This paper presents a means to approximate the dynamic and static equations of stochastic nonlinear systems and to estimate state variables based on radial basis function neural network (RBFNN). After a nonparametric approximate model of the system is constructed from a priori experiments or simulations, a suboptimal filter is designed based on the upper bound error in approximating the original unknown plant with nonlinear state and output equations. The procedures for both training and state estimation are described along with discussions on approximation error. Nonlinear systems with linear output equations are considered as a special case of the general formulation. Finally, applications of the proposed RBFNN to the state estimation of highly nonlinear systems are presented to demonstrate the performance and effectiveness of the method.