Informatics and Applications
2022, Volume 16, Issue 2, pp 85-93
JOINT FILTRATION AND RECOGNITION OF NORMAL PROCESSES IN STOCHASTIC SYSTEMS WITH UNSOLVED DERIVATIVES
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 Xt and nonlinear relatively on Yt algorithm is
described; and (iv) 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.
[+] References (7)
- Sinitsyn, I. N. 2022. Analiticheskoe modelirovanie i otsenivanie nestatsionarnykh normal'nykh protsessov v stokhasticheskikh sistemakh, ne razreshennykh otnositel'no
proizvodnykh [Anatlytical modeling and estmation of nonstationary normal processes with unsolved derivatives]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 32(2):58-71.
- Sinitsyn, I. N. 2021. Analiticheskoe modelirovanie i fil'tratsiya normal'nykh protsessov v integrodifferentsial'nykh
stokhasticheskikh sistemakh, ne razreshennykh otnositel'no proizvodnykh [Analytical modeling and filtering
in integrodifferential systems with unsolved derivatives].
Sistemy i Sredstva Informatiki - Systems and Means of Informatics 31(1):37-56.
- Sinitsyn, I. N. 2021. Analytical modeling and estimation of normal processes defined by stochastic differential equations with unsolved derivates. J. Mathematics Statistics Research 3(1):139. 7 p. doi: 10.36266/JMSR/139.
- Sinitsyn, I. N. 2022. Normalizatsiya sistem, stokhasticheski ne razreshennykh otnositel'no proizvodnykh [Normalization of systems with stochastically unsolved derivatives]. Informatika i ee Primeneniya - Inform. Appl. 16(1):32-38.
- Pugachev, V. S., and I. N. Sinitsyn. 1987. Stochastic differential systems. Analysis and filtering. Chichester, New York: John Wiley & Sons. 549 p.
- Sinitsyn, I. N. 2007. Fil'try Kalmana i Pugacheva [Kalman and Pugachev filters]. 2nd ed. Moscow: Logos. 776 p.
- Pugachev, V. S. 2002. Teoriya veroyatnostey i matematicheskaya statistika [Probability theory and mathematical
statistics]. 2nd ed. Moscow: Fizmatlit. 496p
[+] About this article
Title
JOINT FILTRATION AND RECOGNITION OF NORMAL PROCESSES IN STOCHASTIC SYSTEMS WITH UNSOLVED DERIVATIVES
Journal
Informatics and Applications
2022, Volume 16, Issue 2, pp 85-93
Cover Date
2022-07-25
DOI
10.14357/19922264220211
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
stochastic systems with unsolved derivatives; joint filtration and recognition; regression
Authors
I. N. Sinitsyn  , 
Author Affiliations
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
Moscow State Aviation Institute (National Research University), 4 Volokolamskoe Shosse, Moscow 125933,
Russian Federation
|