Guaranteed consistency between measurements and parameter systems with correlated additive and multiplicative uncertainties

Abstract

The estimation of the parameters of a system by a set membership approach consists in characterizing the set of parameters completely compatible with all the measurements made on the system, the model of this system and the characteristics of the errors and uncertainties that affect the measurements and the system. In this context, it is assumed that the error affecting the measurements is bounded and belongs to a set that is realizable a priori. The estimation problem to be solved then consists in finding the set of admissible values of the model parameters in adequacy with the measurements, the errors and the uncertainties. These uncertainties are handled by an approach that takes into account the unknowns that are the structural error of the model and the values of these parameters. From a practical point of view, the result obtained is a domain of parameters varying in time, domain which is characterized by its bounds. The volume of this domain is minimized, the proposed model explaining the measurements made at each time by optimizing a criterion of precision of the volume in consideration.