Identification of multivariable stochastic linear systems using integrated polyspectrum given noisy input-output data

The problem considered is that of identification of unknown parameters of multivariable, linear "errors-in-variables" models, i.e., linear systems where measurements of both input and output of the system are noise contaminated. Attention is focused on frequency-domain approaches where the integrated polyspectrum (bispectrum or trispectrum) of the input and the integrated cross-polyspectrum, respectively, of the given time-domain input-output data are exploited. We first develop (computable) expressions for the covariance matrix of the system transfer function estimate and show that the system transfer function matrix estimate is asymptotically complex Gaussian. Then we propose and analyze a pseudo-maximum likelihood (PML) estimator of system parameters using the developed statistics of the system transfer function estimate. Finally two simulation examples are presented.