# Auditory Localization in Low-Bitrate Compressed Ambisonic Scenes
## 4 Results
To minimize the directional bias introduced by the pointing interface and focus on the random localization error, the great-circle distance was calculated using the spherical means as the reference directions, not the encoded target directions. Mean spherical direction was calculated for each of the analyzed subsets. Figure 7 shows the set of probability density functions [43] of the localization error obtained experimentally at different Ambisonic orders/codec bitrates and rendering methods. It can be seen that the general shape of presented distributions corresponds to the shape of von Mises-Fisher distribution [44] plotted as the probability density function of the distance between each spherical mean and each sample. However, the experimental distributions exhibit multimodal characteristics caused by the cone of confusion and data collection biases. This limits the use of statistical tests based on parameterized spherical data distributions for a unified analysis of the results. Instead, the Kruskal-Wallis rank-based non-parametric test was used to investigate the spherical concentration [45; 46] of the participant responses under different experimental conditions. Figure 7: Probability density functions of the localization error for different spatial audio rendering methods at different codec bitrates and Ambisonic orders. Continuous line represents loudspeaker reproduction, dashed line—binaural (individual HRTFs), dotted—binaural (generic HRTFs). Kernel bandwidth: \(BW=6\). HRTFs: Head-Related Transfer Functions. The following experimental variables were tested: participants, virtual target sound source direction, codec bitrates, Ambsonic orders, audio content type, and audio reproduction method (loudspeaker-based vs. individualized vs. generic HRTFs). A significant difference in the overall localization task performance between participants has been found in each of the three experimental phases using different spatial audio rendering methods (\(p<0.01\)). The overall localization error median for each participant is shown in Figure 11.  
The effect of the position of the virtual target sound source was significant (\(p<0.01\)); however, no clear trends in data were identified. The localization error median for each direction at different rendering methods is shown in Figure 12. The effect of codec bitrate was analyzed in nine subgroups, grouped by Ambisonic order and rendering method. It was found to be significant (\(p<0.01\)) in two groups: 3 rd-order and 5 th-order scenes reproduced using the loudspeaker array. Significant differences between compressed scenes grouped by Ambisonic order have been found for each of the three rendering methods (\(p<0.01\)). The effect of content type on participant responses was investigated in the raw data and the test result was close to the 95% confidence limit (\(\chi^{2}=3.92\), \(p=0.048\)). Detailed analysis was done in 30 subgroups, grouped by different codec bitrates / Ambisonic orders and spatial audio rendering methods. The difference between simple and complex-scene content has not been found to be significant (\(p>0.01\)) in 29 of the 30 subgroups. Rendering method had significant effect on the localization error (\(p<0.01\)). Figure 8 shows median localization error at different codec bitrates, Ambisonic orders, and rendering methods. It can be seen that generic HRTF reproduction resulted in higher localization error compared to the loudspeaker and individual HRTF reproduction. A decrease in localization error with the increase of Ambisonic order was observed using all three reproduction methods. This effect is most prominent at the loudspeaker-based tests, where the difference between 1 st and 3 rd-order is much more significant than the difference between 3 rd and 5 th-order. The differences in median localization error caused by different bitrates within the same Ambisonic order can be observed; however, they are not significant in most cases.