A PRIORI STOCHASTIC DIFFERENTIAL SYSTEM TRANSFORMATION METHOD EQUATIONS IN NONLINEAR FILTERING PROBLEMS
V. M. Artyushenko1, V. I. Volovach2,3
1Moscow State University of Geodesy and Cartography, Moscow, Russia
2Volga Region State University of Service, Togliatty, Russia
3MIREA - Russian Technological University, Moscow, Russia
Keywords: nonlinear filtering, Markov process, posterior probability density, vector of filtered parameters, evolutionary equation, quasi-optimal filtering, numerical integration
Abstract
Issues related to the variational approach to the problem of non-parametric a priori uncertainty are disclosed is a method of 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 a problem of filtering a new Markov process, characterised by a zero drift vector. The main provisions of the method of independent first integrals are given, allowing to provide the required transformation of linear systems of a priori stochastic differential equations. Filtering algorithms were constructed, in which the method of transforming multidimensional densities is used to restore the initial a priori and a posteriori densities of the probability distribution. An example of filtering the phase of a narrowband random process using the proposed conversion method is given. It has been shown that the proposed method of transformation using numerical integration reduces the requirements for the selection of parameters of the posterior density of the probability distribution of the vector of filtered parameters
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