Identification of ARMAX Models With Noisy Input: A Parametric Frequency Domain Solution

This paper deals with frequency domain parametric identification of ARMAX models when the input is corrupted by white noise. By means of a multivariate ARMA representation, the ARMAX model within the errors-in-variables (EIV) framework is identified by a successive two-stage approach, and all the parameter estimates of the dynamic EIV model are further jointly tuned to achieve minimum variance among unbiased estimators using second-order statistics of input-output data. Sufficient conditions are constructed to obtain the identifiability of the EIV-ARMAX model as well as the multivariate ARMA process. The consistency of the estimator is analyzed, and the uncertainty bound of the estimate is also provided and compared with the Cramér-Rao lower bound. The performance of the proposed method is demonstrated via numerical and real examples.