Informatics and Applications
2016, Volume 10, Issue 1, pp 34-44
ORTHOGONAL SUPOPTIMAL FILTERS FOR NONLINEAR STOCHASTIC SYSTEMS ON MANIFOLDS
Abstract
The authors developed the synthesis theory of suboptimal filers (SOF) based on normal approximation method (NAM), statistical linearization method (SLM), orthogonal expansions method (OEM), and quasi-moment method (QMM) for nonlinear differential stochastic systems on manifolds (MStS) with Wiener and Poisson noises.
Exact optimal (for mean square error criteria) equations for MStS with Gaussian noises in observation equations for the one-dimensional a posteriori characteristic function are derived. Problems of approximate solving of exact equations are discussed. Accuracy and sensitivity equations are presented. A test example for the nonlinear scalar differential equation with additive and multiplicative noises is given. Some generalizations are mentioned.
[+] References (9)
- Sinitsyn, I. N. 2015. Analiticheskoe modelirovanie raspredeleniy na osnove ortogonal'nykh razlozheniy v neliney- nykh stokhasticheskikh sistemakh na mnogoobraziyakh [Analytical modeling in stochastic systems on manifolds based on orthogonal expansions]. Informatika i ee Prime- neniya - Inform. Appl. 9(2):17-24.
- Sinitsyn, I. N. 2015. Primenenie ortogonal'nykhrazlozheniy dlya analiticheskogo modelirovaniya mnogomernykh raspredeleniy v nelineynykh stokhasticheskikh sistemakh na mnogoobraziyakh [Applications of orthogonal expan
sions for analytical modeling of multidimensional distributions in stochastic systems on manifolds]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 25(3):3-22.
- Watanabe, S., and N. Ikeda. 1981. Stochastic differential equations and diffusion processes. Amsterdam - Oxford - New York: North-Holland Publishing Co.; Tokyo: Ko- dansha Ltd. 476 p.
- Korolyuk, V. S., N.I. Portenko, A.V. Skorokhod, and A. F Turbin, eds. 1985. Spravochnikpo teorii veroyatnos- tey i matematicheskoy statistike [Probability theory and
mathematical statistics: Handbook]. Moscow: Nauka. 640 p.
- Pugachev, V. S., and I. N. Sinitsyn. 2001. Stochastic systems. Theory and applications. Singapore: World Scientific. 908 p.
- Sinitsyn, I. N. 2007. Fil'try Kalmana i Pugacheva [Kalman and Pugachev filters]. 2nd ed. Moscow: Logos. 776 p.
- Pugachev, V. S., and I. N. Sinitsyn. 1987. Stochastic dif
ferential systems. Analysis and filtering. Chichester - New York, NY: Jonh Wiley. 549 p.
- Evlanov, A. G., and V. M. Konstantinov. 1976. Sistemy so slozhnymi parametrami [Systems with random parameters]. Moscow: Nauka. 568 p.
- Krasovskii, A. A., ed. 1987. Spravochnik po teorii avtomaticheskogo upravleniya [Handbook for automatic con-trol]. Moscow: Nauka. 712 p.
[+] About this article
Title
ORTHOGONAL SUPOPTIMAL FILTERS FOR NONLINEAR STOCHASTIC SYSTEMS ON MANIFOLDS
Journal
Informatics and Applications
2016, Volume 10, Issue 1, pp 34-44
Cover Date
2016-01-30
DOI
10.14357/19922264160103
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
a posteriori one-dimensional distribution; coefficient of orthogonal expansion; first sensitivity function; normal approximation method; normal suboptimal filter; orthogonal expansion method; orthogonal suboptimal filter; quasi-moment method; quasi-moment; statistical linearization method; stochastic system on manifolds; suboptimal filter; Wiener white noise
Authors
I. N. Sinitsyn 
Author Affiliations
Institute of Informatics Problems, Federal Research Center “Computer Sciences and Control” of the Russian
Academy of Sciences, 44-2 Vavilov Str.,Moscow 119333, Russian Federation
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