Closed-loop subspace identification using the parity space

It is known that many subspace algorithms give biased estimates for closed-loop data due to the existence of feedback. In this paper we present a new subspace identification method using the parity space employed in fault detection in the past. The basic algorithm, known as subspace identification method via principal component analysis (SIMPCA), gives consistent estimation of the deterministic part and stochastic part of the system under closed loop. Column weighting for SIMPCA is introduced which shows improved efficiency/accuracy. A simulation example is given to illustrate the performance of the proposed algorithm in closed-loop identification and the effect of column weighting.