# Acoustic Localization for a Moving Source Based on Cross Array Azimuth
## 4 Experiments
### Experiment Results  
Additional environmental noise cannot be avoided either. This superposed additional noise will negatively affect the correlation of the signals. Therefore, preprocessing of the measured signals is required before obtaining the correlations. Since there were no other obvious sound sources and since the superposed additional noise is of high frequency, the wavelet-filtering method was chosen to remove unwanted noise, whereby the wavelet basis was \"db10\"(No. 10 of Daubechies Series Basis [27]). As the signal was relatively simple, it was decomposed into three layers. Then, the lower part in frequency was taken to perform short-time correlation. The signal-filtering process of one channel is shown in Figure 10.  
Figure 10: Filter process of signal. Figure 9: Path of motion of the sound source. Reference to Figure 10 reveals the noise contained in the test signal. There were two kinds of noise. One is the high-frequency noise for which the amplitude is about 1/20 of test signal. The other is the impulse with about 1/3 of the amplitude. Both of these noise contributions detrimentally affect the correlations of the array signal. Hence, the signal form without noise, as shown in the lower left part of Figure 9, was used to operate correlations. During the path A\(\rightarrow\)B, traveling distance was S = 57.6 m, with associated travel time t = 45.6 s and sampling length N = 228,800. Distance S was divided into 11 elements, while travel time was the same. The localization of the moving source was achieved by locating the central point of the 11 elements. The results obtained are shown in Table 1.  
In Figure 11, it's obvious that basic frequency was 600 Hz with some doubling frequency component. From Section 3.2, it is known that the period of noise \(T\) was \(1/f=1666\)\(\upmu\)s. Maximum traveling time of a single wave between array sensors is \(2\)\(D/c\approx 11.66\) ms. The length of signal extracted for one correlation must be bigger than 11.66 ms. As the sampling interval was 200 \(\upmu\)s, the minimum length of signal extraction was 58. The localization was carried out at the first central point to study the choosing principle of extraction length that participated in one short-time correlation. Based on the signals of Sensor 1 and Sensor 2 in Array 1, the first central was set at point 20,727, and the length of extraction was assigned as 30, 60, 65, 70, 100, 200, and 300. After extraction of the signal and 100 times of interpolations, the correlations of different length were calculated, as shown in Figure 12a. The sampling interval decreased to 2 \(\upmu\)s after 100 times of interpolation. Maximum value is located at N = 3233, while the central point of correlation was N = 3000 when extraction \(n=30\). Then, time delay is \(\tau_{n=30}=(3223-3000)\times 2=446\)\(\upmu\)s and delays of other lengths can be calculated in the same way, as shown in Figure 12b. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Coordinates/m** & **Time/s** & **Central Point** \\ \hline
1 & \((-23.56,\,97.92)\) & 4.15 & 20,727 \\
2 & \((-18.33,\,97.92)\) & 8.30 & 41,454 \\
3 & \((-13.09,\,97.92)\) & 12.45 & 62,181 \\
4 & \((-7.85,\,97.92)\) & 16.60 & 82,908 \\
5 & \((-2.62,\,97.92)\) & 20.75 & 103,635 \\
6 & \((2.62,\,97.92)\) & 24.90 & 124,362 \\
7 & \((7.85,\,97.92)\) & 29.05 & 145,089 \\
8 & \((13.09,\,97.92)\) & 33.20 & 165,816 \\
9 & \((18.33,\,97.92)\) & 37.35 & 186,543 \\
10 & \((23.56,\,97.92)\) & 41.50 & 207,270 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Point information of path A\(\rightarrow\)B.  
Figure 11: Frequency spectrum of the signal. Figure 12 illustrated that it is not possible to obtain correct time delays as time delay varies randomly when \(n\leq 60\). When \(n\geq 65\), delay value only varies marginally and remains steady at a level of about 520 \(\upmu\)s, which represents the correct value of time delay. The locating results of different signal lengths are shown in Table 2.