METHOD FOR SIGNAL PROCESSING BASED ON KOLMOGOROVWIENER PREDICTION OF MFSD PROCESS

Authors

  • V. N. Gorev Dnipro University of Technology, Dnipro, Ukraine, Ukraine
  • Y. I. Shedlovska Dnipro University of Technology, Dnipro, Ukraine, Ukraine
  • I. S. Laktionov Dnipro University of Technology, Dnipro, Ukraine, Ukraine
  • G. G. Diachenko Dnipro University of Technology, Dnipro, Ukraine, Ukraine
  • V. Yu. Kashtan Dnipro University of Technology, Dnipro, Ukraine, Ukraine
  • K. S. Khabarlak Dnipro University of Technology, Dnipro, Ukraine, Ukraine

DOI:

https://doi.org/10.15588/1607-3274-2024-3-2

Keywords:

Kolmogorov-Wiener filter weight function, telecommunication traffic, Galerkin method, MFSD model, Chebyshev polynomials of the first kind, stationary random heavy-tail process

Abstract

Context. We investigate a method to signal processing based on the Kolmogorov-Wiener filter weight function calculation for the prediction of a continuous stationary heavy-tail process in the MFSD (multifractal fractional sum-difference) model. Such a process may describe telecommunication traffic in some systems with data packet transfer, the consideration of the continuous filter may be reliable in the case of the large amount of data.

Objective. The aim of the work is to obtain an approximate solution for the Kolmogorov-Wiener filter weight function and to show the applicability of the method to signal processing used in the paper.

Method. The Galerkin method based on the orthogonal Chebyshev polynomials of the first kind is used for the calculation of the weight function under consideration. The approximations up to the thirteen-polynomial one are investigated. The corresponding integrals are calculated numerically on the basis of the Wolfram Mathematica package. The higher is the packet rate, the higher accuracy of the integral calculation is needed.

Results. It is shown that for rather large number of polynomials the misalignment between the left-hand side and the right-hand side of the Wiener-Hopf integral equation under consideration is rather small for the obtained solutions. The corresponding mean absolute percentage errors of misalignment for different packet rates are calculated. The method to signal processing used in the paper leads to reliable results for the Kolmogorov-Wiener filter weight function for the prediction of a process in the MFSD model.

Conclusions. The theoretical fundamentals of the continuous Kolmogorov-Wiener filter construction for the prediction of a random process in the MFSD model are investigated. The filter weight function is obtained as an approximate solution of the Wiener-Hopf integral equation with the help of the Galerkin method based on the Chebyshev polynomials of the first kind. It is shown that the obtained results for the filter weight function are reliable. The obtained results may be useful for the practical telecommunication traffic prediction. The paper results may also be applied to the treatment of heavy-tail random processes in different fields of knowledge, for example, in agriculture.

Author Biographies

V. N. Gorev, Dnipro University of Technology, Dnipro, Ukraine

PhD, Associate Professor, Head of the Department of Physics

Y. I. Shedlovska, Dnipro University of Technology, Dnipro, Ukraine

PhD, Associate Professor of the Department of Information Technology and Computer Engineering

I. S. Laktionov, Dnipro University of Technology, Dnipro, Ukraine

Dr. Sc., Associate Professor, Professor of the Department of Computer Systems Software

G. G. Diachenko, Dnipro University of Technology, Dnipro, Ukraine

PhD, Associate Professor of the Department of Electric Drive

V. Yu. Kashtan, Dnipro University of Technology, Dnipro, Ukraine

PhD, Associate Professor, Associate Professor of the Department of Information Technology and Computer Engineering

K. S. Khabarlak, Dnipro University of Technology, Dnipro, Ukraine

PhD, Associate Professor of the Department of System Analysis and Control

References

Tian H., Guo K., Guan X. Statistical behavioral characteristics of network communication delay in IPv4/IPv6 Internet, Telecommunication Systems, 2024, Vol. 85, pp. 679–698. DOI: 10.1007/s11235-024-01111-y

Saha S., Haque A., Sidebottom G. Multi-Step Internet Traffic Forecasting Models with Variable Forecast Horizons for Proactive Network Management, Sensors, 2024, Vol. 24, 1871 (29pages). DOI: 10.3390/s24061871

Balabanova I., Georgiev G. Forecasting Teletraffic Performance Using Regression Analysis, FNNN, GRNN and CFNN, Engineerong Proceedings, 2024, Vol. 60, 11 (7 pages). DOI: 10.3390/engproc2024060011

Wang X., Wang Z., Yang K. et al. A Survey on Deep Learning for Cellular Traffic Prediction, Intelligent Computing, 2024, Vol. 3, 0054 (17 pages). DOI:10.34133/icomputing.0054

Li M. Direct Generalized fractional Gaussian noise and its application to traffic modeling, Physica A, 2021, Vol. 579, 126138 (22 pages). DOI: 10.1016j.physa.2021.126138

Sousa-Vieira M. E., Fernández-Veiga M. Efficient Generators of the Generalized Fractional Gaussian Noise and Cauchy Processes, Fractal and Fractional, 2023, Vol. 7, 455 (13 pages). DOI: 10.3390/fractalfract7060455

Anderson D., Cleveland W. S., Xi B. Multifractal and Gaussian fractional sum-difference models for Internet traffic, Performance Evaluation, 2017, Vol. 107, pp. 1–33. DOI:10.1016/j.peva.2016.11.001

Ferreira G. O., Ravazzi C., Dabbene F. et al. Forecasting Network Traffic: A Survey and Tutorial With Open-Source Comparative Evaluation, IEEE Access, 2023, Vol. 11, pp. 6018–6044. DOI:10.1109/ACCESS.2023.3236261

Gorev V., Gusev A., Korniienko V. et al. On the use of the Kolmogorov-Wiener filter for heavy-tail process prediction, Journal of Cyber Security and Mobility, 2023, Vol. 12, № 3, pp. 315–338. DOI: 10.13052/jcsm2245-1439.123.4.

Pooja, Kumar J., Manchanda P. Numerical Solution of First Kind Fredholm Integral Equations Using Wavelet Collocation Method, Journal of Advances in Mathematics and Computer Science, 2024, Vol. 39., Issue 6, pp. 66–79. DOI: 0.9734/jamcs/2024/v39i61902

Gorev V. N., Gusev A. Yu., Korniienko V. I. Kolmogorov-Wiener filter for continuous traffic prediction in the GFSD model, Radio Electronics, Computer Science, Control. – 2022, No. 3, pp. 31–37. DOI: 10.15588/1607-3274-2022-3-3.

Gorev V. N., Gusev A. Yu., Korniienko V. I. et al.bGeneralized fractional Gaussian noise prediction based on the Walsh functions, Radio Electronics, Computer Science, Control, 2023, No. 3, pp. 48–54. DOI: 10.15588/1607-3274-2023-3-5

Gorev V. N., Gusev A. Yu., Korniienko V. I. et al. On the Kolmogorov-Wiener filter for random processes with a power-law structure function based on the Walsh functions, Radio Electronics, Computer Science, Control, 2021, No. 2. pp. 39–47. DOI: 10.15588/1607-3274-2021-2-4

Koroviaka Y., Pinka J., Tymchenko S. et al. Elaborating a scheme for mine methane capturing while developing coal gas seams, Mining of Mineral Deposits, 2020, Vol. 14, Issue 3, pp. 21–27. DOI: 10.33271/mining14.03.021

Li S., Song G., Ye M. et al. Multiband SHEPWM Control Technology Based on Walsh Functions, Electronics, 2020, Vol. 9, Issue 6, 1000 (16 pages). DOI: 10.3390/electronics9061000

Yang Y. Long-range dependence and rational Gaussian noise, A Journal of Theoretical and Applied Statistics. – 2024, Vol. 58, Issue 2, pp. 364–382. DOI: 10.1080/02331888.2024.2344689

Baul T., Karlan D., Toyama K. et al. Improving smallholder agriculture via video-based group extension, Journal of Development Economics, 2024, Vol. 169, 103267 (26 pages). DOI: 10.1016/j.jdeveco.2024.103267

Laktionov I., Diachenko G., Koval V. et al. Computer-Oriented Model for Network Aggregation of Measurement Data in IoT Monitoring of Soil and Climatic Parameters of Agricultural Crop Production Enterprises, Baltic Journal of Modern Computing, 2023, Vol. 11, Issue 3, pp. 500–522. DOI: 10.22364/bjmc.2023.11.3.09

Malashkevych D., Petlovanyi M., Sai K.et al. Research into the coal quality with a new selective mining technology of the waste rock accumulation in the mined-out area, Mining of Mineral Deposits, 2022, Vol. 16, Issue 4, pp. 103–114. DOI: 10.33271/mining16.04.103

Lymperi O. A., Varouchakis E. A. Modeling Extreme Precipitation Data in a Mining Area, Mathematical Geosciences, 2024. DOI: 10.1007/s11004-023-10126-1

Downloads

Published

2024-11-03

How to Cite

Gorev, V. N., Shedlovska, Y. I., Laktionov, I. S., Diachenko, G. G., Kashtan, V. Y., & Khabarlak, K. S. (2024). METHOD FOR SIGNAL PROCESSING BASED ON KOLMOGOROVWIENER PREDICTION OF MFSD PROCESS. Radio Electronics, Computer Science, Control, (3), 19. https://doi.org/10.15588/1607-3274-2024-3-2

Issue

No. 3 (2024): Radio Electronics, Computer Science, Control

Section

Mathematical and computer modelling

License

Copyright (c) 2024 В. М. Горєв, Я. І. Шедловська, І. С. Лактіонов, Г. Г. Дяченко, В. Ю. Каштан, К. С. Хабарлак

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Creative Commons Licensing Notifications in the Copyright Notices

The journal allows the authors to hold the copyright without restrictions and to retain publishing rights without restrictions.

The journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles.

The journal allows to reuse and remixing of its content, in accordance with a Creative Commons license СС BY -SA.

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License CC BY-SA that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.