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Error Estimation of Indirect Measurement Results for Certain Quantities

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Measurement Techniques Aims and scope

The basic mathematical provisions that determine the necessary and sufficient conditions for the application of the method of linearization of nonlinear functions of random arguments in estimating the errors of indirect measurements are considered. The necessity of assessing the emerging systematic component of the error and the degree of approximate representation of functions is noted. Within the framework of necessary and sufficient conditions for expanding an arbitrary function into a Taylor series, a new analytical formula is obtained for approximating a nonlinear function in the form of a quotient of independent random arguments. When using this formula for estimating the errors of the results of the indicated indirect measurements, it is possible not to refine the results obtained by adding terms to the Taylor series and not to evaluate the degree of approximation of the nonlinear function from the values of the corresponding remainder terms. The proposed formula allows one to determine practical conditions under which, for estimating the errors of the corresponding results, one can use well-known and fairly simple formulas for estimating the absolute and relative errors without preliminary processing of the results of direct measurements.

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References

  1. International Vocabulary of Metrology: Basic and General Concepts and Related Terms [Russian translaion], NPO Professional, St. Petersburg (2010), 2nd ed.

  2. A. S. Doynikov, Lectures on Metrology, VNIIFTRI, Mendeleevo (2018).

    Google Scholar 

  3. H. Cramer, Mathematical Methods of Statistics [Russian translaion], Mir, Moscow (1975).

    Google Scholar 

  4. O. V. Denisenko, V. I. Dobrovolsky, S. I. Donchenko, and E. V. Eremin, “Tests of satellite navigation equipment,” Partn. i Konkur., No. 9, 32–38 (2002).

  5. O. V. Denisenko, S. I. Donchenko, and E. V. Eremin, “A set of standards for testing the equipment of consumers of signals from satellite navigation systems GLONASS/GPS,” Izmer. Tekhn., No. 2, 13–21 (2003).

  6. E. V. Eremin, “On the correct presentation of the values of quantities and indicators of accuracy of the results of indirect measurements,” Pribory, No 9, 46–54 (2019)

  7. E. S. Ventzel, Probability Theory, Vys. Shkola, Moscow (1998).

    Google Scholar 

  8. N. V. Smirnov and I. V. Dunin-Barkovsky, Course in Probability Theory and Mathematical Statistics for Technical Applications, Nauka, Moscow (1969).

    Google Scholar 

  9. G. M. Fichtengolts, Course of Differential and Integral Calculus, Fizmatlit, Moscow (2003), Vol. 1.

  10. M. N. Selivanov, A. E. Fridman, and J. F. Kudryashova, Measurement Quality: Metrological Ref. Book, Lenizdat, Leningrad (1987).

  11. V. A. Granovsky and T. N. Siraya, Methods for Processing Experimental Data during Measurements, Energoatomizdat, Leningrad (1990).

    Google Scholar 

  12. A. E. Friedman, Fundamentals of Metrology. Modern Course, NPO Professional, St. Petersburg (2008).

  13. G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers [Russian translation], Nauka, Moscow (1974).

    MATH  Google Scholar 

  14. N. S. Piskunov, Differential and Integral Calculus, Mifril, St. Petersburg (1996), Vol 1.

  15. J. Taylor, An Introduction to Error Analysis [Russian translation], Mir, Moscow (1985).

    Google Scholar 

  16. E. G. Mironov and N. P. Bessonov, Metrology and Technical Measurements, KNORUS, Moscow (2015).

    Google Scholar 

  17. S. G. Rabinovich, Measurement Errors, Energia, Leningrad (1978).

    Google Scholar 

  18. G. D. Burdun and B. N. Markov, Fundamentals of Metrology, Izd. Standartov, Moscow (1985).

    Google Scholar 

  19. S. G. Rabinovich, Measurement Errors and Uncertainties: Theory and Practice, Springer-Verlag, New York (2005).

    MATH  Google Scholar 

  20. T. N. Siraya, “Methods of data processing during measurements and metrological models,” Izmer. Tekhn., No. 1, 9–14 (2018), DOI: 10.32446/0368-1025it.2018-1-9-14.

  21. V. D. Gvozdev, “MI 2083-90. GSI. Indirect Measurements. Determination of Measurement Results and Their Errors. On the Taylor series remainder term,” Zakonodat. Prikl. Metrol., No 3, 52–54 (2011).

  22. V. M. Dengub and V. G. Smirnov, Units of Quantities: Dictionary and Reference, Izd. Standartov, Moscow (1990).

    Google Scholar 

  23. A. G. Chertov, Physical Quantities (terminology, definitions, notation, dimensions, units), Vys. Shkola, Moscow (1990).

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Authors and Affiliations

  1. All-Russia Research Institute of Physicotechnical and Radio Measurements (VNIIFTRI), Mendeleevo, Russia

    E. V. Eremin

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  1. E. V. Eremin
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Correspondence to E. V. Eremin.

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Translated from Izmeritel’naya Tekhnika, No. 1 pp. 18–24, January, 2020.

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Eremin, E.V. Error Estimation of Indirect Measurement Results for Certain Quantities. Meas Tech 63, 15–22 (2020). https://doi.org/10.1007/s11018-020-01743-x

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  • DOI: https://doi.org/10.1007/s11018-020-01743-x

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