Parameter estimation in an uncertain and noisy environment via set inversion

The goal of this paper is to present a guaranteed and deterministic method for estimating physical parameters of a sample and quantifying uncertainties related to this estimation in presence of measurement noise. We represent this noise by a set with known bounds. Then, we proceed to parameters estimation via set inversion. The experiment used to identify parameters is the hot plane device which is a dynamical method providing the estimation of 2 parameters at once. By comparing with the classical estimator of least square, the classical method usually used for this type of problems, and for different scenarios, we had good results with acceptable uncertainty on estimated parameters.