Frequency-domain identification of multivariable linear systems with noisy input

The problem considered is that of identifiability 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 input-output are exploited. Two new classes of parametric, frequency domain approaches are proposed and analysed. An integrated polyspectrum based persistence of excitation condition on system input is defined and related to parameter identifiability of the multivariable system. Both classes of the parameter estimators are shown to be consistent in any measurement noise sequences with vanishing bispectra when integrated bispectrum-based approaches are used. The proposed parameter estimators are shown to be 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