On consistency of closed-loop subspace identification with innovation estimation

In this paper, we show that the consistency of closed-loop subspace identification methods (SIMs) can be achieved through innovation estimation. Based on this analysis, a sufficient condition for the consistency of a new proposed closed-loop SIM is given. A consistent estimate of the Kalman gain under closed-loop conditions is also provided based on the algorithm. A multi-input-multi-output (MIMO) simulation shows that it is consistent under closed-loop condition, when traditional SIMs fail to provide consistent estimates.