Statistical Filtering of Random Measurement Errors
( Pp. 11-19)
More about authors
Bogdanov Alexander N.
chief engineer, .
PJSC “Sberbank”
Moscow, Russian Federation Ivanyugin Victor M. Cand. Sci. (Eng.), Senior Researcher; associate professor, Department of Computer and Information Security, Institute of Artificial Intelligence, .
MIREA – Russian Technological University
Moscow, Russian Federation
PJSC “Sberbank”
Moscow, Russian Federation Ivanyugin Victor M. Cand. Sci. (Eng.), Senior Researcher; associate professor, Department of Computer and Information Security, Institute of Artificial Intelligence, .
MIREA – Russian Technological University
Moscow, Russian Federation
Abstract:
In life, we often have to take into account the accuracy of measurements. There is obviously a desire to have the measured value as accurately as possible. This applies to both static and dynamic measurements. Measurements may be made using one or more meters and involve errors that may be systematic or random. The usual approach to obtaining a more accurate value of a measured parameter is the averaging method. This is a simple and quite effective method, especially if the measurements are equally accurate. If there are n measurements, then the averaging method is the addition of n measurements with the same weighting coefficients. The larger n, the more accurate the estimate will be. But with different-precision measurements, the result may not be optimal. To obtain an optimal estimate (estimates with minimal error variance) for multi-precision measurements, the weighting coefficients must take into account their statistical accuracy. Optimal weighting coefficients should ensure a minimum variance of the estimation error. This is the method of statistical filtering of random errors. Statistical filtering of random errors is also applicable for multidimensional problems. For example, its special case is the so-called “Kalman filter”.
How to Cite:
Bogdanov A.N., Ivanyugin V.M. Statistical Filtering of Random Measurement Errors. Computational Nanotechnology. 2024. Vol. 11. No. 5. Pp. 11–19. (In Rus.). DOI: 10.33693/2313-223X-2024-11-5-11-19. EDN: BNGXEH
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Gapeeva V.D., Tsybenko V.A. Filtering out gross errors in measurement results using various criteria in the Excel environment. Young Scientist. 2021. No. 49 (391). Pp. 20–27. (In Rus.)
Gmurman V.E. Probability theory and mathematical statistics. Textbook for universities. Moscow: Yurait, 2022. 479 p.
Darbinyan A.A. Probability estimate of the covariance matrix for the Kalman filter for polar coordinate systems. In: Research of young scientists. Materials of the XII Inter. scientific conf. (Kazan, July 2020). Kazan: Young Scientist, 2020. Pp. 1–3.
Kaladze V.A. Filtering models of statistical dynamics. Bulletin of the Voronezh State University. Series: Systems Analysis and Information Technology. 2011. No. 1. Pp. 22–28. (In Rus.)
Obidin M.V., Serebrovsky A.P. Signal cleaning from noise using the wavelet transform and the Kalman filter. Information Processes. 2013. Vol. 13. No. 3. Pp. 198–205. (In Rus.)
Rudenko E.A. Finite-dimensional recurrent algorithms for optimal nonlinear logical-dynamic filtering. Bulletin of the Russian Academy of Sciences. Control Theory and Systems. 2016. No. 1. Pp. 43–65. (In Rus.)
Surina A.V. Probability theory: Basic formulas. Textbook manual. St. Petersburg, 2022. 56 p.
Taranenko Yu.K., Oleynik O.Yu. Model of the adaptive Kalman filter. Technology of Instrument Making. 2017. No. 1. Pp. 9–11. (In Rus.)
Babikir A., Mwambi H. Factor augmented artificial neural network model. Neural Processing Letters. 2016. Vol. 45. Issue 2. Pp. 507–521.
Stano P., Lendek Z., Braaksma J. et al. Parametric Bayesian filters for nonlinear stochastic dynamical systems: A survey. IEEE Transactions on Cybernetics. 2013. Vol. 43. Issue 6. Pp. 1607–1624.
Keywords:
measurements, estimation errors, statistical accuracy, error variance, optimal weighting coefficients, Kalman filter.