Identification of multivariable dynamic errors-in-variables system with arbitrary inputs

The present work deals with the identification of multivariable linear dynamic system from noisy input-output observations, where the input signal is arbitrary and the input-output noises are mutually correlated. A frequency domain identification framework is developed, in which the consistent estimator of the multivariable plant model parameters and of the input-output noise covariance matrix is defined as the solution of a set of normal equations and sufficient conditions for the uniqueness of the parameter estimate are established based on the rank property of the matrix of the normal equation. The uncertainty bound of the parameter estimates is constructed and compared with the Cramér-Rao lower bound. The proposed methodology is validated on a simulated multivariable dynamic system.