This paper proposes a decentralized algorithm for real-time estimation of the dynamic states of a power system. The scheme employs phasor measurement units (PMUs) for the measurement of local signals at each generation unit, and subsequent state estimation using unscented Kalman filtering (UKF). The novelty of the scheme is that the state estimation at one generation unit is independent from the estimation at other units, and therefore the transmission of remote signals to a central estimator is not required. This in turn reduces the complexity of each distributed estimator, and makes the estimation process highly efficient, accurate and easily implementable. The applicability of the proposed algorithm has been thoroughly demonstrated on a representative model.