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Although the optimal solution to the problem of filtering non-linear state equations and observation confused with white Gaussian noise is given by the Kushner equation for the conditional density of a failed state with respect to the observations (see [48] or [ 41], Theorem 6.5, formula (6.79) or [70], Subsection 5.10.5, formula (5.10.23)), there are very few known examples of nonlinear systems where the Kushner equation can be reduced to a finite dimension closed system of filtering equations for a given number of children conditional moments. The most famous result, the Kalman-Bucy filter [42] is relevant to the case of linear state and observation equations, where only two moments, the estimate itself and its variance, the shape of a closed system of filtering equations. However, the optimal nonlinear finite-dimensional filter can be obtained in some other cases, if, for example, the state vector can take only a finite number of admissible states [91] or the observation equation is linear and drift term in the equation of state satisfies the Riccati equation df / dx + f 2 = x 2 (see [15]). The classification of the "overall situation" cases (this means that no special assumptions about the structure of state and observation equations and initial conditions), where the optimal nonlinear finite-dimensional filter exists, it gives in [95]. There is also a considerable bibliography on robust filtering of the "overall situation" systems (see eg [55, 74, 75, 76]).