Seminar Details
2008-10-28 (14.00) : "Applications of Real Rational Modules in System Identification"
At Euler
Organized by Mathematical Engineering
Speaker :
Ivanov, Tzvetan
Abstract :
We 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 auto-covariance with respect to frequency. This auto-covariance is in fact the integral kernel reproducing the tangent space of the model manifold at the true (or fixed) system w.r.t. the Fisher-information metric. We show how to exploit the fact that the tangent space forms a rational module in order to quantify this kernel in terms of the poles and zeros of the true system and the input spectrum.