Proposal and validation of an analytical generative model of SRP-PHAT power maps in reverberant scenarios

• A novel parametric analytical model to predict SRP-PHAT power maps is formulated.
• An exhaustive evaluation is done on both synthetic and real data.
• Results show high accuracy for very different acoustical and geometrical conditions.
• The paper also addresses practical issues in the model implementation.

The algorithms for acoustic source localization based on PHAT filtering have been profusely used with good results in reverberant and noisy environments. However, there are very few studies that give a formal explanation of their robustness, most of them providing just an empirical validation or showing results on simulated data. In this work we present a novel analytical model for predicting the behavior of both the SRP-PHAT power maps and the GCC-PHAT functions. The results show that they are only affected by the signal bandwidth, the microphone array topology, and the room geometry, being independent of the spectral content of the received signal. The proposed model is shown to be valid in reverberant environments and under far and near field conditions. Using this result, an analysis study on how the aforementioned factors affect the SRP-PHAT power maps is presented providing well supported theoretical and practical considerations. The model validation is based on both synthetic and real data, obtaining in all cases a high accuracy of the model to reproduce the SRP-PHAT power maps, both in anechoic and non-anechoic scenarios, becoming thus an excellent tool to be exploited for the improvement of real world relevant applications related to acoustic localization.