This paper proposes a decentralized method for estimation of dynamic states of a power system. The method remains robust to time-synchronization errors and high noise levels in measurements. Robustness of the method has been achieved by incorporating internal angle in the dynamic model used for estimation and by decoupling the estimation process into two stages with continuous updation of measurement-noise variances. Additionally, the proposed estimation method does not need measurements obtained from phasor measurement units; instead, it just requires analog measurements of voltages and currents directly acquired from instrument transformers. This is achieved through statistical signal processing of analog voltages and currents to obtain their magnitudes and frequencies, followed by application of unscented Kalman filtering for nonlinear estimation. The robustness and feasibility of the method have been demonstrated on a benchmark power system model.