Previously, conventional state estimation techniques have been used for state estimation in power systems. These conventional methods are based on steady state models. As a result of this, power system dynamics during disturbances or transient conditions are not adequately captured. This makes it challenging for operators in control centers to perform visual tracking of the system, proper fault diagnosis and even take adequate preemtive control measures to ensure system stability during voltage dips. Another challenge is that power systems are nonlinear in nature. There are multiple power components in operation at any given time making the system highly dynamic in nature. Consequently, the need to study and implement better dynamic estimation tools that capture system dynamics during disturbances and transient conditions is necessary. For this thesis work, we present the Unscented Kalman Filter (UKF) which integrates Unscented Transformation (UT) to Kalman Filtering. Our algorithm takes as input the output of a synchronous machine modeled in MATLAB/Simulink as well as data from a PMU device assumed to be installed at the terminal bus of the synchronous machine, and estimate the dynamic states of the system using a Kalman Filter. We have presented a detailed and analytical study of our proposed algorithm in estimating two dynamic states of the synchronous machine, rotor angle and rotor speed. Our study and result shows that our proposed methodology has better efficiency when compared to the results of the Extended Kalman Filter (EKF) algorithm in estimating dynamic states of a power system.  Our results are presented and analyzed on the basis of how accurately the algorithm estimates the system states following various simulated transient and small-signal disturbances.