# Individualized Interaural Feature Learning and Personalized Binaural Localization Model +
## 6 Experiments With Simulated Data
### 3-D Space Localization with Probabilistic Model
#### 6.2.1 Performance Measurements and Simulation Configuration  
The received signals are generated by convolving the simulated Binaural Room Impulse Response (BRIR) and speech utterances. The speech utterances are obtained from the PASCAL 'CHiME' Speech Separation and Recognition Challenge database [32], which includes 34 speakers and every speaker has 500 utterances. Each testing speech utterance has around 1 s duration.  
The BRIRs used in the testing are generated with CIPIC HRTF subject '003' and the Roomsim MATLAB program [34] based on the image method in four empty'shoebox' rooms. A rectangular room with room sizes 5 m \(\times\) 5 m \(\times\) 3 m is created in the simulation. The subject head is fixed at (2.5, 2.5, 1.2) m and the sound source is positioned around the subject with the same position scheme as used in the CIPIC database, so there are 1250 source positions (25 azimuths \(\times\) 50 elevations) in total during the tests. The distance between the sound source and the center of the head is fixed as 1.5 m so that the acoustical environment can be considered a far-field environment. The strengths of reflections are manipulated by the absorption coefficients \(\beta\) on the walls. In the additive noise test, four sets of data are generated and tested with different SNRs. The absorption coefficients are set as \(\beta=1\), so no reflections present and the interference is entirely caused by noise. As for the reverberation test, the absorption coefficients are tuned from 0.8 to 0.2, and the corresponding \(T_{60}\) varies from 100 to 500 ms approximately.  
The localization accuracy is evaluated by the correct rate of localization. An estimation is considered correct if the difference between the estimated sound direction and ground truth source position is below a certain tolerance threshold. To objectively demonstrate the 3-D position differences between  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Localization Approach**} & \multicolumn{2}{c}{**Mean Angular Localization Error**} \\ \cline{2-4}  & **10 dB** & **20 dB** & **30 dB** \\ \hline
**Proposed learning** & 5.63\({}^{\circ}\) & 0.89\({}^{\circ}\) & 0.14\({}^{\circ}\) \\
**Composite feature**[25] & 24.30\({}^{\circ}\) & 5.11\({}^{\circ}\) & 0.85\({}^{\circ}\) \\
**Cross-Correlation**[31] & 67.65\({}^{\circ}\) & 58.55\({}^{\circ}\) & 51.58\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: 3-D space localization performance comparison.  
the ground truth source position and the estimated direction, the angular error defined by the absolute angular difference between two directional vectors in a Cartesian coordinate system is calculated as:  
\[\epsilon=\arccos\frac{\mathbf{d}_{<a,\beta>}\cdot\mathbf{\hat{d}}_{<\hat{a},\hat{ \beta}>}}{|\mathbf{d}_{<a,\beta>}||\mathbf{\hat{d}}_{<\hat{a},\hat{\beta}>}|} \tag{19}\]  
where \(\mathbf{d}_{<\alpha,\beta>}\) and \(\mathbf{\hat{d}}_{<\hat{a},\hat{\beta}>}\) are the ground truth source direction vector and the estimation direction vector in Cartesian coordinate system, respectively. The azimuth and elevation correct rate in the interaural-polar system are also presented.