Analysis of the estimation error in a parsimonious temperature-temperature characterization technique

Characterization of systems often relies on a single point response that is a convolution product between a transfer function, an impedance, and the strength of a source. This requires perfect knowledge or measurement of this source. Another possibility is to measure two point responses in such systems. These are also linked, under certain causality conditions, by a different convolution product based on another type of transfer function, called here a transmittance. It is shown that using this kind of transmittance-based model, with one of the two responses as a pseudo-source to explain the other one, leads to a model with fewer parameters, which is very interesting for parameter estimation. Replacement of the exact strength of the source by a noised response in a non-linear least square minimization process does not bring any additional bias and the standard deviations of the parameter estimates can be calculated on a theoretical stochastic basis. An example of such an estimation technique in a thermal characterization of a light insulating sample by the three-layer method is used to show the practical interest of this estimation method and to validate the assessment of the estimation errors through a Monte Carlo approach. Finally a counting of the number of parameters present in the transmittance model, within a very general context of a one-dimension heat transfer characterization experiment, shows its parsimonious character when compared with impedance-based parameter estimation techniques.