## 4 Experiments
### Discussion  
One finding is that the cWMM-based localization algorithm performs generally better than the SRP-PHAT algorithm. By looking closely, there are the following differences between the two methods.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Noise Type**} & \multicolumn{3}{c}{**N0**} & \multicolumn{3}{c}{**N1**} \\ \hline  & **SIR** & \(\mathbf{-5}\) & \(\mathbf{0}\) & \(\mathbf{5}\) & \(\mathbf{-5}\) & \(\mathbf{0}\) & \(\mathbf{5}\) \\ \hline \multirow{4}{*}{160 ms} & SRP-PHAT & 62.49 & 34.38 & 13.14 & 54.82 & 36.32 & 12.86 \\  & cWMM & 55.42 & 32.14 & 16.54 & 49.46 & 39.92 & 17.65 \\  & cWMM-TF & **28.26** & 12.62 & **5.71** & 30.23 & **13.16** & **5.17** \\  & cWMM-ORC & 1.82 & 1.69 & 1.71 & 1.55 & 1.92 & 1.55 \\ \hline \multirow{4}{*}{360 ms} & SRP-PHAT & 58.43 & 28.98 & 18.26 & 51.80 & 31.41 & 17.53 \\  & cWMM & 53.26 & 29.55 & 23.38 & 47.47 & 32.62 & 19.71 \\  & cWMM-TF & 28.99 & 19.71 & 7.40 & **24.67** & 14.56 & 8.70 \\  & cWMM-ORC & 2.54 & 1.53 & 1.59 & 1.70 & 1.75 & 1.85 \\ \hline \multirow{4}{*}{610 ms} & SRP-PHAT & 50.92 & 37.30 & 15.28 & 58.21 & 36.51 & 13.65 \\  & cWMM & 45.59 & 37.82 & 15.57 & 52.91 & 37.79 & 17.87 \\ \cline{1-1}  & cWMM-TF & 31.73 & **11.97** & 7.85 & 33.56 & 15.71 & 8.19 \\ \cline{1-1}  & cWMM-ORC & 2.97 & 1.87 & 1.61 & 1.87 & 2.06 & 2.07 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The MAE (\({}^{\circ}\)) of the algorithms in different test environments with competing speakers. The bold numbers indicate the best results excluding cWMM-ORC for each SIR.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Noise Type**} & \multicolumn{3}{c}{**N0**} & \multicolumn{3}{c}{**N1**} & \multicolumn{3}{c}{**N2**} \\ \hline  & **SNR** & \(\mathbf{0}\) & \(\mathbf{5}\) & \(\mathbf{10}\) & \(\mathbf{0}\) & \(\mathbf{5}\) & \(\mathbf{10}\) & \(\mathbf{0}\) & \(\mathbf{5}\) & \(\mathbf{10}\) \\ \hline \multirow{4}{*}{360 ms} & SRP-PHAT & 3.94 & 3.92 & 3.22 & 16.01 & 7.65 & 6.28 & 59.53 & 46.04 & 23.22 \\  & cWMM & 2.70 & 1.84 & 1.30 & 28.08 & 10.28 & 5.55 & 53.41 & 38.65 & 24.03 \\  & cWMM-TF & 2.18 & 1.97 & 1.52 & 10.22 & 6.01 & 3.95 & 23.81 & 12.97 & 10.12 \\  & cWMM-ORC & 1.94 & 1.92 & 1.50 & 5.32 & 2.83 & 2.51 & 2.09 & 2.02 & 1.66 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The MAE (\({}^{\circ}\)) of the algorithms in different test environments with competing noises.  
Rewriting the distance function in Equation (4), \(|\mathbf{a}^{H}\mathbf{z}|^{2}=\mathbf{a}^{H}\mathbf{z}\mathbf{z}^{H}\mathbf{a}= \frac{1}{||\mathbf{y}||^{2}}\mathbf{a}^{H}\mathbf{y}\mathbf{y}^{H}\mathbf{a}\), we see that the cWMM-based algorithm also utilizes the cross-channel correlation, but with a global normalization term rather than separately normalizing the correlation coefficients as in SRP-PHAT. The global normalization keeps the original cross-channel level difference, while the separate normalization does not. The cWMM-based localization algorithm applies a concentration parameter for weighting different frequency contributions and properly normalizes its value. The SRP-PHAT algorithm generally treats different frequencies equally.  
The other finding is that the time-frequency selection plays an essential part in the localization performance. Localizing a target speaker in a multi-speaker environment would not be successful without additional post-processing using methods such as speaker identification [4] or visual information [5]. The proposed method provides a different solution by first performing separation relying on a reference utterance from the speaker and infers the target location using the established non-discriminative localization methods. The idea of time-frequency weighting has proved its effectiveness for general source localization [17], and it is further validated here. The task of target speaker localization could benefit from this thanks to the recent advances made in monaural speech separation with deep learning techniques [20].