Geodesic
Distributed dynamic system identification using extended Kalman filter
Informacionnye tehnologii i vyčislitelnye sistemy, no. 2 (2021), pp. 75-83

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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. 
@article{ITVS_2021_2_a7,
     author = {A. V. Kopytin and E. A. Kopytina and M. G. Matveev},
     title = {Distributed dynamic system identification using extended {Kalman} filter},
     journal = {Informacionnye tehnologii i vy\v{c}islitelnye sistemy},
     pages = {75--83},
     publisher = {mathdoc},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ITVS_2021_2_a7/}
}
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A. V. Kopytin; E. A. Kopytina; M. G. Matveev. Distributed dynamic system identification using extended Kalman filter. Informacionnye tehnologii i vyčislitelnye sistemy, no. 2 (2021), pp. 75-83. http://geodesic.mathdoc.fr/item/ITVS_2021_2_a7/