Systems and Means of Informatics
2019, Volume 29, Issue 3, pp 16-28
CONDITIONALLY OPTIMAL LINEAR ESTIMATION OF NORMAL PROCESSES IN VOLTERRA STOCHASTIC SYSTEMS
- I. N. Sinitsyn
- V. I. Sinitsyn
Abstract
On the basis of Pugachev's conditionally optimal estimation (filtering and extrapolation) and previous investigations of the present authors, two estimation approximate conditionally optimal methods for normal stochastic processes in Volterra stochastic systems (VStS) reducible to linear StS with additive and parametric noises are developed. Some approaches for synthesis of Pugachev's filters and extrapolators by replacing parametric noises with equivalent corresponding additive noises are given. Test examples for onedimensional VStS are presented. The given theory and test examples may be simply generalized to VStS with autocorrelated noises and VStS with hereditary and nonlinear interaction functions.
[+] References (8)
- Pugachev, V.S., and I.N. Sinitsyn. 2000, 2004. Teoriya stokhasticheskikh sistem [Stochastic systems: Theory and applications]. Moscow: Logos. 1000 p.
- Sinitsyn, I.N., and V.I. Sinitsyn. 2018. Analiticheskoe modelirovanie normal'nykh protsessov v vol'terrovskikh stokhasticheskikh sistemakh [Analytical modeling of normal processes in Volterra stochastic systems]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 28(2):4-19.
- Sinitsyn, I.N., and V. I. Sinitsyn. 2018. Analiticheskoe modelirovanie raspredeleniy s invariantnoy meroy v vol'terrovskikh stokhasticheskikh sistemakh [Analytical modeling of distributions with invariant measure in Volterra stochastic systems]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 28(3):4-25.
- Sinitsyn, I.N., and V. I. Sinitsyn. 2019. Analiticheskoe modelirovanie protsessov v vol'terrovskikh stokhasticheskikh sistemakh metodom kanonicheskikh razlozheniy. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 29(1): 109-127.
- Sinitsyn, I. N. 2007. Fil'try Kalmana i Pugacheva. 2nd ed. Moscow: Logos. 776 p.
- Sinitsyn, I.N. 2009. Kanonicheskie predstavleniya sluchaynykh funktsiy i ikh primene- nie v zadachakh komp'yuternoy podderzhki nauchnykh issledovaniy [Canonical expansions of random functions and their applications in computer aided support]. Moscow: TORUS PRESS. 768 p.
- Vol'terra, V. 1976. Matematicheskaya teoriya bor'by za sushchestvovanie [Mathematical theory of survival]. Moscow: Nauka. 286 p.
- Svirezhev, Yu. M. 1987. Nelineynye volny, dissipativnye struktury i katastrofy v ekologii [Nonlinear waves, dissipative structures and catastrophes]. Moscow: Nau- ka. 368 p.
[+] About this article
Title
CONDITIONALLY OPTIMAL LINEAR ESTIMATION OF NORMAL PROCESSES IN VOLTERRA STOCHASTIC SYSTEMS
Journal
Systems and Means of Informatics
Volume 29, Issue 3, pp 16-28
Cover Date
2019-10-30
DOI
10.14357/08696527190302
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
Volterra stochastic systems (VStS); method of analytical modeling (MAM); method of canonical expansions (MCE); method of normal approximation (MNA); method of statistical linearization (MSL); stochastic system (StS); stochastic process (StP); Pugachev conditionally optimal filters and extrapola- tors; Kalman filters and extrapolators
Authors
I. N. Sinitsyn  and V. I. Sinitsyn
Author Affiliations
Institute of Informatics Problems, Federal Research Center "Computer Science
and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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