A Theoretical Framework of Robust H-Infinity Unscented Kalman Filter and Its Application to Power System Dynamic State Estimation

This paper presents a new theoretical framework that, by integrating robust statistics and robust control theory, allows us to develop a robust dynamic state estimator of a cyber-physical system. This state estimator combines the generalized maximum-likelihood-type (GM) estimator, the unscented Kalman filter (UKF), and the H-infinity filter into a robust H-infinity UKF filter in the Krein space, which is able to handle large system uncertainties as well as suppress outliers while achieving a good statistical efficiency under Gaussian and non-Gaussian process and observation noises. Specifically, we first use the statistical linearization approach to build a linearlike regression model in the Krein space. Then, we show that the H-infinity UKF is just the Krein space Kalman filter that exhibits a bounded estimation error in presence of system uncertainties while minimizing the least squares criterion; consequently, it suffers from a lack of robustness to outliers and non-Gaussian noise. Because the GM estimator is able to handle outliers, but it may yield large estimation errors in the presence of system uncertainties, we propose to combine it with the H-infinity UKF in a robust H-infinity UKF. We carry out a theoretical analysis to demonstrate the connections that our filter has with the H-infinity UKF and the GM-UKF. The good performance of the new filter is demonstrated via extensive simulation performed on the IEEE 39-bus power system.