Criterion based equivalence for equation error models

The problem of modeling an input-output data sequence is considered when applying equation error (least-squares) identification methods to matrix fraction description (MFD) models. In the case that a set of models has been parametrized using the notion of I/O (input/output) equivalence, it is shown that the identified model will be essentially dependent on the specific parameterization chosen. As an alternative, a notion of model equivalence is introduced that is related to the identification criterion. The pseudocanonical or overlapping parametrization of MFD models appears to constitute a set of canonical forms for this least-squares-based model equivalence