Numerical algorithms for identification of parameters Gegenbauer autoregressive with noise observations

D. Ivanov

doi:10.12737/15974

NUMERICAL ALGORITHMS FOR IDENTIFICATION OF PARAMETERS GEGENBAUER AUTOREGRESSIVE WITH NOISE OBSERVATIONS Numerical algorithms for identification of parameters Gegenbauer autoregressive with noise observations

АА Аа

Published in Actual directions of scientific researches of the XXI century: theory and practice · Volume 3, Issue 5, p. 2 · Pages 75–79 · Rubric: Sekciya: «Effektivnye metody i instrumenty issledovaniya modeley sistem i mehanizmov»

DOI: https://doi.org/10.12737/15974

Received: 24.11.2015 Accepted: 24.11.2015 Published: 24.11.2015 Language of publication: RUS

Authors

D. Ivanov

ABSTRACT

This paper proposes a numerical algorithm, which allows to solve the problem of estimating the parameters of Gegenbauer autoregression with noise. Not using direct methods for finding the global extremum of the nonlinear function, and only by solving a system of linear equations.

KEYWORDS

observation noise, Gegenbauer autoregressive, least square method.

Text

УДК 519.254.1

ЧИСЛЕННЫЙ АЛГОРИТМ ИДЕНТИФИКАЦИИ параметров авторегрессии ГеГЕнбаура с помехой наблюдения

NUMERICAL ALGORITHMS FOR IDENTIFICATION OF PARAMETERS GEGENBAUER AUTOREGRESSIVE WITH NOISE OBSERVATIONS

Иванов Д.В., к.ф.-м.н.

ФГБОУ ВПО « Самарский государственный университет путей сообщения»,

г. Самара, Россия

E-mail: dvi85@list.ru

DOI: 10.12737/15974

Аннотация: В статье предложен численный алгоритм, позволяющий решить задачу оценивания параметров авторегрессии Гегенбауэра с помехой наблюдения не применяя прямых методов отыскания глобального экстремума нелинейной функции, а только решая системы линейных уравнений.

Summary: This paper proposes a numerical algorithm, which allows to solve the problem of estimating the parameters of Gegenbauer autoregression with noise. Not using direct methods for finding the global extremum of the nonlinear function, and only by solving a system of linear equations.

Ключевые слова: помеха наблюдения, авторегрессия Гегенбауэра, метод наименьших квадратов.

Keywords: observation noise, Gegenbauer autoregressive, least square method.

В настоящее время активно развиваются методы состоятельного оценивания динамических систем на основе минимизации нелинейных критериев [1,2] и их рекуррентных модификаций [3,4], обобщение результатов на системы, описываемые уравнениями с производными и разностями дробного порядка [5-9].

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2. Katsyuba O.A., Kozlov E.V. Otsenivanie parametrov mnogosvyaznoy lineynoy dinamicheskoy sistemy raznogo poryadka pri nalichii atvokorrelirovannykh pomekh vo vkhodnykh i vykhodnykh signalakh// Sistemy upravleniya i informatsionnye tekhnologii. 2011. T. 45. № 3.1. S. 151-154.

3. Katsyuba O.A., Zhdanov A.I. Rekurrentnoe otsenivanie parametrov stokhasticheskikh lineynykh dinamicheskikh sistem s oshibkami po vkhodu i vykhodu. Izvestiya Rossiyskoy akademii nauk. Teoriya i sistemy upravleniya. 1986. № 3. S. 191.

4. Ivanov D.V., Katsyuba O.A. Rekurrentnaya parametricheskaya identifikatsiya mnogomernykh lineynykh dinamicheskikh sistem na osnove metoda nelineynykh naimen´shikh kvadratov. Vestnik Samarskogo gosudarstvennogo tekhnicheskogo universiteta. Seriya: Tekhnicheskie nauki. 2010. № 2 (27). S. 78-86.

5. Ivanov D.V. Identifikatsiya lineynykh dinamicheskikh sistem netselogo poryadka s pomekhoy v vykhodnom signale //Vestnik Tambovskogo universiteta. Seriya: Estestvennye i tekhnicheskie nauki. 2013. T. 18. № 5-2. S. 2534-2536.

6. Ivanov D.V., Shirinov I.R. Identifikatsiya mnogomernykh po vkhodu lineynykh dinamicheskikh sistem drobnogo poryadka s pomekhoy v vykhodnom signale //Vestnik Samarskogo instituta upravleniya, №4 (27) S.144-151.

7. Ivanov D.V. O sostoyatel´nosti otsenok parametrov ARX-sistem drobnogo poryadka s pomekhoy v vykhodnom signale //Stokhasticheskaya optimizatsiya v informatike. - Tom 1, №2, 2013. - S.21-32.

8. Ivanov D.V. Chislennyy algoritm otsenivaniya parametrov lineynykh dinamicheskikh sistem drobnogo poryadka s pomekhoy v vykhodnom signale.. Evristicheskie algoritmy i raspredelennye vychisleniya. 2014. T. 1. № 1. S. 53-63.

9. Ivanov D.V. Otsenivanie parametrov lineynykh ARX-sistem drobnogo poryadka s pomekhoy nablyudeniya vo vkhodnom signale// Vestnik Tomskogo gosudarstvennogo universiteta. Upravlenie, vychislitel´naya tekhnika i informatika. - №2(27), 2014. S.43-50.

10. Ivanov D.V. Otsenivanie parametrov avtoregressii Gegenbauera pri nalichii pomekhi nablyudeniya. Informatsionnye tekhnologii i nanotekhnologii. Materialy Mezhdunarodnoy konferentsii i molodezhnoy shkoly. Federal´noe gosudarstvennoe avtonomnoe obrazovatel´noe uchrezhdenie vysshego obrazovaniya«Samarskiy gosudarstvennyy aerokosmicheskiy universitet imeni akademika S.P. Koroleva (natsional´nyy issledovatel´skiy universitet)». Samara 2015. S. 266-270.

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GOST

Ivanov D. Numerical algorithms for identification of parameters Gegenbauer autoregressive with noise observations // Actual directions of scientific researches of the XXI century: theory and practice. 2015. no. 5. pp. 75-79. DOI: https://doi.org/10.12737/15974. (Date of access 19.10.2026).

MLA

D. Ivanov. "Numerical algorithms for identification of parameters Gegenbauer autoregressive with noise observations." Actual directions of scientific researches of the XXI century: theory and practice 3.5 (2015): 75-79. DOI: https://doi.org/10.12737/15974.

APA

Ivanov D. (2015). Numerical algorithms for identification of parameters Gegenbauer autoregressive with noise observations. Actual directions of scientific researches of the XXI century: theory and practice, 3(5), 75-79. https://doi.org/10.12737/15974

Chicago

D. Ivanov. "Numerical algorithms for identification of parameters Gegenbauer autoregressive with noise observations." Actual directions of scientific researches of the XXI century: theory and practice 3, no. 5 (2015): 75-79. https://doi.org/10.12737/15974.

WIKI

{{cite journal | author = Ivanov D. | title = Numerical algorithms for identification of parameters Gegenbauer autoregressive with noise observations | journal = Actual directions of scientific researches of the XXI century: theory and practice | year = 2015 | volume = 3 | issue = 5 | pages = 75-79 | doi = 10.12737/15974 }}

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NUMERICAL ALGORITHMS FOR IDENTIFICATION OF PARAMETERS GEGENBAUER AUTOREGRESSIVE WITH NOISE OBSERVATIONS Numerical algorithms for identification of parameters Gegenbauer autoregressive with noise observations

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