Identification of multivariable stochastic linear systems via spectral analysis given time-domain data

Estimation of the parametric multiple-input-multiple-output (MIMO) infinite impulse response transfer function given time-domain input-output (IO) data is considered. We first propose a frequency-domain solution to the least-squares equation error multivariable system 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 and consistent identification in colored noise and the sufficient-order case. We then investigate an iterative pseudo-maximum likelihood approach and analyze its consistency under sufficient-order modeling. Finally, a computer simulation example is provided to illustrate the two approaches.