This paper presents a robust parametric estimation method of the Prony exponential model that is able to suppress white impulsive noise. The method consists of the following steps. Firstly, the Prony parametric estimation problem is reformulated as a parameter estimation of an Auto-Regressive (AR) model of a known order. Secondly, 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 (IPPC); the latter is a robust estimator of correlation for complex-valued Gaussian processes, which has been extended here to handle outliers in the magnitude and in the phase angle of voltage phasor measurements. Finally, the Burg algorithm is applied using a robustly estimated autocorrelation sequence to estimate the AR parameters. The Burg algorithm is chosen over the Yule-Walker technique because it leads to stable AR models even when the processed data samples are of short durations and when the roots of the characteristic polynomial are close to the unit circle, which is precisely the case for power systems with poorly damped excited modes. The good performance of the proposed method is demonstrated on some simulations carried out on the two-area test system. The method is very fast to compute and compatible with real-time application requirements.