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.