Dynamic and relative calibration of temperature sensors in the case of uncertain parameters

The paper addresses sensor bias calibration when only differential bias is of interest as in relative calibration of different sensors. Temperature sensors are considered. Relative calibration is of interest in control problems where precise thermal gradients must be generated, or uniform and stable temperatures must be guaranteed. Static (or steady-state) and dynamic calibration are compared both theoretically and experimentally. Dynamic calibration has the advantage of employing any available measurement, but requires to dispose of a suitable dynamic model of the calibration equipment. A simple equipment with three sensors is considered in the paper, but the results can be extended to more complex ones. A further advantage is to perform calibration on any apparatus with the constraint (used in the paper) that the dynamic model is of the same order as the sensor size. Identifiability conditions are proved. Calibration is obtained through a nonlinear Weighted Least Squares problem, which is solved in an iterative way. Convergence, consistency and asymptotic efficiency are proved and verified with Monte Carlo simulations.