## 6 Experimental Validation
### Results of Directional Localization  
No inside-the-head localization was reported in all the raw localization results. For both the proposed and conventional algorithms, the percentages of front-back and up-down confusions in directional localization (calculated over all the target source distances, directions, and judgments) were less than 5% and 1%, respectively. It is well established that binaural cues including interaural time difference (ITD) and interaural level difference (ILD) account for lateral localization. However, binaural cues are unable to provide enough information for front-back and vertical localizations, especially in the cone of confusion in which the ITD and ILD are approximately constants. It is also well accepted that both individualized spectral cue (caused by the diffraction of pinnae and head) and dynamic cue caused by head turning contribute to front-back and vertical localization. However, the information provided by spectral cue and dynamic cue is somewhat redundant, one cue alone allows for front-back and vertical localization to some extent [29]. Therefore, the low percentage of front-back and up-down confusions is due to the incorporation of dynamic localization cues in dynamic VAD, which alleviate the dependence of individualized spectral cues in front-back and vertical localization.  
Table 3 lists the mean angular errors across all direction and judgments at different target distances. It is observed that mean angular errors lies between 12.6\({}^{\circ}\) and 14.3\({}^{\circ}\), which is basically consistent with previous results in dynamic VAD [12]. Generally, larger angular errors occurred in proximal regions. The mean angular errors tended to decrease as the target distance increased for all cases.  
Because the perceived directions are distributed in a spherical coordinate system, we chose to use a statistical graph to represent the explicit performance of directional localization according to the method suggested by [PERSON] [30]. Figure 3 is the graphical representation of the mean perceived direction across target distances and judgments. The results are demonstrated on the surface of a sphere and viewed from the front, right, and rear, respectively. In the figures, notation '\(+\)' denotes the target virtual source direction; the red points at the center of the ellipses are the average perceived directions; the ellipses centered around the centroid represent the confidence region at the significance level of \(\alpha=0.05\). The ellipses drawn with a blue line indicate that the data are highly symmetric around the mean. Otherwise, it is drawn with a green line. It is also observed that the proposed and conventional algorithms yield similar directional localization performances. The larger localization errors usually occur at the directions below and behind the subject, and the smaller localization errors usually occur at the frontal and lateral directions in the horizontal plane. This feature of localization errors may be due to the fact that the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & \(r=0.2\) m & \(r=0.3\) m & \(r=0.5\) m & \(r=0.75\) m & \(r=1.0\) m \\ \hline Conventional & 13.3 & 13.4 & 14.3 & 13.3 & 12.6 \\ Proposed & 14.0 & 13.7 & 12.9 & 13.5 & 13.3 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Mean angular errors (\({}^{\circ}\)) across all directions and judgments at different target distances.  
directional localization accuracy of a human being is inherently lower at the below and back directions.  
A multi-way ANOVA on the mean angular errors indicates that, at a significance level of 0.05, the difference between the mean angular error of proposed and conventional algorithms is insignificant. Therefore, the proposed algorithm yields a directional localization performance similar to that of the conventional algorithm.