High order filtering for nonlinear dynamical systems

We present a sequential and workable approach for high order filtering of nonlinear dynamical systems. First, an explicit form of the algorithm using the multidimensional Taylor series expansion of the Kushner-Stratonovitch equations is given, no restriction on the upper bound of the order is needed. Next, we generalize the formula for the expectation of the product of four to Gaussian random variables in order to establish the final form of the filtering algorithm.