Geodesic
Identification of fractional-order ARX Wiener systems in the presence of noise in the input signals
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 2, pp. 41-46.

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The paper describes the parametric identification of fractional-order Wiener ARX (Autoregressive with exogenous input) systems in the presence of noise in the input signals. The criterion for evaluating the parameters of these systems is proposed which is a generalization of the method of least squares. It is proved that the interference class martingale-difference derived parameter estimates will have the property of strong consistency. It is shown that in the case of constant noise variance to obtain consistent estimates it is sufficient to know the ratio of their variances.
Keywords: parametric identification, Wiener system, a difference of fractional order, errors in variables, least squares, consistent estimator. 
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D. V. Ivanov. Identification of fractional-order ARX Wiener systems in the presence of noise in the input signals. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 2, pp. 41-46. http://geodesic.mathdoc.fr/item/SVMO_2016_18_2_a5/

[1] A. M. Nakhushev, Drobnoe ischislenie i ego primenenie, FIZMATLIT, M., 2003, 272 pp.

[2] V. V. Uchaikin, Metod drobnykh proizvodnykh, Izdatelstvo «Artishok», Ulyanovsk, 2008, 512 pp.

[3] V. V. Mishunin, Sistemy avtomaticheskogo upravleniya i kontrolya s drobno-irratsionalnymi peredatochnymi funktsiyami, Izd-vo BGTU im. V.G. Shukhova, Belgorod, 2004, 255 pp.

[4] I. V. Boikov, N. P. Krivulin, “Parametricheskaya identifikatsiya sistem, matematicheskie modeli kotorykh opisyvayutsya differentsialnymi uravneniyami s proizvodnymi drobnykh poryadkov”, Metrologiya, 2013, no. 9, 3–16

[5] I. V. Boikov, N. P. Krivulin, “Parametricheskaya identifikatsiya ereditarnykh sistem s raspredelennymi parametrami”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Tekhnicheskie nauki., 2013, no. 2(26), 120–129

[6] D. V. Ivanov, O. A. Katsyuba, “O sostoyatelnosti otsenok parametrov ARX-sistem drobnogo poryadka s pomekhoi v vykhodnom signale”, Stokhasticheskaya optimizatsiya v informatika, 2013, no. 1(2), 21–32

[7] D. V. Ivanov, “Otsenivanie parametrov lineinykh ARX-sistem drobnogo poryadka s pomekhoi nablyudeniya vo vkhodnom signale”, Vestnik Tomskogo gosudarstvennogo universiteta. Upravlenie, vychislitelnaya tekhnika i informatika, 2014, no. 2(27), 43–50

[8] D. V. Ivanov, “Chislennyi algoritm otsenivaniya parametrov lineinykh dinamicheskikh sistem drobnogo poryadka s pomekhoi v vykhodnom signale”, Evristicheskie algoritmy i raspredelennye vychisleniya, 2014, no. 1(1), 53–63 | MR

[9] O. A. Katsyuba, Teoriya identifikatsii stokhasticheskikh dinamicheskikh sistem v usloviyakh neopredelennosti, SamGUPS, Samara, 2008, 119 pp.

[10] O. A. Katsyuba, A. I. Zhdanov, “Osobennosti primeneniya MNK dlya otsenivaniya lineinykh raznostnykh operatorov v zadachakh identifikatsii ob'ektov upravleniya”, Avtomatika i telemekhanika, 1979, no. 8, 86–90 | MR

[11] O. A. Katsyuba, A. I. Zhdanov, “Identifikatsiya metodom naimenshikh kvadratov parametrov uravnenii avtoregressii s additivnymi oshibkami izmerenii”, Avtomatika i telemekhanika, 1982, no. 2, 29–38 | MR | Zbl