Informatics and Applications
2024, Volume 18, Issue 3, pp 12-20
CONDITIONALLY OPTIMAL FILTERING IN STOCHASTIC SYSTEMS WITH RANDOM PARAMETERS AND UNSOLVED DERIVATIVES
Abstract
For observable differential Gaussian stochastic systems (StS) with random parameters in the form of
multicomponent integral canonical expansions (MC ICE) and StS with unsolved derivatives (USD),methodological
support for synthesis of conditionally optimal filters is presented. A survey in the fields of analytical modeling
and sub- and conditionally optimal filtering, extrapolation, and identification is presented. Necessary information
concerning MC ICE is given. Special attention is paid to mean square regressive linearization including MC ICE.
The stochastic systems with USD reducible to differential are considered. Basic results in normal conditionally
optimal filtering (COF) are presented for StS USD reducible to differential. The theory of COF application to StS
USD with multiplicative noises is developed. An illustrative example for scalar StS USD reducible to differential is
given. For future COF generalization, (i) methods of moments, quasi-moments, and one- and multidimensional
densities of orthogonal expansions and (ii) development for stochastic inclusions are recommended.
[+] References (14)
- Sinitsyn, I.N. 2022. Analiticheskoe modelirovanie
i otsenivanie nestatsionarnykh normal’nykh protsessov
v stokhasticheskikh sistemakh, ne razreshennykh otnositel’no
proizvodnykh [Analytical modeling and estimation
of nonstationary normal processors with unsolved
derivatives]. Sistemy i Sredstva Informatiki — Systems
and Means of Informatics 32(2):58–71. doi: 10.14357/08696527220206. EDN: YMGERJ.
- 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 for integrodifferential systems with unsolved
derivatives]. Sistemy i Sredstva Informatiki — Systems
and Means of Informatics 31(1):37–56. doi: 10.14357/
08696527210104. EDN: PLYOSF.
- Sinitsyn, I.N. 2021.Analytical modeling and estimation of
normal processes defined by stochastic differential equations
with unsolved derivatives. J. Mathematics Statistics
Research 3(1):139. 7 p. doi: 10.36266/JMSR/139.
- Sinitsyn, I.N. 2022. Sovmestnaya fil’tratsiya i raspoznavanie
normal’nykh protsessov v stokhasticheskikh sistemakh,
ne razreshennykh otnositel’no proizvodnykh
[Joint filtration and recognition of normal prosesses in
stochastic systems with unsolved derivatives]. Informatika
i ee Primeneniya — Inform. Appl. 16(2):85–93. doi:
10.14357/19922264220211. EDN: SMJCBB.
- Sinitsyn, I.N. 2024. Suboptimal’naya fil’tratsiya
v stokhasticheskikh sistemakh, ne razreshennykh otnositel’no
proizvodnykh, so sluchaynymi parametrami
[Suboptimal filtering in stochastic systems with random
parameters and unsolved derivatives]. Informatika i ee
Primeneniya — Inform. Appl. 18(1):2–10. doi: 10.14357/
19922264240101. EDN: KUWMKJ.
- Sinitsyn, I.N. 2023. Kanonicheskie predstavleniya
sluchaynykh funktsiy. Teoriya i primeneniya [Canonical expansions
of random functions. Theory and application].
Moscow: TORUS PRESS. 816 p.
- Pugachev, V. S. 2002. Teoriya veroyatnostey i matematicheskaya
statistika [Probability theory and mathematical
statistics]. 2nd ed.Moscow: Fizmatlit. 496 p.
- Sinitsyn, I.N. 2007. Fil’try Kalmana i Pugacheva [Kalman
and Pugachev filters]. 2nd ed.Moscow: Logos. 776 p.
- Tolstonogov, A.A., and I.A. Finogenko. 1980. On
functional-differential inclusions in a Banach space with
a nonconvex right-hand side. Soviet Mathematics Doklady
22:320–324.
- Finogenko, I.A. 1980. K voprosu o resheniyakh
funktsional’no-differentsial’nykh vklyucheniy [On the issue
of solutions of functional-differential inclusions].
Prikladnaya matematika i pakety prikladnykh programm
[Applied mathematics and application software packages].
Irkutsk: SEISO AN SSSR. 95–107.
- Finogenko, I.A. 1981. Svoystva mnozhestva resheniy
funktsional’no-differentsial’nykh vklyucheniy [Properties
of the solution set of functional differential inclusions].
Kraevye zadachi [Boundary value problem]. Perm: PPI.
145–149.
- Kolmanovskiy, V. B., and V.R. Nosov. 1981. Ustoychivost’
i periodicheskie rezhimy reguliruemykh sistems posledstviem
[Stability and periodic modes of regulated systems with
consequences]. Moscow: Nauka. 448 p.
- Finogenko, I. A. 1983. O neyavnykh funktsional’nodifferentsial’nykh
uravneniyakh v banakhovom prostranstve
[On implicit functional differential equations in
a Banach space]. Dinamika nelineynykh sistem [Dynamics
of nonlinear systems]. Novosibirsk: Nauka.
151–164.
- Azbelev, N. V., V. P. Maksimov, and L.F. Rakhmatulina.
1991. Vvedenie v teoriyu funktsional’no-differentsial’nykh
uravneniy [Introduction to the theory of functional differential
equations]. Moscow: Nauka. 280 p.
[+] About this article
Title
CONDITIONALLY OPTIMAL FILTERING IN STOCHASTIC SYSTEMS WITH RANDOM PARAMETERS AND UNSOLVED DERIVATIVES
Journal
Informatics and Applications
2024, Volume 18, Issue 3, pp 21-29
Cover Date
2024-09-20
DOI
10.14357/19922264240303
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
regression linearization; stochastic system with unsolved derivatives (StS USD); stochastic process; conditionally optimal filtering (COF)
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
|