Systems and Means of Informatics
2016, Volume 26, Issue 3, pp 4-25
MATHEMATICAL SOFTWARE FOR SUBOPTIMAL NORMAL FILTERING IN STOCHASTIC SYSTEMS WITH COMPLEX FRACTION-RATIONAL NONLINEARITIES
- I. N. Sinitsyn
- V. I. Sinitsyn
- I. V. Sergeev
- E. R. Korepanov
- V. V. Belousov
- V. S. Shorgin
- E. S. Agafonov
Abstract
The paper describes the instrumental algorithms and software tools for the module "StS-CFRN.Filter" in numerical library "StS-Filter." The module is based on series approximations. It gives the opportunity to synthesize differential and difference normal suboptimal filters for specific nonlinear stochastic systems.
Such StS have the following peculiarities: observation equations do not include Poisson noise and coefficient at Wiener noise does not depend on state variables. Special attention is paid to the software tools based on symbolic and nonsymbolic algorithms. The practical efficiency of the software tools has been illustrated.
[+] References (17)
- Sinitsyn, I.N., and V. I. Sinitsyn. 2014. Analiticheskoe modelirovanie normal'nykh protsessov v stokhasticheskikh sistemakh so slozhnymi nelineynostyami [Analytical modeling of normal processes in stochastic systems with complex nonlinearities]. Informatika i ee Primeneniya - Inform. Appl. 8(3):2-4.
- Sinitsyn, I.N., V. I. Sinitsyn, I.V. Sergeev, V.V. Belousov, and V. S. Shorgin.
2014. Matematicheskoe obespechenie analiticheskogomodelirovaniyastokhasticheskikh sistem so slozhnymi nelineynostyami [Mathematical software for analytical modeling of stochastic systems with complex nonlinearities]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 24(3):4-29.
- Sinitsyn, I. N., V. I. Sinitsyn, and E. R. Korepanov. 2015. Modelirovanie normal'nykh protsessov v stokhasticheskikh sistemakh so slozhnymi irratsional'nymi nelineynostyami [Modeling of normal processes in stochastic systems with complex irrational nonlinearities]. Informatika i ee Primeneniya - Inform Appl. 9(1):2-8.
- Sinitsyn, I.N., V. I. Sinitsyn, I.V. Sergeev, E.R. Korepanov, V.V. Belousov, and V. S. Shorgin. 2015. Matematicheskoe obespechenie modelirovaniya normal'nykh protsessov v stokhasticheskikh sistemakh so slozhnymi irratsional'nymi nelineynostyami [Mathematical software for modeling of normal processes in stochsatic systems with complex irrational nonlinearities]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 25(2):3-19.
- Sinitsyn, I. N., V. I. Sinitsyn, and E. R. Korepanov. 2015. Modelirovanie normal'nykh protsessov v stokhasticheskikh sistemakh so slozhnymi transtsendentnymi nelineyno- styami [Modeling of normal processes in stochastic systems with complex transcendental nonliearities]. Informatika i ee Primeneniya - Inform Appl. 9(2):23-29.
- Sinitsyn, I.N., V. I. Sinitsyn, and E.R. Korepanov. 2015. Analiticheskoe modelirovanie normal'nykh protsessov v stokhasticheskikh sistemakh so slozhnymi drobno- ratsional'nymi nelineynostyami [Analytical modeling of normal processes in stochastic systems with complex fractional-rational nonlinearities]. Informatika i ee Primeneniya - Inform Appl. 9(4):3-17.
- Sinitsyn, I.N., V. I. Sinitsyn, I.V. Sergeev, E.R. Korepanov, V.V. Belousov, and V. S. Shorgin. 2016. Matematicheskoe obespechenie modelirovaniya normal'nykh protsessov v stokhasticheskikh sistemakh so slozhnymi drobno-ratsional'nymi nelineyno- styami [Software tools for analytical modeling of normal processes in stochastic systems with fraction-rational nonlinearities]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 26(1):227-247.
- Sinitsyn, I.N., 2016. Normal'nye i ortogonal'nye suboptimal'nye fil'try dlya ne- lineynykh stokhasticheskikh sistem na mnogoobraziyakh [Normal orthogonal suboptimal filters for nonlinear stochastic systems on manifolds]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 26(1):199-226.
- Pugachev, V. S., and I. N. Sinitsyn. 2001. Stochastic systems. Theory and applications. Singapore: World Scientific. 908 p.
- Sinitsyn, I.N., and V.I. Sinitsyn. 2013. Lektsii po normal'noy i ellipsoidal'noy approksimatsii raspredeleniy v stokhasticheskikh sistemakh [Lectures on normal and ellipsoidal approximation in stochastic systems]. Moscow: TORUS PRESS. 488 p.
- Sinitsyn, I.N. 2007. Fil'try Kalmana i Pugacheva [Kalman and Pugachev Filters]. 2nd ed. Moscow: Logos. 776 p.
- Korn, G. A., andT. M. Korn. 1968. Mathematical handbook. New York, NY: McGraw- Hill. 943 p.
- Popov, B.A., and G. S. Tesler. 1984. Vychislenie funktsiy na EVM: Spravochnik [Calculation of functions on the computer: Handbook]. Kiev: Naukova Dumka. 599 p.
- Buchberger, B., G.E. Collins, R. Loos, and R. Albrecht, eds. 1983. Computer algebra: Symbolic and algebraic computation. 2nd ed. Wien-New York: Springer- Verlag. 410 p.
- D'yakonov, V. P. 2009. Entsiklopediya komp'yuternoy algebry [Computer algebra encyclopedia]. Moscow: DMK Press. 1264 p.
- Sinitsyn, I. N., E. R. Korepanov, V. V. Belousov, and A. V. Kutsenko. 2007. Razvitie metodicheskogo i programmnogo obespecheniya na osnove simvol'nykh vychisleniy dlya issledovaniya stokhasticheskikh sistem [Development of methodological and program software tools on symbolic computing for stochastic systems research]. 6th Conference (International) on System Identification and Control Problems Proceedings. CD- ROM. 1447-1462.
- Sinitsyn, I. N., V. I. Sinitsyn, E. R. Korepanov, V. V. Belousov, and E. S. Agafonov.
2009. Simvol'noe matematicheskoe obespechenie dlya analiza i modelirovaniya stokha- sticheskikh sistem, osnovannoe na kanonicheskikh razlozheniyakh sluchaynykh funktsiy [Symbolic mathematical software for analysis and modeling of stochastic systems based on canonical representation of random functions]. 8th Conference (International) on System Identification and Control Problems Proceedings. CD-ROM. 1059-1072.
[+] About this article
Title
MATHEMATICAL SOFTWARE FOR SUBOPTIMAL NORMAL FILTERING IN STOCHASTIC SYSTEMS WITH COMPLEX FRACTION-RATIONAL NONLINEARITIES
Journal
Systems and Means of Informatics
Volume 26, Issue 3, pp 4-25
Cover Date
2016-08-30
DOI
10.14357/08696527160301
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
complex fraction-rational nonlinearities (CFRN); module "StS- CFRN.Filter;" normal approximation method (NAM); numerical library "StS- Filter;" stochastic linearization method (SLM); stochastic systems (StS)
Authors
I. N. Sinitsyn  , V. I. Sinitsyn ,
I. V. Sergeev , E. R. Korepanov ,
V. V. Belousov , V. S. Shorgin ,
and E. S. Agafonov
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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