Subspace identification with non-steady Kalman filter parameterization

• We analyze the deficiency of subspace identification schemes with finite data.
• We propose a non-steady Kalman filter based subspace identification method.
• We show that the proposed method is superior for finite data horizon.
• We demonstrate that the proposed method is insensitive to horizon lengths.

Most existing subspace identification methods use steady-state Kalman filter (SKF) in parameterization, hence, infinite data horizons are implicitly assumed to allow the Kalman gain to reach steady state. However, using infinite horizons requires collecting infinite data which is unrealistic in practice. In this paper, a subspace framework with non-steady state Kalman filter (NKF) parameterization is established to provide exact parameterization for finite data horizon identification problems. Based on this we propose a novel subspace identification method with NKF parameterization which can handle closed-loop data and avoid assumption on infinite horizons. It is shown that with finite data, the proposed parameterization method provides more accurate and consistent solutions than existing SKF based methods. The paper also reveals why it is often beneficial in practice to estimate a bank of ARX models over a single ARX model.