Unbiased equation error identification and approximations: a frequency-domain solution and its performance analysis

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. Asymptotic performance analysis is carried out for both sufficient-order and reduced-order cases. Computer simulation results are presented to illustrate the proposed approach