Abstract
For the identification of linear system on the basis of both input and output data, equation error methods (EEM) (often indicated as prediction error methods) are frequently used rather than output error methods (OEM) This is mainly caused by the fact that the minimum of the EE-criterion can easily be found, in contrast to the OE-criterion which often displays multiple local minima.
Nevertheless we have the impression that for many applications (simulation, diagnosis, control) a proper fit of the impulse response witch corresponds to an OEM is indispensable.
In fact for both methods the model set for the input-output behaviour of the system under study is the same, except for the point where the disturbances are supposed to enter. It is this similarity that often leads to an inconsiderate use of the identification results for various applications irrespective of the chosen identifidation criterion.
In many practical situations the real system under study will be of infinite order which implies that the systems will result in essentially different models based on either EEM or OEM identification. We will try to characterize this class of systems and give some examples.
Next we want to discuss the impact of this discrepancy on applications.
