On parameter estimation of transfer function models

This paper is concerned with parameter estimation of transfer function models of discrete-time systems subject to colored disturbances. On the basis of the bias-correction scheme, a new least-squares type method is presented. It is shown that the developed method is consistent, regardless of whether the noise contribution on the sampled data can be modeled exactly. Using the two flexibly chosen weighting matrices, some recently proposed bias-correction based methods are now included as the special cases of the developed method. Moreover, with the developed method, a more general type of instruments may be constructed in a simple and yet efficient way. This can be useful when applying the instrumental variables methods to estimate transfer function parameters in the presence of colored process noise.