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UDC 519-7
Joint use of Kalman filter and minimax filter in the assessment problem of parameters for random process model
Anton Sergeevich Sheludko, engineer of Applied Mathematics Department of South Ural State University, Chelyabinsk, Russian Federation, antonsheludko@gmail.com
Vladimir Ivanovich Shiryaev, Doctor of Science (Engineering), professor, head of Control Systems Department of South Ural State University, Chelyabinsk, Russian Federation, vis@susu.ac.ru
Abstract
The article considers the problem of reconstruction of a random process model by a singular realization in terms of a small number of available measurements. The problem of parameters assessment is shown as the problem of assessment of state vector in the model of a dynamic system with variable matrix of measurement. The possibility of a joint use of filtration algorithm to specify multiple estimation of a state vector is studied.
Keywords
random process, Kalman filter, minimax filter
References
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2. Nechaev, YU.I. Informacionnye tekhnologii i upravlenie v bortovyh intellektual'nyh sistemah novyh pokolenij / YU.I. Nechaev // Mekhatronika, avtomatizaciya, upravlenie. – 2010. – № 1. – S. 42–53.
3. Nikul'chev, E.V. Modelirovanie sistem s nelinejnoj dinamikoj na osnovanii ehksperimental'nyh dannyh / E.V. Nikul'chev // Mekhatronika, avtomatizaciya, upravlenie. – 2006. – № 5. – S. 6–14.
4. Smirnov, D.A. Rekonstrukciya uravnenij dinamiki i diagnostika vzaimodejstviya nelinejnyh kolebatel'nyh sistem po vremennym ryadam: avtoref. … d-ra fiz.-mat. nauk / D.A. Smirnov. – Saratov, 2010. – 34 s.
5. Antipov, O.I. Prognozirovanie i fraktal'nyj analiz haoticheskih processov diskretno-nelinejnyh sistem s pomoshch'yu nejronnyh setej / O.I. Antipov, V.A. Neganov // Doklady AN. – 2011. – T. 436, № 1. – S. 34–37.
6. Parameters identification of chaotic system by chaotic gravitational search algorithm / C. Li, J. Zhou, J. Xiao, H. Xiao // Chaos, Solitons & Fractals. – 2012. – Vol. 45. – P. 539–547.
7. Parameter identification of commensurate fractional-order chaotic system via differential evolution / Y. Tang, X. Zhang, C. Hua, L. Li, Y. Yang // Phys. Lett. A. – 2012. – Vol. 376. – P. 457–464.
8. Voss, H.U. Nonlinear dynamical system identification form uncertain and indirect measurements / H.U. Voss, J. Timmer, J. Kurths // International Journal of Bifurcation and Chaos. – 2004. – Vol. 14. – № 6. – P. 1905–1933.
9. Erramilli, A. An application of deterministic chaotic maps to model packet traffic / A. Erramilli, R.P. Singh, P. Pruthi // Queueing Systems. – 1995. – Vol. 20. – P. 171–206.
10. Elsakov, S.M. O mnogoehkstremal'nosti v zadachah ocenivaniya sistem determinirovannogo haosa / S.M. Elsakov, V.I. SHiryaev // Vestnik YUUrGU. Seriya «Komp'yuternye tekhnologii, upravlenie, radioehlektronika». – 2009. – № 3. – S. 37–41.
11. O reshenii zadach parametricheskoj identifikacii processov s haoticheskoj dinamikoj / I.V. Grishin, A.S. SHelud'ko, V.I. SHiryaev i dr. // Vestnik YUUrGU. Seriya «Komp'yuternye tekhnologii, upravlenie, radioehlektronika». – 2008. – № 3. – S. 44–50.
12. Kozhihova, N.A. Prognozirovanie vremennogo ryada s uchetom haoticheskoj komponenty / N.A. Kozhihova, V.I. SHiryaev // Vestnik YUUrGU. Seriya «Komp'yuternye tekhnologii, upravlenie, radioehlektronika». – 2010. – № 22. – S. 22–25.
13. Uhanov, M.V. Algoritmy postroeniya informacionnyh mnozhestv dlya realizacii minimaksnogo fil'tra / M.V. Uhanov, V.I. SHiryaev // Vestnik YUUrGU. Seriya «Matematika, fizika, himiya». – 2002. – № 3. – S. 19–33.
14. Kalman, R.E. Identifikaciya sistem s shumami / R.E. Kalman // UMN. – 1985. – T. 40, № 4. – S. 27–41.
15. CHernous'ko, F.L. Ob optimal'nom ehllipsoidal'nom ocenivanii dinamicheskih sistem, podverzhennyh neopredelennym vozmushcheniyam / F.L. CHernous'ko // Kibernetika i sistemnyj analiz. – 2002. – № 2. – S. 85–94.
16. SHmatkov, A.M. Postroenie analoga fil'tra Kalmana dlya garantirovannoj ocenki sostoyaniya dinamicheskoj sistemy / A.M. SHmatkov // Izv. RAN. Teoriya i sistemy upravleniya. – 2011. – № 5. – S. 33–40.
Source
Bulletin of the South Ural State University. Ser. Computer Technologies, Automatic Control, Radio Electronics, 2012, iss. 17, no. 35 (294)
, pp. 59-64. (in Russ.) (The main)