System identification via membership set constraints with energy constrained noise

Abstract

In this paper the identification of constant unknown parameters of a linear system is studied. Rather than finding an estimate of the parameters vector, a membership set for this vector is constructed such that any vector in this set is consistent with the measurements and noise specifications. The usual statistical specification of the noise is replaced here by energy constraints. Convergence of the membership set to a single point (the "true" vector) is studied. The convergence results are related to the convergence of the identification algorithm in the probability sense.