A Priori Stochastic Differential Equation System Transformation Method in Nonlinear Filtering Problems

A method for converting a system of a priori stochastic differential equations, which enables to reduce the initial problem of nonlinear filtering of a multidimensional Markov process to the problem of filtering a new Markov process characterized by a zero drift vector is proposed. The filtering algorithms are constructed in which the method of multidimensional densities transformation is used to restore the initial a priori and a posteriori probability density distributions. An example of filtering the phase of a narrow-band random process using the proposed conversion method is presented. It has been shown that the proposed method for transformation using numerical integration reduces the requirements to the selection of parameters of a posteriori density of the probability distribution of the vector of filtered parameters.