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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2019, Volume 12, Issue 2, Pages 82–96 (Mi vyuru490)  

This article is cited in 5 scientific papers (total in 5 papers)

Mathematical Modelling

Reconstruction of observation from distorted data for the optimal dynamic measurement problem

M. A. Sagadeeva

South Ural State University, Chelyabinsk, Russian Federation

Abstract: The theory of optimal dynamic measurements is based on the minimization of the difference between the values of virtual observation, i.e. an observation obtained with the help of a computational model, and experimental data, which are usually distorted by some noise. The article describes a mathematical model of optimal dynamic measurement in the presence of various types of interference. In addition, the article proposes an algorithm to reconstruct the values of observation from the values obtained during the experiment, which are assumed to be distorted by some random influences. It is assumed that the experimental data are influenced by “white noise”, which is understood as a derivative of Nelson–Gliklich from the Wiener process. In order to reconstruct observation values, we use a priori information about the form of the function describing the observation values. The reconstruction procedure consists of two stages. At the first stage, we formulate the criterion for determining the position of the extreme point of the signal using a special type of statistics. At the second stage, we describe the procedure to reconstruct the signal values on the basis of information about the position of the extreme point and the shape of the signal convexity.

Keywords: Wiener process, Brownian motion, Nelson–Gliklikh derivative, statistical hypothesis.

DOI: https://doi.org/10.14529/mmp190207

Full text: PDF file (267 kB)
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UDC: 517.9
MSC: 49J15, 62M86, 60H40
Received: 06.12.2018

Citation: M. A. Sagadeeva, “Reconstruction of observation from distorted data for the optimal dynamic measurement problem”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 12:2 (2019), 82–96

Citation in format AMSBIB
\Bibitem{Sag19}
\by M.~A.~Sagadeeva
\paper Reconstruction of observation from distorted data for~the~optimal dynamic measurement problem
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2019
\vol 12
\issue 2
\pages 82--96
\mathnet{http://mi.mathnet.ru/vyuru490}
\crossref{https://doi.org/10.14529/mmp190207}
\elib{https://elibrary.ru/item.asp?id=38225239}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. V. Bychkov, N. N. Soloveva, G. A. Sviridyuk, “Matematicheskaya model akusticheskikh voln v ogranichennoi oblasti s «belym shumom»”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 11:3 (2019), 12–19  mathnet  crossref  elib
    2. M. A. Sagadeeva, “Postroenie nablyudeniya v modeli Shestakova–Sviridyuka pri ego iskazhenii mnogomernym «belym shumom»”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 12:4 (2020), 41–50  mathnet  crossref
    3. E. V. Bychkov, A. V. Bogomolov, K. Yu. Kotlovanov, “Stochastic mathematical model of internal waves”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 13:2 (2020), 33–42  mathnet  crossref
    4. A. I. Kibzun, A. S. Shalaev, V. M. Azanov, A. N. Ignatov, “Statistical analysis module for weight design of aircraft elements”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 13:3 (2020), 29–42  mathnet  crossref
    5. A. L. Shestakov, S. A. Zagrebina, N. A. Manakova, M. A. Sagadeeva, G. A. Sviridyuk, “Numerical optimal measurement algorithm under distortions caused by inertia, resonances, and sensor degradation”, Autom. Remote Control, 82:1 (2021), 41–50  mathnet  crossref  crossref  isi
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