Prediction Error Method Identification is an Eigenvalue Problem

This article explores the link between prediction error methods, nonlinear polynomial systems and generalized eigenvalue problems. It is shown how the global minimum of the sum of squared prediction errors can be found from solving a nonlinear polynomial system. An algorithm is provided that effectively counts the number of affine solutions of the nonlinear polynomial system and determines these solutions by solving a generalized eigenvalue problem. The proposed method is illustrated by means of an example.