Identification of linear systems captured in a feedback loop

The identification of model parameters using measured input-output data from linear systems operating in closed loop is discussed. A frequency domain maximum likelihood estimator (MLE) which takes into account the correlation between the input and output disturbances is presented. It is shown that the Gaussian MLE is asymptotically inefficient if the measurements are disturbed by more than one independent noise source. The MLE properties are analyzed and illustrated by simulation examples and real measurements