Robust Kalman filter design via Krein space

We propose a new robust Kalman filter for discrete-time system with norm-bounded parametric uncertainty. The uncertainty is described by energy bound constraints, i.e., sum quadratic constraints (SQC). It is shown that the SQC can be converted into indefinite quadratic cost function to be minimized in Krein space, and it is also found that the Krein space Kalman filter is a solution of this minimization problem. Since the resulting robust Kalman filter has the same recursive structure as a nominal Kalman filter has, a robust filtering scheme can be readily designed via the proposed method. Simulation results show the improved performance and the robustness of the proposed filter.