for stochastic nonlinear systems with uncertain dynamics

A novel filter design is presented for a class of multivariate nonlinear stochastic systems with uncertain dynamics. The system is subject to non-Gaussian process noises. The entire filter system is proved to be bounded in terms of a specified performance index, provided that the weighting function satisfies a certain condition. An analytical solution of optimal filter gain matrix is also given. Further, the estimation error system is exponentially and ultimately bounded in the mean square sense, even with the presence of system uncertainties. Finally, a simulation example is demonstrated to validate the proposed scheme.