This paper deals with the problems of estimating state variable for dynamic System (either linear or non-linear).If We limit our problems in linear estimating algorithm，then the minimum variance estimator is sufficiently optimum. But in general，the optimal estimator may not be the linear case. For this purpose，we discuss the approximations of the non-linear. filtering problems. we present the methods for two types of approximations，the first，Gram-Charlier approximation; and the second，the statistical second order approximation. In order to facilitate calculation，in this paper the approximate solution in recurrence form is given. The generalized Kalman filtering method and statistical lineanzation method are used only as the particular cases.