Incorporating Fixed Pole Information in the Data-Driven Least Squares Realization Problem

Abstract: In practical least squares realization problems, partial information about the poles of the dynamical model may be known a priori. Existing techniques for incorporating prior knowledge, such as prefiltering the given data, are typically heuristic and lack theoretical guarantees. We extend our previously developed globally optimal approach for the least squares realization problem to accommodate fixed poles. In particular, we reformulate the problem as a (rectangular) multiparameter eigenvalue problem, the eigenvalues of which characterize all local and global minimizers of the constrained estimation problem. We present numerical examples to demonstrate the effectiveness of the proposed method and experimentally validate this letter's central hypothesis: incorporating a priori information on the poles enhances the estimation results.