Efficient estimation of uncertainty in weakly non-linear algorithms for measurand reconstruction

Abstract

Evaluation of measurement uncertainty is a key issue in measurement science since the practical value of any measurement result depends on how precise that uncertainty is assessed. This statement applies, in particular, to measurand reconstruction being a fundamental operation in any measuring system. Thus, the algorithms of measurand reconstruction should be provided with mechanisms for evaluating the uncertainty of the results of computation. If those algorithms are linear with respect to the data and all intermediate results of computation, and if they do not use the data or intermediate results more than once, then the linear propagation of uncertainties, executed step by step for each operation, yields a satisfactory solution to the problem of uncertainty analysis. Otherwise, a tendency for overestimating the uncertainty appears. An effective method for dealing with this problem in linear and weakly non-linear algorithms of measurand reconstruction is proposed in this paper. Its computational efficiency is demonstrated using weakly non-linear algorithms, viz., a non-recursive Cauchy filter and a recursive quadratic filter.