The Role of Vector Autoregressive Modeling in Predictor Based Subspace Identification

In this paper we shall discuss the link between these “predictor-based” methods; to this purpose we exploit the role which Vector Auto Regressive with eXogenous input models play in all these algorithms. The results of this paper provide a unifying framework under which all these algorithms can be viewed; also the link with VARX modeling have important implications as to computational complexity is concerned, leading to very computationally attractive implementations. We also hope that this framework, and in particular the relation with VARX modeling followed by model reduction will turn out to be useful in future developments of subspace identification, such as the quest for efficient procedures and the statistical analysis with finite-data.