Propagation of Uncertainty and Comparison of Interpolation Schemes

TEMPMEKO 2016
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Part of the following topical collections:
  1. TEMPMEKO 2016: Selected Papers of the 12th International Symposium on Temperature, Humidity, Moisture and Thermal Measurements in Industry and Science

Abstract

The numerical information in the calibration reports for indicating instruments is typically sparse, often comprising a simple table of corrections or indicated values against a small number of reference values. Users are left to interpolate between the tabulated values using one of several well-known interpolation algorithms, including straight-line, spline, Lagrange, and least-squares interpolation. Although these algorithms are well known, there has apparently been no comparison of their performance in respect of uncertainty propagation. This paper provides an overview of the advantages and disadvantages of the most common interpolation algorithms with respect to uncertainty propagation, immunity to interpolation error, and sensitivity to data spacing. Secondly, the paper illustrates an unconventional method for the uncertainty analysis. The method exploits the linear dependence of the interpolations on measurements of the interpolated quantity, and is easily applied to any linear functional interpolation. In many respects, the best all-round interpolation scheme is a polynomial fitted by least-squares methods, which has a low propagated uncertainty, continuity to the chosen order of the fitted polynomial, and a good immunity to large gaps in the data.

Keywords

Interpolation Lagrange interpolation Least-squares Linear interpolation Measurement uncertainty Spline 
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Notes

Acknowledgements

The author gratefully acknowledges members of the Metrology Group on LinkedIn whose questions prompted this study.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Measurement Standards LaboratoryLower HuttNew Zealand

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