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A novel fault detection (FD) method for nonlinear systems using the residuals generated by the unscented Kalman filter (UKF) is proposed. The errors of the UKF are derived and sufficient conditions for the convergence of the UKF are presented. As the local approach is a powerful statistical technique for detecting changes in the mean of a Gaussian process, it is used to devise a hypothesis test to detect faults from residuals obtained from the UKF. Further, it is demonstrated that the selection of a sample number is important in improving the performance of the local approach. To illustrate the implementation and performance of the proposed technique, it is applied to detect sensor faults in the measurement of satellite attitude.