## 3 Sound Source Localization Fusion Algorithm of a Three-Plane Five-Element Microphone Array
### Influence of Time-Delay Estimation Error on Sound Source Localization Performance  
The influence of the time-delay estimation error on the localization performance of the sound source is studied. Through simulation, the relationship between the time-delay estimation error and the direction-finding precision is obtained. The time-delay estimation error \(\sigma_{\tau}\) is between 1-100 us, the array element spacing \(a\) is 1 m, and the sound velocity \(c\) is 340 m/s. The relationship between the time-delay estimation error and the elevation angle measurement precision is shown in Figure 5 for an elevation angle \(\theta\) of 15\({}^{\circ}\). Figure 4: Comparison and analysis of the horizontal angle estimation error of the sound source caused by a horizontal angle change. Figure 5: Relationship between the time-delay estimation error and elevation angle measurement precision. Figure 5 shows that as the time-delay estimation error \(\sigma_{\tau}\) increases, the elevation angle estimation error \(\sigma_{\theta}\) measured in the X0Y plane shows the greatest increase. The X0Z and Y0Z measurement errors increase minimally, and the error of three-plane array is close to that of the X0Z and Y0Z planes, with a small increase. When the time-delay estimation error \(\sigma_{\tau}\) is 100 \(\upmu\)s, the error \(\sigma_{\theta}\) is only 0.025\({}^{\circ}\). The relationship between the time-delay estimation error and the horizontal angle measurement precision is shown in Figure 6 for a horizontal angle \(\varphi\) of 45\({}^{\circ}\) and an elevation angle \(\theta\) of 15\({}^{\circ}\). Figure 6 shows that as the time-delay estimation error \(\sigma_{\tau}\) increases, the horizontal angle estimation error \(\sigma_{\varphi}\) shows the greatest increase in the X0Z plane. The error in the three-plane array is close to that of the Y0Z plane, and the error increase is large. When the time-delay estimation error \(\sigma_{\tau}\) is 100 \(\upmu\)s, the error \(\sigma_{\varphi}\) is approximately 0.036\({}^{\circ}\), and the error \(\sigma_{\varphi}\) increase in the X0Y plane is minimized. Figures  
the single-plane error is 0.8945\({}^{\circ}\); therefore, the elevation angle measurement precision is improved 1.9101-fold. The horizontal angle error measured by the fusion algorithm is 2.1921\({}^{\circ}\), while the error measured by the single-plane microphone array is 3.2518\({}^{\circ}\); thus, the horizontal angle measurement precision is increased 1.4834-fold. According to Table 3, the ranging error of the fusion algorithm is 0.0729 m, while the error measured by the single-plane microphone array is 0.1045 m; therefore, the ranging precision is improved 1.4335-fold. The elevation angle error measured by the fusion algorithm is 0.3943\({}^{\circ}\), while the single-plane error is 0.7518\({}^{\circ}\); hence, the elevation angle measurement precision is improved 1.9067-fold. The horizontal angle error measured by the fusion algorithm is 0.9974\({}^{\circ}\), while the error measured by the single-plane sound source array is 1.0625\({}^{\circ}\); therefore, the horizontal angle measurement precision is increased 1.0653-fold. According to Table 4, the ranging error of the fusion algorithm is 0.0430 m, while the error measured by the single-plane microphone array is 0.0896 m; therefore, the ranging precision is improved 2.0837-fold. The elevation angle error measured by the fusion algorithm is 0.1745\({}^{\circ}\), while the single-plane error is 0.4740\({}^{\circ}\); thus, the elevation angle measurement precision is improved 2.7163-fold. The horizontal angle error measured by the fusion algorithm is 0.6579\({}^{\circ}\), while the error measured by the single-plane microphone array is 1.4654\({}^{\circ}\); therefore, the horizontal angle measurement precision is increased 2.2274-fold.