## 2 Psychoacoustic Principles of Auditory Distance Perception
### Compared with Directional Localization Cues  
In contrast to distance perception, auditory directional localization is unbiased. Human hearing is able to localize the direction of a sound source with adequate accuracy. For example, the minimal audible angle of a horizontal-frontal source is 1-3\({}^{\circ}\)[2], although the acuity of directional localization decreases for other source directions. The cues and mechanisms of auditory directional localization in a free field are relatively clear [2; 7]. Directional localization is also the consequence of a comprehensive process based on multiple cues. For a far-field sound source, the interaural phase delay difference (ITDp) at low frequencies below 1.5 kHz and the ILD at high frequencies above 2-3 kHz are lateral localization cues. Spectral cues created by the scattering and diffraction \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Condition**} & \multicolumn{5}{c}{**Distance Cue**} \\ \cline{2-6}  & **Level** & **Spectra** & \multicolumn{2}{c}{**HRTF**} & \multirow{2}{*}{**DRR**} \\ \cline{2-6}  & & & **ILD** & & **Parallax** & \\ \hline Free field & Yes & Yes & Yes & Yes & No \\ \hline Reverberation field & Yes & Yes & Yes? &? & Yes \\ \hline Absolute or relative distance perception & Relative & Relative & Absolute & Absolute & Absolute \\ \hline Source direction & Frontal and lateral & Frontal and lateral & Lateral & Frontal & Frontal and lateral \\ \hline Source distance & Proximal and distant & \textgreater{}15 m & Proximal & Proximal & Proximal and distant \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of various auditory distance perception cues. The question mark (?) indicates that the existing research on this problem has not been clarified. of anatomical structures (especially by pinnae) at high frequencies above 5-6 kHz and dynamic cues (especially dynamic ITD variation at low frequencies below 1.5 kHz) caused by head turning contribute to front-back and vertical localization. Notably, for a source at proximal distance, ITD varies slightly with source and, thus, is not an effective distance perception cue. However, an ILD below 3 kHz and pinna-related spectra are also distance perception cues. Directional localization is enhanced if multiple cues are available. However, the information provided by multiple directional localization cues may be somewhat redundant. Directional localization may still be possible in the absence of some localization cues or even with the existence of conflicting localization cues. For example, when either a high-frequency spectral cue or a dynamic cue is eliminated, another cue alone still enables vertical and front-back localization to some extent [20]. ITD dominates lateral localization as long as the wideband stimuli include low frequencies regardless of conflicting ILDs [21]. However, if too many conflicts or losses exist in localization cues, the accuracy and quality of localization likely degrade, split virtual sources are perceived, or localization may become impossible [22; 23; 24]. As a comparison, distance perception is also achieved through multiple cues, but the relationships and redundancies of distance perception cues are not as clear as those of directional localization cues. Summing directional localization with multiple sound sources (loudspeakers) is an important psychoacoustic phenomenon [2]. For appropriate multiple sound source configurations (loudspeakers) and correlated source signals, if the relative level and arrival time of each sound sources satisfy certain conditions, the listener perceives a summing virtual source. Summing a virtual source with relative level differences among the sources (interchannel level differences) is due to the superposed sound waves at two ears creating an appropriate ITD at low frequency, which dominates the lateral localization.