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Availability of the synchronous machine angle and speed variables give us an accurate picture of the overall condition of power networks leading therefore to an improved situational awareness by system operators. In addition, they would be essential in developing local and global control schemes aimed at enhancing system stability and reliability. In this paper, the extended Kalman filter (EKF) technique for dynamic state estimation of a synchronous machine using phasor measurement unit (PMU) quantities is developed. The simulation results of the EKF approach show the accuracy of the resulting state estimates. However, the traditional EKF method requires that all externally observed variables, including input signals, be measured or available, which may not always be the case. In synchronous machines, for example, the exciter output voltage Efd may not be available for measuring in all cases. As a result, the extended Kalman filter with unknown inputs, referred to as EKF-UI, is proposed for identifying and estimating the states and the unknown inputs of the synchronous machine simultaneously. Simulation results demonstrate the efficiency and accuracy of the EKF-UI method under noisy or fault conditions, compared to the classic EKF approach and confirms its great potential in cases where there is no access to the input signals of the system.