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A robust linear phase unwrapping method is proposed to solve the 2π discontinuities in the phase of the cross power spectrum from the binaural inputs using two omnidirectional microphones. The relative incident angle of the interested sound is then estimated according to the time difference of arrival (TDOA) which is obtained from the unwrapped phase of the cross power spectrum. The frequency components associated with the high power are clustered into groups by the phase and frequency distance, and the dominant group is then used to obtain the initial slope estimation. The phase is unwrapped by checking the difference between the actual and the predicted phase by the estimated slope. The re-estimation is then performed by the unwrapped phase. The algorithm is tested under different incident angles and signal to noise ratio (SNR) using real speech signal and white Gaussian noise. The simulation results show the high accuracy and the robustness. This method is also Implemented to control a robot to adaptively adjust itself to the position facing the sound source directly. The satisfactory result was achieved in an open house demonstration.