# AMBIQUAL: Towards a Quality Metric for Headphone Rendered Compressed Ambisonic Spatial Audio
## 5 Validation Experiments  
### Full Sphere Localization Accuracy Prediction  
Building on the initial exploration in [4], a dataset of one second duration, pink noise audio signals, sampled at 48 kHz were synthetically generated. Third-order Ambisonics B-format was used to render the reference audio sources to 22 fixed locations, evenly distributed over a quarter of a sphere. The test Ambisonic audio signals were rendered at 206 fixed locations evenly distributed on the whole sphere (i.e., with 30\({}^{\circ}\) horizontal and 10\({}^{\circ}\) vertical steps as illustrated in Figure 13). Localization accuracy was computed for each combination of the reference and test audio sources.  
Figure 12: Localization accuracy-subjective vs. AMBIQUAL results: (**a,b**) aggregated subjective localization accuracy scores by encoding scheme (one point audio sources and multi-point audio sources respectively) showing mean values with 95% confidence intervals shown. Plots (**c,d**) show aggregated AMBIQUAL results by encoding scheme (one and multi-point sources respectively). Plots (**e,f**) scatter of subjective vs. AMBIQUAL results by encoding (one and multi-point sources respectively), (**g,h**) scatter of subjective vs. AMBIQUAL results by sample type (one and multi-point sources respectively).  
Figure 13: Localization accuracy scores distributed on a sphere. The reference audio source was localized at azimuth = 60\({}^{\circ}\), elevation = 60\({}^{\circ}\) (the red circle represents the reference audio source). Reproduced from [4].  
Figure 13 presents an example of results for one reference signal, marked in red where the test signal accuracy of \(LA\) predictions are in grayscale, descending light to dark. In this example, the source was anchored at 60\({}^{\circ}\) azimuth and 60\({}^{\circ}\) elevation. As can be seen, the test localization accuracy decreases as it gets further from the reference source. This is indicated by the grey dots getting darker as the test signal location gets further from the reference.  
Figure 14 presents the \(LA\) predictions for the same example reference source. Localization accuracy, \(LA\), is plotted as a function of azimuth (i.e., from \(-180^{\circ}\) to \(180^{\circ}\) at 30 \({}^{\circ}\) angle steps) and 7 elevation angles (i.e., from \(-90^{\circ}\) to \(90^{\circ}\) in \(30^{\circ}\) angle steps).  
The procedure was repeated for 22 fixed reference audio source locations. Figure 15 shows localization accuracy predictions on a sphere where the reference audio source was located at 30\({}^{\circ}\) azimuth and 30\({}^{\circ}\) elevation and Figure 16 presents the \(LA\) predictions as a function of azimuth and elevation angles.  
Validation testing conforms that as the test audio source moves away from the reference audio source, localization accuracy can be seen to decrease monotonically. This was validated using test signals rendered on a sphere. A point of inflection is reached at around \(\pm 90^{\circ}\) angle in relation to the audio source localization which corresponds to human localization at \(\pm 90^{\circ}\).  
Figure 14: Localization accuracy as a function of azimuth and elevation with fixed reference audio source, localized at an offset point of azimuth = 60\({}^{\circ}\), elevation = 60\({}^{\circ}\). The asymmetry in the results is caused by the source being closer to one ear than the other. Reproduced from [4].  
Figure 15: Localization accuracy scores distributed on a sphere. In this case, the reference audio source was localized at azimuth = 30\({}^{\circ}\), elevation = 30\({}^{\circ}\) (the red circle represents the reference audio source).