Asymptotic Properties of Bias Compensated State Space Model Identification Method

The authors proposes a bias-compensated state space model identification (BCSS) method in order to relax the order of the persistent excitation (PE) condition. Most of the subspace identification methods utilize instrumental variables (IV) to obtain an unbiased estimate while the proposed method introduces a bias compensation technique to the Ordinary MOESP type method. In this paper, S/N ratios of certain matrices in the proposed method and the PI-MOESP method are analyzed and compared. It is shown that the S/N ratio in the proposed method is better than that in the PI-MOESP method especially when a pole of the plant is near 1 and the number of the block rows of the IV matrix is small.