Subspace Identification of Closed-Loop EIV System Based on Instrumental Variables Using Orthoprojection

This paper proposes a subspace identification method for closed-loop EIV (errors-in-variables) problems based on instrumental variables . First, a unified framework is derived, and then the reason is discussed why some existing subspace methods based on instrumental variables could be biased under closed-loop conditions. Afterwards a remedy is given to eliminate the bias by simply replacing the instrumental variable. Using orthogonal projection, the resulting instrumental variable method is very simple and easy to extend. In addition, simulation studies illustrate the effects of different instrumental variables.