Application of Real Rational Modules in System Identification

This paper introduces a real rational module framework in the context of Prediction Error Identification using Box-Jenkins model structures. This module framework, which can easily be extended to other model structures, allows us to solve and/or extend a number of problems related to the computation of error norms that arise in system identification. Our main contribution to system identification is an extension of the asymptotic variance formulas for Box-Jenkins models derived by Ninness and Hjalmarsson to asymptotic autocovariance with respect to frequency. This is achieved by viewing the sensitivity space of the prediction error as a so-called rational module. The auto-covariance of the transfer function estimates at different frequencies can then be quantified in terms of the poles and zeros of the underlying system and the input spectrum.