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

We consider a frequency-domain solution to the leastsquares equation error identi cation problem using the power spectrum and the cross-spectrum of the IO (inputoutput) data to estimate the IO parametric transfer function. The proposed approach is shown to yield a unimodal performance surface, consistent identi cation in colored noise and su cient-order case, and stable tted models under undermodeling for arbitrary stationary inputs so long as they are persistently exciting of su ciently high order. Asymptotic performance analysis is carried out for both su cient-order and reduced-order cases. Computer simulation results are presented to illustrate the proposed approach.