Non-stationary Kalman filter parametrization of subspace models with applications to MPC

In this paper, a non-stationary Kalman filter parametrization of subspace identification models is adopted to deal with finite data windows. We show that the non-stationary Kalman filter parametrization is the solution to the least squares estimation of the Markov parameters from high-order ARX models. A recursive conversion between observer Markov parameters and system Markov parameters is developed under the non-stationary Kalman filter structure. The system Markov parameters can be obtained and further applied to disturbance modeling in model predictive control. Simulations are carried out to show the effect of the non-stationary Kalman filter parametrization with finite data.