The propagation of uncertainty with calibration equations

Abstract

A new method for propagating uncertainty, based on interpolation theory, is developed to solve the problem of propagating uncertainty in linear interpolating equations. The method is extended to nonlinear equations, and to over-determined linear or nonlinear equations fitted by least-squares methods. The paper also provides an algebraic explanation of the rationale for calibration, describes some effects of correlation on uncertainty propagation and investigates the properties of interpolation errors. Several examples are described showing the application of the method to polynomial interpolation, the amplification of uncertainty with extrapolation and the effects of correlation between uncertainties in corrections.

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