Radiotekhnika
Publishing house Radiotekhnika

"Publishing house Radiotekhnika":
scientific and technical literature.
Books and journals of publishing houses: IPRZHR, RS-PRESS, SCIENCE-PRESS


Тел.: +7 (495) 625-9241

 

Autoregressive models with multiple roots of the characteristic equations

Keywords:

K.K. Vasiliev – Dr.Sci. (Eng.), professor at Ulyanovsk State Technical University. E-mail: vkk@ulstu.ru


It is proposed to use autoregressive processes with multiple roots of the characteristic equations generated by dynamic systems as models describing real-time signals and noises with smooth realizations. Correlation functions and parameters of autoregressive processes are found. Special attention is paid to the case of characteristic equation with root multiplicity equal to 2. Generalization for causal models of images on multidimensional grids with properties close to isotropic random fields is considered. Algorithms of Kalman filtering of autoregressive sequences observed against additive noise background are presented.
References:

  1. Boks Dzh., Dzhenkins G. Analiz vremenny'x ryadov. Prognoz i upravlenie: per. s angl. / pod red. V.F. Pisarenko. M.: Mir. 1974. Vy'p. 1. 406 s.
  2. Kash'yap R.L., Rao A.R. Postroenie dinamicheskix stoxasticheskix modelej po e'ksperimental'ny'm danny'm: per. s angl. / pod red. V.S. Pugachyova. M.: Nauka. 1983. 384 s.
  3. Vasil'ev K.K., Dragan Ja.P., Kazakov V.A., Krasheninnikov V.R., Kunchenko Ju.P., Omel'chenko V.A., Trifonov A.P., Spektor A.A. Prikladnaya teoriya sluchajny'x proczessov i polej / pod red. Vasil'eva K.K. i Omel'chenko V.A. Ul'yanovsk: UlGTU. 1995. 256 s.
  4. Vasil'ev K.K., Popov O.V. Avtoregressionny'e modeli sluchajny'x polej s kratny'mi konyami // Trudy' 4-j konferenczii «ROAI: novy'e informaczionny'e texnologii» Novosibirsk. 1998. 4.1. S. 258-260.
  5. Vasil'ev K.K., Dement'ev V.E. Avtoregressionny'e modeli mnogomerny'x izobrazhenij // Naukoemkie texnologii. 2013. № 5. S. 12-16.
  6. Vasil'ev K.K., V.R.Krasheninnikov, Tashlinskij A.G. Statistichekij analiz posledovatel'nostej mnogomerny'x izobrazhenij // Naukoemkie texnologii. 2013. № 5. S. 5-11.
  7. Vasil'ev K.K. Priem signalov s diskretny'm vremenem. E'lektronnoe ucheb. posobie. Ul'yanovsk: UlGTU. 2014. 105 s.

June 24, 2020
May 29, 2020

© Издательство «РАДИОТЕХНИКА», 2004-2017            Тел.: (495) 625-9241                   Designed by [SWAP]Studio