Katulev, A.N., Malevinskii, M.F., Jygolnikov, S.V.

By criteria of maximum aposteriory probability a new filter that is statistical quadratic recurrent filter for nonlinear estimation of vector of current state of dynamic system is expounded. Substantiate of filter is realized at two stages. In the first stage statistical quadratic approximation of nonlinearity that has been in equation is formed. In the second stage nonlinear recurrent equations are substantiated. Elaborated filter is generalization of Kazakov-Buton-s method of statistical linearization. It is investment to stohcastic theory of filtration and nonlinear estimation. By modeling find out that new filter has high efficiency, its error is in two-three times smaller of error of Kalman-s known quadratic filter