# A Planer Moving Microphone Array for Sound Source Localization
## 4 Conclusions  
When applying SSL algorithms with huge computation complexity, the size of the applied microphone array can increase, severely affecting the robot/structure's ability to acquire high-quality audio. Focusing on data collection, in this paper, we proposed a four-planar moving microphone structure to achieve our aim of creating a space-saving SSL system. This kind of active planar microphone array structure can consider the total amount of data, microphone size, and 3D SSL ability simultaneously. By comparing the proposed FPMMS with a linear rotating 1 \(\times\) 4 microphone array, a circular rotating 6-microphone array, and a 16-microphone array, we found that the proposed structure displays good performance in angular estimation and planar distance estimation, and benefits can be yielded from its ability to form special patterns, The proposed FPMMS also performs well in vertical height estimation. Generally, the FPMMS could achieve about 80-90% of the SSL estimation accuracy of the 16-microphone array. For practical usage, the sound source moving speed and service robot moving speed should both be considered because of the Doppler effect, TDOA estimation error, and the signal correlation problem. In this study, we gave a theory derivation as a reference based on the scenario described above. First, the Doppler effect would not be severe since relative speed and speech frequencies are low. Second, in our experiments, the aperture of the FPMMS was around 0.21 m, the microphone moving time duration was 0.5 s, and the distance between the sound source and the FPMMS was 1.5 m or 2 m. The relative speed causing a TDOA change is  
\[\tau_{max}=\frac{0.21\;\text{m}}{343\;\text{m}/\text{s}}\approx 0.00061\;\text{s} \tag{20}\]  
\[\Delta d=0.5\;\text{s}\times v \tag{21}\]  
\[\Delta\tau=\frac{\Delta d\times cos\theta}{c} \tag{22}\]  
\(\tau_{max}\) is the maximum TDOA change that can be tolerated by the FPMMS design parameters. \(\Delta\tau\) is the change in TDOA. \(\theta\) is the angle between the sound source and microphone array. \(\Delta d\) is the sound source moving distance, and \(v\) is moving speed. \(c\) is the sound speed. Suppose an extreme situation, wherein \(\theta\) is zero degrees; then, the maximum speed of the sound source is around 0.05 m/s for a sound source frequency of 500 hz. Even if the parameters are not so extreme, for example, 45 degrees, the maximum speed of the sound source can be 0.07 m/s. The robot speed limitation is the same. This result indicates that time duration severely limits the relative speed between the sound source and the robot. If considering a movement-based scenario, researchers need to use better motors to reduce the moving time duration. For instance, with better  
Figure 38: Azimuth, distance, and height average estimation error percentage, alongside values for active microphone array operation space. motor control, a moving duration of 0.1 s, and a sound source in the range of 30-60 degrees relative to the structure, the relative speed can be 0.53 m/s. The correlation problem caused by relative speed can be similarly analyzed. The phase change caused by the sound source movement should be less than \(\pi/2\):  
\[\frac{2\pi f\times\Delta d}{c}<\frac{\pi}{2} \tag{23}\]  
\(f\) is the signal frequency. Consider the speech signal frequency range, 200 hz-2 khz. The relative sound moving speed limitation can be 0.343-3.43 m/s, for reference. Finally, the FPMMS is a framework proposed to achieve an optimal balance between data collection amount and microphone array size. Researchers, through using smaller motors, better MEMS microphones, and stronger PCBs, could build a more practical FPMMS for use in service robots. Conceptualization, C.W. ; methodology, C.W. and Y.C. ; validation, C.W., K.C. and Y.C. ; formal analysis, C.W., K.C. and Y.C. ; investigation, C.W. ; writing--original draft preparation, C.W. ; writing--review and editing, K.C. and Y.C. ; visualization, C.W. ; supervision, K.C. and Y.C.