Identification of multivariable stochastic linear systems via polyspectral analysis given noisy input-output time-domain data

The paper considers the problem of identification of unknown parameters of multivariable, linear “errors-invariables” models. 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. Two new classes of parametric frequency-domain approaches are proposed and analyzed. An integrated polyspectrum-based persistence of excitation condition on system input is defined. Both classes of the parameter estimators are shown to be strongly consistent in any measurement noise sequences with vanishing bispectra when integrated bispectrum-based approaches are used. The proposed parameter estimators are shown to be strongly consistent in Gaussian measurement noise when integrated trispectrum-based approaches are used. The input to the system need not be a linear process but must have nonvanishing bispectrum or trispectrum