Asymptotic Equivalence of Certain Closed Loop Subspace Identification Methods

Subspace identification for closed loop systems has been recently studied by several authors. Even though results are available which allows to compute the asymptotic variance of the estimated parameters for several algorithms, less clear is the situation as to relative performance is concerned. In this paper we partly answer this last question showing that the SSARX algorithm introduced by Jansson, which requires preliminary ARX modeling, and its “geometric version” called PBSID in the literature, which does not require any preliminary estimation step, are asymptotically equivalent. The question as to which is to be preferred in practice when working with finite data size remains open.