Geodesic
One-dimensional Kalman filter in algorithms for numerical solution of the problem of optimal dynamic measurement
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 14 (2021) no. 4, pp. 120-125

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The article proposes the use of a digital one-dimensional Kalman filter in the implementation of numerical algorithms for solving the problem of optimal dynamic measurements to restore a dynamically distorted signal in the presence of noise. The mathematical model of a complex measuring device is constructed as a Leontief-type system, the initial state of which reflects the Showalter–Sidorov condition. The main position of the theory of optimal dynamic measurements is the modeling of the desired input signal as a solution to the optimal control problem with minimization of the penalty functional, in which the discrepancy between the simulated and observed output (or observed) signal is estimated. The presence of noise at the output of the measuring device makes it necessary to use digital filters in the numerical algorithms. Smoothing filters used for unknown probabilistic parameters of interference are not effective enough for filtering peak-like signals over a short time interval. In addition, the dynamics of measurements actualizes the consideration of filters that respond to rapidly changing data. The article proposes the inclusion of the procedure for filtering the observed signal into previously developed numerical algorithms, which makes it possible to either expand their application or simplify the penalty functionality.
Keywords: optimal dynamic measurement, Kalman filter, numerical solution algorithm, Leontief type system. 
@article{VYURU_2021_14_4_a10,
     author = {A. L. Shestakov and A. V. Keller},
     title = {One-dimensional {Kalman} filter in algorithms for numerical solution of the problem of optimal dynamic measurement},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {120--125},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2021_14_4_a10/}
}
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A. L. Shestakov; A. V. Keller. One-dimensional Kalman filter in algorithms for numerical solution of the problem of optimal dynamic measurement. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 14 (2021) no. 4, pp. 120-125. http://geodesic.mathdoc.fr/item/VYURU_2021_14_4_a10/