This solution would still be insufficient to resolve ambiguity within the cone of confusion. Recall from Section 11.3 that the pinna shape distorts sounds in a direction-dependent way. To fully take into account the pinna and other parts of the head that may distort the incoming sound, the solution is to develop a head-related transfer function (HRTF). The idea is to treat this distortion as a linear filter, which can be characterized in terms of its transfer function (recall Figure 11.12). This is accomplished by placing a human subject into an anechoic chamber and placing sound sources at different locations in the space surrounding the head. At each location, an impulse is generated on a speaker, and the impulse response is recorded with a small microphone placed inside of the ear canal of a human or dummy. The locations are selected by incrementally varying the distance, azimuth, and elevation; recall the coordinates for localization from Figure 11.10. In many cases, a far-field approximation may be appropriate, in which case a large value is fixed for the distance. This results in an HRTF that depends on only the azimuth and elevation.

It is, of course, impractical to build an HRTF for every user. There is significant motivation to use a single HRTF that represents the ``average listener''; however, the difficulty is that it might not be sufficient in some applications because it is not designed for individual users (see Section 6.3.2 of [341]). One compromise might be to offer a small selection of HRTFs to users, to account for variation among the population, but they may be incapable of picking the one most suitable for their particular pinnae and head. Another issue is that the transfer function may depend on factors that frequently change, such as wearing a hat, putting on a jacket with a hood or large collar, or getting a haircut. Recall that adaptation occurs throughout human perception and nearly all aspects of VR. If people adapt to frequent changes in the vicinity of their heads in the real world, then perhaps they would also adapt to an HRTF that is not perfect. Significant research questions remain in this area.

Steven M LaValle 2020-01-06