Performance analysis of a frequency-domain solution to unbiased equation error system identification

We consider a frequency-domain solution to the least-squares equation error identification problem using the power spectrum and the cross-spectrum of the IO (input-output) data to estimate the IO parametric transfer function. The proposed approach is shown to yield a unimodal performance surface, consistent identification in colored noise and sufficient-order case, and stable fitted models under undermodeling for arbitrary stationary inputs so long as they are persistently exciting of sufficiently high order. Some of the well-known time-domain approaches (including the prediction error, the output error, the Steiglitz-McBride, the least-squares and the instrumental variable methods) fail to satisfy one or more of these properties. Asymptotic performance analysis is carried out for both sufficient-order and reduced-order cases. Computer simulation results are presented to illustrate the proposed approach.