The generalized cross-correlation (GCC) based inverse model is a promising time domain localization technique for a broadband acoustic source. Its performance is affected by the temporal width threshold of the propagation model matrix. The appropriate threshold should vary with focus distance, array geometry, and array size, but there is still a lack of uniform and effective methods to determine it. To solve this issue and perfect the technique, a method is proposed based on the cumulative probability of all differences of time delay estimation between the focus point and the microphone pair. Further, an alternative propagation model matrix is derived, which circumvents the threshold. Both proposed methods are effective under different simulation and experimental configurations, with strong stability and adaptability to focus distance, array geometry, and array size. The GCC based inverse model with either proposed method not only enjoys satisfactory source localization performance, including narrow mainlobes, few spurious sources, and highlighted source positions, but also can correctly estimate the sound level, which is comparable to that with the preset appropriate temporal width threshold. In terms of the computational time, the inverse model with the latter proposed method outperforms that with the former one.
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