Methodology of random processes high-precision filtering in stochastic dynamic systems with fixed structure. (Part 1)

Аuthors

Kosachev I. M.^1*, Chugai K. N.^2**, Rybackov K. A.^3***

1. Military Academy of the Republic of Belarus, 220, prospekt Nezavisimosti, Minsk, 220057, Belarus'
2. Scientific Research Institute of the Armed Forces, 4/3, str. Slavinsky, Minsk, 220103, Belarus
3. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: kosachev1301@mail.ru
**e-mail: konstantin.ch40@gmail.com
***e-mail: rkoffice@mail.ru

Abstract

The article presents a methodical approach to high-precision nonlinear filtering of multidimensional non-Gaussian random processes in continuous-time stochastic dynamical systems with a fixed structure. The high accuracy of the developed algorithms for the optimal nonlinear filtering problem is stipulated by application of a posteriori higher order central moments of the filtered process. The adaptability of the developed high-precision nonlinear filtering algorithms is ensured by computing in real time a posteriori skewness and excess kurtosis for all phase coordinates of the filtered random process. Further, they are compared with the threshold values corresponding to the Gauss random process, and, if necessary, accounting for by iteration way filtering algorithms of a posteriori higher central moments of the filtered process.

The methodology under consideration for high-precision nonlinear filtering of multidimensional non-Gaussian random processes may be employed for eight basic options of filtering problems. Though engineering algorithms are presented only for the problem of filtering with adaptive noises in mathematical model of the stochastic dynamic system.

The methodical approach to high-precision nonlinear filtering of multidimensional non-Gaussian random processes can be used for eight basic variants of filtering problems, but engineering algorithms are given only for the filtering problem with additive noises in the mathematical model of the stochastic dynamical system.

The first part of the article describes three stages of the proposed methodical approach:

1. Obtaining universal stochastic integro-differential equations for a posteriori arbitrary order central moments of the filtered process.

2. Obtaining stochastic integro-differential equations for a posteriori the required order central moments based on the given mathematical model of the stochastic dynamical system.

3. Obtaining stochastic differential equations for a posteriori central moments of the required order by expansion of averaging in corresponding stochastic integro-differential equations by the non-linearities statistical approximation method.

Other stages of the proposed technique will be described in the second part of the article.

Keywords:

high-precision filtering, random process, dynamical system, stochastic system, fixed structure

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