Abstract: The precision of cubature Kalman filter(CKF) is bad or even divergent when the states change suddenly or slowly because of faults. We propose a new method called strong tracking CKF to solve this problem. This method computes the posterior mean and the variance of the nonlinear function directly using cubature numerical integration. Meanwhile, the method adjusts the gain matrix and increases the weights of the new data by taking in the fading factor in predicted error covariance. The method has better filtering characteristics than CKF in fault diagnosis of nonlinear systems. The simulation results show that this method has better precision and robustness for typical fault diagnosis problems such as sudden change or slow change of the states of the nonlinear systems.