This paper develops a robust estimator of correlation as a data preprocessing stage to the Prony method that is able to suppress white impulsive noise. The method consists of the following steps. First, the bus voltage magnitudes and phase angles are combined to build a set of complex-valued measurements. Second, the outliers of the complex-valued data samples, which are induced by impulsive noise, are identified and suppressed using the iteratively reweighted phase-phase correlator; the latter is a robust estimator of correlation for complex-valued Gaussian processes, which has been extended here to handle outliers in both magnitude and phase angle of voltage phasor measurements. Finally, the classical Prony method is applied on the robustly estimated voltage phase angles. The good performance of the proposed method is demonstrated through simulations carried out on the two-area four-machine system, on the simplified WECC 179-bus system, as well as on real PMU data. Simulation results show that the method is very fast to compute and is compatible with real-time application requirements.