Identification of dynamic errors-in-variables systems with quasi-stationary input and colored noise

This paper studies the linear dynamic errors-in-variables (EIV) problem in a fairly general condition where the input–output disturbing noises are colored and the input is quasi-stationary. A novel formulation of the extended frequency domain maximum likelihood (ML) estimator is developed which reduces the number of nonlinear normal equations to be solved. Sufficient conditions are provided to achieve local identifiability of the EIV model for specified noise cases of interest. The parameter estimates are calculated via a numerically stable Gauss–Newton minimization scheme started by an initial value generation strategy. Also, both the consistency and accuracy of the extended ML estimate are analyzed in detail. The performance of the proposed method is finally demonstrated on simulated dynamic systems.