One of the main areas of psychoacoustics is localization, which means estimating the location of a sound source by hearing it. This is crucial for many VR experiences. For example, if people are socializing, then their voices should seem to come from the mouths of corresponding avatars. In other words, the auditory and visual cues should match. Any kind of sound effect, such as a car or zombie approaching, should also have matched cues.

Figure 11.9: Spherical coordinates are used for the source point in auditory localization. Suppose the head is centered on the origin and facing in the $ -z$ direction. The azimuth $ \theta $ is the angle with respect to the forward direction after projecting the source into the $ xz$ plane. The elevation $ \phi $ is the interior angle formed by a vertical triangle that connects the origin to the source and to the projection of the source into the plane. The radius $ r$ is the distance from the origin to the source.

Figure 11.10: Plots of the minimum audible angle (MAA) as a function of frequency. Each plot corresponds to a different azimuth angle.

The JND concept is applied for localization to obtain the minimum audible angle (MAA), which is the minimum amount of angular variation that can be detected by a human listener. A spherical coordinate system is usually used for localization, in which the listener's head is at the origin; see Figure 11.9. The angle in the horizontal plane between the forward direction and the source is called the azimuth, which extends from $ -180$ to $ 180$ degrees. The angle corresponding to deviation of the source from the horizontal plane is called the elevation, which extends from $ -90$ to $ 90$ degrees. The third coordinate is the radius or distance from the origin (head center) to the source. The MAA depends on both frequency and the direction of the source. Figure 11.10 shows a plot of the MAA as a function of frequency, at several values for azimuth. The amount of variation is surprising. At some frequencies and locations, the MAA is down to $ 1$ degree; however, at other combinations, localization is extremely bad.

Steven M LaValle 2020-01-06