Consistent Impulse-Response Estimation and System Realization From Noisy Data

A novel method for the estimation of a finite part of the impulse response is presented. The method is consistent in case the measured output data are prone to colored noise. The combination of Kung´s realization algorithm yields a consistent system identification algorithm that is particularly useful for the identification of systems with uncoupled deterministic and stochastic dynamics. This algorithm is called IREAR. A detailed linear sensitivity analysis of the impulse response estimation and Kung´s realization algorithms yields novel error and covariance formulae for the estimated impulse response and system matrices and the poles and frequency-response functions that result from the identified system description.