Келлер И.А., Замышляева И.А., Манакова И.А., Колесников И.А. Algorithmic Approach to Selecting Digital Filtering Methods for Processing Dynamic Measurement Results
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https://doi.org/10.15688/mpcm.jvolsu.2025.4.2
Alevtina V. Keller
Doctor of Physical and Mathematical Sciences, Professor, Department of Applied Mathematics and Mechanics, Voronezh State Technical University
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https://orcid.org/0009-0005-5840-9727
20 let Oktyabrya street, 84, 394006, Voronezh, Russian Federation
Alena A. Zamyshlyaeva
Doctor of Physical and Mathematical Sciences, Head of the Institute of Natural and Exact Sciences, South Ural State University
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https://orcid.org/0000-0002-4530-4820
Pr. Lenina, 76, 454080, Chelyabinsk, Russian Federation
Natalya A. Manakova
Doctor of Physical and Mathematical Sciences, Head of the Department of Mathematical Physics Equations, South Ural State University
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https://orcid.org/0000-0001-8078-8026
Pr. Lenina, 76, 454080, Chelyabinsk, Russian Federation
Ivan A. Kolesnikov
Graduate student, Department of Mathematical and Computer Modelling, South Ural State University
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https://orcid.org/0000-0002-4530-4820
Pr. Lenina, 76, 454080 Chelyabinsk, Russian Federation
Abstract. The restoration of dynamically distorted signals over short time intervals represents a complex inverse problem in dynamic measurements. In the presence of various types of noise, the output signal becomes corrupted, further complicating the task. To date, the theory of optimal dynamic measurements has been developed, employing methods from optimal control theory, Sobolev-type equations, and stochastic differential equations, alongside advanced numerical techniques. Previously, the authors conducted multiple studies advancing numerical methods for retrieving the input signal as a solution to the optimal control problem of dynamic measurement and proposed a new numerical algorithm for its resolution. When noise is present in the output signal, it is crucial not only to ensure the efficiency of the signal recovery algorithm, considering the measuring device’s inertia, but also to select the most effective digital filter. This article presents an algorithm within a software tool that facilitates the selection of one of three filters: a moving average filter, the Savitzky—Golay filter (based on the least squares method) followed by the optimal dynamic measurement algorithm, and the MSA method (an author-developed technique based on spline methods followed by averaging). The MSA method is not merely a digital filter; it integrates comprehensive noise filtering with an algorithm for optimal dynamic measurement. Moreover, it can be applied both in the presence and absence of noise and other disturbances. The novelty of these results lies in a systematic and comprehensive evaluation of the effectiveness and applicability of noise filtering methods for restoring dynamically distorted signals. This article provides the necessary theoretical background, general algorithmic schemes, experimental data, and results demonstrating the performance of the proposed approaches.
Key words: Optimal dynamic measurements, digital signal filtering, algorithm, computational experiments, Leontief-type system.
Algorithmic Approach to Selecting Digital Filtering Methods for Processing Dynamic Measurement Results by Келлер И.А., Замышляева И.А., Манакова И.А., Колесников И.А. is licensed under a Creative Commons Attribution 4.0 International License.
Citation in English: Mathematical Physics and Computer Simulation. Vol. 28 No. 4 2025, pp. 24-42
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