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The most important reference quantities for monitoring and controlling transient stability in real time are the rotor angle and speed of the synchronous generators. If these quantities can be estimated with sufficient accuracy, they can be used in global and local control methods. In the classic state estimation methods, such as the extended Kalman filter (EKF) technique, the linear approximations of the system at a given moment in time may introduce errors in the states. In order to overcome the drawbacks of the EKF, the authors of this paper have applied the unscented Kalman filter (UKF) to estimating and predicting the states of a synchronous machine, including rotor angle and rotor speed, using phasor measurement unit (PMU) quantities. The UKF algorithm propagates the pdf of a random variable in a simple and effective way and is accurate up to the second order in estimating the mean and covariance. The overall impression is that the performance of the UKF is better than the EKF in terms of robustness, speed of convergence, and also different levels of noise. Simulation results including saturation effects and grid faults show the accuracy and efficiency of the UKF method in state estimation of the system, especially at higher noise ratios.