On the choice of parameterization for identification

The effect on an identification procedure of the choice of system parameterization is considered. First, a formal framework is presented in which to assess this effect and some previous results are reviewed in this framework. Then the class of methods that minimize an input-output objective function are studied. Sufficient conditions on identifiable parameterizations of linear models are stated which render the associated model estimators equally accurate in asymptotic, statistical terms. These are shown to apply to parameterizations with "maximal number of free parameters."