This article is cited in 3 papers

Joint filtration and recognition of normal proсesses in stochastic systems with unsolved derivatives

I. N. Sinitsyn<sup>ab

a</sup> Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
^b Moscow State Aviation Institute (National Research University), 4 Volokolamskoe Shosse, Moscow 125933, Russian Federation

Abstract: Methodological and algorithmic support for analytical modeling, estimation, identification, and calibration for essentially nonstationary (e. g., shock) stochastic systems with unsolved derivatives (StS USD) is worked out. It is supposed that state equations contain observation vector. After survey, classes of regression equations for StS USD are considered. Basic results: ($i$) for general StS USD, optimal algorithms of joint filtration and recognition are presented; ($ii$) for linear Gaussian equations, optimal algorithms of joint linear filtration and recognition are given; ($iii$) for StS USD, linear relatively on $X_t$ and nonlinear relatively on $Y_t$ algorithm is described; and ($i\nu$) in case of result ($iii$), using the method of normal approximation, the corresponding algorithm is developed. A scalar example of nonlinear StS USD with Gaussian noise corresponding algorithm is given and discussed. Some potential generalizations are presented.

Keywords: stochastic systems with unsolved derivatives, joint filtration and recognition, regression model.

Received: 09.06.2021

DOI: 10.14357/19922264220211