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This paper proposes a novel Bayesian stochastic filtering approach for the simultaneous phase drift estimation and symbol detection in digital communications. The posterior density of the phase drift is propagated in a recursive fashion by implementing a prediction and a filtering step in each iteration. The prediction step is supported on a random walk model playing the role of prior for the phase drift process; the filtering step is supported on a Gaussian sum approximation for the probability density of the current observation, i.e., the so-called sensor factor. The Gaussian sum approximation turns out to be the key element allowing to derive a fast and efficient stochastic filter, which otherwise would be very hard to compute. The detection of the digital symbols is then carried out based on the inferred statistics of the phase drift. The effectiveness of the proposed method is illustrated for BPSK signals in the presence of strong phase drift.