Free-knot cubic spline modelling in cryogenic thermometer calibration

In a calibration process of thousands of thermometers, optimization of the experimental design is an important step to save time and costs. In this paper, a modelling procedure is proposed for the construction of a suitable cubic spline approximation of the R–T characteristic of cryogenic thermometers. An iterative algorithm is used to estimate the parameters of a free-knot cubic spline model. Moreover, the minimum number of measurement points and their locations in the experimental design, as related to the spline parameters, are obtained via an heuristic study.