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. © 2014 Elsevier Ltd.
Bibliographical noteFinancial support from the Texas-Wisconsin-California Control Consortium (TWCCC) and Center for Interactive Smart Oilfield Technologies (CiSoft) of University of Southern California is gratefully acknowledged.
- Closed-loop identification
- High order ARX
- Markov parameters
- Non-steady state Kalman filter
- Subspace identification