A frequency-domain solution to unbiased equation error system identification and reduced order approximation

Estimation of the parametric input-output (IO) infinite impulse response (IIR) transfer function is considered. Some of the desirable properties of any approach to this problem are: unimodality of the performance surface, consistent identification in the sufficient-order case, and stability of the fitted model under undermodeling. Some of the well-known approaches fail to satisfy one or more of these properties. The time-domain equation error method (EEM) yields a unimodal performance surface, biased estimates in colored noise and sufficient-order case, and stable fitted models under undermodeling if the input is autoregressive. We propose a frequency-domain solution to the least-squares equation error identification problem using the power spectrum and the cross-spectrum of the IO 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