Abstract
This paper discusses the properties of leastsquares estimators for over-parametrized pulse transfer function model. The estimators have the biases in the presence of measurement noise, but the higher model order becomes, the closer the step response calculated from the estimated parameters gets to the true one. This attractive property is explained through the poles and zeros of the estimates, and the basic equation of the biases for overparametrized model is derived. We show a guide to choose the model order so that the identification experiment can easily be performed by only least-squares method without considering for the model structure and the identification algorithm. This over-parametrized identification is very practical and usefull to get the rough characteristics of the system, because least-squares method is very simple and effective.
