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The way sound is shaped by the head and body before reaching the ears of a listener is described by a head-related transfer function (HRTF). There is a different HRTF for every angle of incidence.

A head-related transfer function summarizes ITD, ILD, and spectral cues for sound-source localization.

Talagala et al. measured the head-related transfer function (HRTF) of a dummy head and body in a semi-anechoc chamber and used this HRTF for sound source localization experiments.

Talagala et al.'s system can reliably localize sounds in all directions around the dummy head.

Sound-source localization using head-related impulse response functions is precise, but computationally expensive.

Wan et al. use simple cross-correlation (which is computationally cheap, but not very precise) to localize sounds roughly. They then use the rough estimate to speed up MacDonald's cross-channel algorithm which uses head-related impulse response functions.

MacDonald proposes two methods for sound source localization based on head-related transfer functions (actually the HRIR, their representation in the time domain).

The first method for SSL proposed by MacDonald applies the inverse of the HRIR $F^{(i,\theta)}$ to the signal recorded by $i$ For each microphone $i$ and every candidate angle $\theta$. It then uses the Pearson correlation coefficient to compare the resultant signals. Only for the correct angle $\theta$ should the signals match.

The second method for (binaural) SSL proposed by MacDonald applies the HRIR $F^{(o,\theta)}$ to the signals recorded by the left and right microphones every candidate angle θ, where $F^{(o,\theta)}$ is the respective opposite microphone. It then uses the Pearson correlation coefficient to compare the resultant signals. Only for the correct angle θ should the signals match.

The binaural sound-source localization methods proposed by MacDonald can be extended to larger arrays of microphones.