Reliable Parameter Estimation in Presence of Uncertain Variables That Are Not Estimated

In a bounded-error context, reliable set-inversion algorithms such as Sivia provide guaranteed estimates of the set of all the parameters deemed compatible with the selected model and the collected data, assuming that all the uncertain variables of the model are those to be estimated. In this paper we propose a new approach to estimate the parameters of interest assuming that there are other parameters that will not be estimated. This leads to the idea of set projection. A new algorithm for set projection is proposed and applied to the estimation of thermal quantities via a new experimental device to be calibrated.