We study the linear combinations of the process and its shifts that produce a process independent of the input. The set of all such linear combinations, called the orthogonalizers, has a module structure and under identifiability conditions completely specifies the deterministic part of the ARMAX system. Computing a module basis for the orthogonalizers is a deterministic identification problem.
We propose an ARMAX identification algorithm, which has three steps: first compute the deterministic part of the system via the orthogonalizers, then the AR part, which also has a module structure, and finally the MA part.
@InProceedings{MWDM06, author = {I. Markovsky and J. C. Willems and B. {De Moor}}, title = {The module structure of {ARMAX} systems}, booktitle = {Proceedings of the 41st Conference on Decision and Control}, OPTpages = {811--816}, year = {2006}, address = {San Diego, USA} }