# Individualized Interaural Feature Learning and Personalized Binaural Localization Model +
## 6 Experiments With Simulated Data
### 3-D Space Localization with Probabilistic Model
#### 6.2.3 Localization Performance with Additive Noise  
A localization accuracy comparison with the presence of additive noise is shown in Figure 8. In general, the proposed method outperforms the state-of-the-art method with both feature vector types. It can be concluded that the RF algorithm in the proposed method is capable of constructing a finer mapping between the feature characteristics and source locations, and this mapping shows robustness to additive noise. Further, through comparing the performance with different feature vectors yet the same localization method, it can be observed that better performance is obtained by using a full IID and IPD spectrum in the proposed method, while a more accurate result is achieved by using the  
Figure 7: Comparing the localization accuracy with different training conditions. The angular error tolerance is \(2.5^{\circ}\).  
full-spectrum ILD and low-frequency IPD (ILPD) vector in PPAM. This different feature preference proves that the proposed method successfully exploits the non-linear cues in the high-frequency IPD spectrum, and such cues will contribute to a more accurate result.  
A more detailed comparison between the azimuth and elevation estimation is provided in Table 2. Again, better estimation results can be obtained from the proposed method in general. In Table 2a, the proposed method using full ILD/IPD spectrum vectors achieves the best result and maintains a high estimation accuracy in a severe condition. Meanwhile, the result from the proposed method using ILPD features has comparably good performance in a noise-free environment, yet degrades rapidly with decreased SNR. There are two causes of this phenomenon. First, a longer feature vector increases the diversity of available feature candidates at each splitting node; hence, the independence between decision trees increases and the forest becomes more robust. Second, the RF algorithm extracts the spatial cues at high-frequency IPD spectrum (e.g., the group delay) and those cues contribute to the estimation even in a noisy environment. In Table 2b, although the elevation estimation accuracy from all methods decreases obviously with increased noise level, the proposed method can provide a precise estimation in the high SNR scenario, compared with the results from PPAM, which indicates that elevation-related feature characteristics extracted by the RF algorithm are non-linear and more sensitive to interference.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**SNR** & \multicolumn{2}{c}{**No Noise**} & \multicolumn{2}{c}{**30 dB**} & \multicolumn{2}{c}{**20 dB**} & \multicolumn{2}{c}{**10 dB**} \\ \hline
**Tolerance** & \(\leq\)**2.5\({}^{\circ}\)** & \(\leq\)**5\({}^{\circ}\)** & \(\leq\)**2.5\({}^{\circ}\)** & \(\leq\)**5\({}^{\circ}\)** & \(\leq\)**2.5\({}^{\circ}\)** & \(\leq\)**5\({}^{\circ}\)** & \(\leq\)**2.5\({}^{\circ}\)** & \(\leq\)**5\({}^{\circ}\)** \\ \hline Proposed - FULL & 99.44\% & 100.0\% & 98.88\% & 100.0\% & 97.20\% & 99.60\% & 94.40\% & 97.92\% \\ PPAM - FULL & 79.92\% & 91.12\% & 79.52\% & 90.72\% & 75.36\% & 87.6\% & 61.36\% & 73.84\% \\ Proposed - ILPD & 95.68\% & 97.12\% & 87.68\% & 90.56\% & 78.96\% & 86.00\% & 68.64\% & 79.44\% \\ PPAM - ILPD & 89.28\% & 96.96\% & 86.64\% & 95.68\% & 73.84\% & 89.44\% & 55.04\% & 73.84\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Azimuth and elevation estimation accuracy comparison in noisy environment.  
Figure 8: Comparing the localization accuracy between proposed and PPAM methods using different feature vector types. The angular error tolerance is 2.5\({}^{\circ}\).