Robust Kalman filter-based least squares identification of a multivariable system

A novel direct identification using the residual model of Kalman filter (KF) is proposed for multiple-input and multiple-output Box–Jenkins model of the system formed of the signal and disturbance models using the residual model relating the input and output of the system without any a priori knowledge of the statistics of the disturbance and measurement noise corrupting the output. To avoid a non-linear optimisation, the auto-regressive and moving average (MA) residual model is approximated by a high-order MA model, so that the unknown parameters of the KF enter the residual model linearly. A key property of the KF is established, namely that the transfer matrix of the signal model is the matrix fraction description (MFD) model relating the residual and the system input and output. A two-stage identification method is developed here. In stage 1, a high-order KF of the system is identified using the robust, and computationally efficient least-squares method to capture completely both the signal and disturbance models. In stage 2, the KF for the signal is derived using the balanced model reduction technique. The signal model is derived using the key MFD property. The performance of the proposed scheme is successfully evaluated on both simulated and physical systems.