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

Estimation of parametric multiple-input-multiple-output (MIMO) infinite impulse response transfer functions given time-domain input-output (IO) data, 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. In this paper 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, 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. 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