Modified state prediction algorithm based on UKF

The state prediction based on the unscented Kalman filter (UKF) for nonlinear stochastic discrete-time systems with linear measurement equation is investigated. Predicting future states by using the information of available measurements is an effective method to solve time delay problems. It not only helps the system operator to perform security analysis, but also allows more time for operator to take better decision in case of emergency. In addition, predictive state can make the system implement real-time monitoring and achieve good robustness. UKF has been popular in state prediction because of its advantages in handling nonlinear systems. However, the accuracy of prediction degrades notably once a filter uses a much longer future prediction. A confidence interval (CI) is proposed to overcome the problem. The advantages of CI are that it provides the information about states coverage, which is useful for treatment-plan evaluation, and it can be directly used to specify the margin to accommodate prediction errors. Meanwhile, the CI of prediction errors can be used to correct the predictive state, and thereby it improves the prediction accuracy. Simulations are provided to demonstrate the effectiveness of the theoretical results.