Source: http://journals.uran.ua/eejet/article/view/157288
Timestamp: 2019-04-25 04:01:32+00:00

Document:
The study deals with the problem of identification of non-stationary parameters of a linear object which can be described by first-order Markovian model, with the help of the simplest in computational terms single-step adaptive identification algorithms – modified algorithms by Kaczmarz and Nagumo-Noda. These algorithms do not require knowledge of information on the degree of non-stationarity of the studied object. When building the model, they use the information only about one step of measurements. Modification involves the use of the regularizing addition in the algorithms to improve their computing properties and avoid division by zero. Using a Markovian model is quite effective because it makes it possible to obtain analytic estimates of the properties of algorithms.
It was shown that the use of regularizing additions in identification algorithms, while improving stability of algorithms, leads to some slowdown of the process of model construction. The conditions for convergence of regularizing algorithms by Kaczmarz and Nagumo-Noda at the evaluation of stationary parameters in mean and root-mean-square and existing measurement interference were determined.
Cypkin, Ya. Z., Kaplinskiy, A. I., Larionov, K. A. (1970). Algoritmy adaptacii i obucheniya v nestacionarnyh usloviyah. Izvestiya AN SSSR. Tekhnicheskaya kibernetika, 5, 9–21.
Ljung, L., Soderstrom, T. (1983). Theory and practice of recursive identification. Cambridge, MA: MIT Press, 529.
Goodwin, G. C., Sin, K. S. (1984). Adaptive filtering prediction and control. Prentice-Hall, 536.
Chadeev, V. M. (1964). Opredelenie dinamicheskih harakteristik ob'ektov v processe ih normal'noy ekspluatacii dlya celey samonastroyki. Avtomatika i telemekhanika, 25 (9), 1302–1306.
Raybman, N. S., Chadeev, V. M. (1966). Adaptivnye modeli v sistemah upravleniya. Moscow: Sovetskoe radio, 156.
Aved'jan, A. D. (1971). Bestimmung der Parameter linearer Modelle stationarer und instationarer Strecken. Messen, steuern, regeln, 9, 348–350.
Rudenko, O. G. (1982). Ocenka skorosti skhodimosti odnoshagovyh ustoychivyh algoritmov identifikacii. Doklady AN USSR. Ser. A. Fiz-mat i tekhn. nauki, 1, 64–66.
Clarkson, P. M. (1993). Optimal and Adaptive Signal Processing. CRC Press, 560.
Haykin, S. (2014). Adaptive Filter Theory. Boston: Pearson, 913.
Liberol', B. D., Rudenko, O. G., Bessonov, A. A. (2018). Issledovanie skhodimosti odnoshagovyh adaptivnyh algoritmov identifikacii. Problemy upravleniya i informatiki, 5, 19–32.
Okrug, A. I. (1981). A dynamic Kaczmarz algorithm. Avtomatika i telemekhanika, 1, 74–79.
Lelashvili, Sh. G. (1965). Primenenie odnogo iteracionnogo metoda dlya analiza mnogomernyh avtomaticheskih sistem. Skhemy avtomaticheskogo upravleniya, 19–33.
Lelashvili, Sh. G. (1967). Nekotorye voprosy postroeniya statisticheskoy modeli mnogomernyh ob'ektov. Avtomaticheskoe upravlenie, 59–96.
Avehvyan, E. D. (1978). Modified Kaczmarz algorithms for estimating the parameters of linear plants. Avtomatika i telemekhanika, 5, 64–72.
Liberol', B. D., Rudenko, O. G., Timofeev, V. A. (1995). Modificirovannyy algoritm Kachmazha dlya ocenivaniya parametrov nestacionarnyh ob'ektov. Problemy upravleniya i informatiki, 4, 81–89.
Ishchenko, L. A., Liberol', B. D., Rudenko, O. G. (1986). O svoystvah odnogo klassa mnogoshagovyh adaptivnyh algoritmov identifikacii. Kibernetika, 1, 92–96.
Liberol', B. D., Rudenko, O. G. (1990). O svoystvah proekcionnyh algoritmov ocenivaniya parametrov nestacionarnyh ob'ektov. Doklady AN USSR. Ser. A, 4, 71–74.
Cypkin Ya. Z., Kaplinskiy A. I., Larionov K. A. Algoritmy adaptacii i obucheniya v nestacionarnyh usloviyah // Izvestiya AN SSSR. Tekhnicheskaya kibernetika. 1970. Issue 5. P. 9–21.
Ljung L., Soderstrom T. Theory and practice of recursive identification. Cambridge, MA: MIT Press, 1983. 529 р.
Goodwin G. C., Sin K. S. Adaptive filtering prediction and control. Prentice-Hall, 1984. 536 p.
Chadeev V. M. Opredelenie dinamicheskih harakteristik ob'ektov v processe ih normal'noy ekspluatacii dlya celey samonastroyki // Avtomatika i telemekhanika. 1964. Vol. 25, Issue 9. P. 1302–1306.
Raybman N. S., Chadeev V. M. Adaptivnye modeli v sistemah upravleniya. Moscow: Sovetskoe radio, 1966. 156 p.
Aved'jan A. D. Bestimmung der Parameter linearer Modelle stationarer und instationarer Strecken // Messen, steuern, regeln. 1971. Vol. 9. P. 348–350.
Rudenko O. G. Ocenka skorosti skhodimosti odnoshagovyh ustoychivyh algoritmov identifikacii // Doklady AN USSR. Ser. A. Fiz-mat i tekhn. nauki. 1982. Issue 1. P. 64–66.
Clarkson P. M. Optimal and Adaptive Signal Processing. CRC Press, 1993. 560 p.
Haykin S. Adaptive Filter Theory. 5-th ed. Boston: Pearson, 2014. 913 p.
Liberol' B. D., Rudenko O. G., Bessonov A. A. Issledovanie skhodimosti odnoshagovyh adaptivnyh algoritmov identifikacii // Problemy upravleniya i informatiki. 2018. Issue 5. P. 19–32.
Okrug A. I. A dynamic Kaczmarz algorithm // Avtomatika i telemekhanika. 1981. Issue 1. P. 74–79.
Lelashvili Sh. G. Primenenie odnogo iteracionnogo metoda dlya analiza mnogomernyh avtomaticheskih sistem // Skhemy avtomaticheskogo upravleniya. 1965. P. 19–33.
Lelashvili Sh. G. Nekotorye voprosy postroeniya statisticheskoy modeli mnogomernyh ob'ektov // Avtomaticheskoe upravlenie. 1967. P. 59–96.
Avehvyan E. D. Modified Kaczmarz algorithms for estimating the parameters of linear plants // Avtomatika i telemekhanika. 1978. Issue 5. P. 64–72.
Liberol' B. D., Rudenko O. G., Timofeev V. A. Modificirovannyy algoritm Kachmazha dlya ocenivaniya parametrov nestacionarnyh ob'ektov // Problemy upravleniya i informatiki. 1995. Issue 4. P. 81–89.
Ishchenko L. A., Liberol' B. D., Rudenko O. G. O svoystvah odnogo klassa mnogoshagovyh adaptivnyh algoritmov identifikacii // Kibernetika. 1986. Issue 1. P. 92–96.
Liberol' B. D., Rudenko O. G. O svoystvah proekcionnyh algoritmov ocenivaniya parametrov nestacionarnyh ob'ektov // Doklady AN USSR. Ser. A. 1990. Issue 4. P. 71–74.

References: V. 
 V. 
 V. 
 V. 
 V. 
 V.