ПРИКЛАДНЫЕ АСПЕКТЫ ИНФОРМАТИКИ
ОБРАБОТКА ИНФОРМАЦИИ И АНАЛИЗ ДАННЫХ
УПРАВЛЕНИЕ И ПРИНЯТИЕ РЕШЕНИЙ
A. V. Kopytin, E. A. Kopytina, M. G. Matveev Distributed Dynamic System Identification Using Extended Kalman Filter
A. V. Kopytin, E. A. Kopytina, M. G. Matveev Distributed Dynamic System Identification Using Extended Kalman Filter
Abstract. 

A combined method for identifying equations of mathematical physics describing the dynamics of spatially distributed processes based on experimental multidimensional time series is proposed. The first component of the method is to obtain OLS estimates of the parameters of the Crank-Nicholson difference scheme. However, these estimates turn out to be biased due to the presence of errors in the regressors. In order to reduce the indicated bias, the extended Kalman filter is used as the second component of the method. A computational experiment confirming the effectiveness of the proposed method is given.

Keywords: 

parameter estimation, LSM, Crank-Nicholson difference scheme, extended Kalman filter.

PP. 75-83.

DOI 10.14357/20718632210208
 
References

1. Putter H., Heisterkamp S. H., Lange J. M. A., De Wolf F. A Bayesian approach to parameter estimation in HIV dynamical models // Statistics in Medicine. 2002. Vol. 21. Pp. 2199-2214.
2. Huang Y., Liu D., Wu H. Hierarchical Bayesian methods for estimation of parameters in a longitudinal HIV dynamic system // Biometrics. 2006. Vol. 62. Pp. 413-423.
3. Huang Y., Wu H. A Bayesian approach for estimating antiviral efficacy in HIV dynamic models // Journal of Applied Statistics. 2006. Vol. 33. Pp. 155-174.
4. Ramsay J. O., Hooker G., Campbell D., Cao, J. Parameter estimation for differential equations: a generalized smoothing approach (with discussion) // Journal of the Royal Statistical Society. Series B. 2007. Vol. 69. Pp. 741-796.
5. Liang H., Wu H. Parameter estimation for differential equation models using a framework of measurement error in regression models // Journal of the American Statistical Association. 2008. Vol. 103. Pp. 1570-1583.
6. Chen J., Wu H. Efficient local estimation for time-varying coefficients in deterministic dynamic models with applications to HIV-1 dynamics // Journal of the American Statistical Association. 2008. Vol. 103. Pp. 369-384.
7. Cao J., Huang J. Z., Wu H. Penalized nonlinear least squares estimation of time-varying parameters in ordinary differential equations // Journal of Computational and Graphical Statistics. 2012. Vol. 21. Pp. 42-56.
8. Muller T., Timmer J. Fitting parameters in partial differential equations from partially observed noisy data // Physical Review, D. 2002. Vol. 171. Pp. 1-7.
9. Muller T., Timmer J. Parameter identification techniques for partial differential equations // International Journal of Bifurcation and Chaos. 2004. Vol. 14. Pp. 2053-2060.
10. Xun X. и др. Parameter estimation of partial differential equation models // Journal of the American Statistical Association. 2013. Vol. 108.  Pp. 1009-1020.
11. Matveev M. G., Kopytin A. V., Sirota E. A., Kopytina E. A. Modeling of nonstationary distributed processes on the basis of multidimensional time series // Procedia Engineering. 2017. Vol. 201. Pp. 511516.
12. Matveev M. G., Sirota E. A., Semenov M. E., Kopytin A.V. Verification of the convective diffusion process based on the analysis of multidimensional time series // CEUR Workshop Proceedings. 2017. Vol. 2022. Pp. 354-358.
13. Matveev M. G., Kopytin A. V., Sirota E. A. Parameters identification of a distributed dynamical model using combined approach // Journal of Physics: Conference Series. 2018. Vol. 1096. 012068.
14. Kopytin, A. V., E. A. Kopytina, and M. G. Matveev. 2018. Primeneniye rasshirennogo fil'tra Kalmana dlya identifikatsii parametrov raspredelennoy dinamicheskoy sistemy [Application of the extended Kalman filter to identify the parameters of a distributed dynamic system]. Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya Sistemnyy analiz i informatsionnyye tekhnologii [Proceedings of Voronezh State University. Series Systems Analysis and Information Technologies]. 3:44-50.
15. Kopytin, A. V., and E. A. Kopytina. 2019. Primeneniye integral'nogo metoda identifikatsii parametrov raspredelennoy dinamicheskoy sistemy [Application of the integral method for identifying the parameters of a distributed dynamic system]. Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya Sistemnyy analiz i informatsionnyye tekhnologii [Proceedings of Voronezh State University. Series Systems Analysis and Information Technologies]. 1:21-26.
16. Ben-Moshe D. Identification of linear regressions with errors in all variables // Econometric Theory. 2020. Pp. 1-31.
17. Fogler H. R. A pattern recognition model for forecasting // Management science. 1974. Vol. 20. Pp. 1178-1189.
18. Conejo A. J., Plazas M. A., Espinola R., Molina A. B. Day-ahead electricity price forecasting using the wavelet transform and ARIMA models // IEEE transaction on power systems. 2005. Vol. 20.  Pp. 1035-1042.
19. Chui C. K., Chen G. Kalman filtering with real-time applications. Berlin: Springer-Verlag Berlin Heidelberg, 2009. 241 p.
 
2021 / 02
2021 / 01
2020 / 04
2020 / 03

© ФИЦ ИУ РАН 2008-2018. Создание сайта "РосИнтернет технологии".