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Acoustic source localization is used in many underwater applications. Acquiring an accurate directional angle for an acoustic source is crucial for source localization. To achieve this purpose, this paper presents a method for directional angle estimation of underwater acoustic sources using a marine vehicle. It is assumed that the vehicle is equipped with two hydrophones and that the acoustic source transmits a specific signal repeatedly. The proposed method provides a probabilistic model for time delay estimation. The probability is recursively updated by prediction and update steps. The prediction step performs a probability transition using the angular displacement of the marine vehicle. The predicted probability is updated using a generalized cross correlation function with a verification process using entropy measurement. The proposed method can provide a reliable and accurate estimation of the directional angles of underwater acoustic sources. Experimental results demonstrate good performance of the proposed probabilistic directional angle estimation method in both an inland water environment and a harbor environment.