COMPOSITE MODELING OF TRANSFER-FUNCTIONS

The problem under consideration is how to estimate the frequency function of a system and the associated estimation error when a set of possible model structures is given and then one of them is known to contain the true system. The ''classical'' solution to this problem is to, first, use a consistent model structure selection criterion to discard all but one single structure, second, estimate a model in this structure and, third, conditioned on the assumption that the chosen structure contains the true system, compute an estimate of the estimation error, For a finite data set, however, one cannot guarantee that the correct structure is chosen, and this ''structural'' uncertainty is lost in the previously mentioned approach. In this contribution a method is developed that combines the frequency function estimates and the estimation errors from all possible structures into a joint estimate and estimation error. Hence, this approach bypasses the structure selection problem, This is accomplished by employing a Bayesian setting,Special attention is given to the choice of priors. With this approach it is possible to benefit from a priori information about the frequency function even though the model structure is unknown.