## 3 Sound Field Simulation and Its Analysis Using Acoustic Parameters
### Simulation Test for the Reverberant Environment
#### 3.1.2 Simulation Results and Analysis  
Figure 9 shows the result images of the active localization method by changing the absorption coefficient of the boundary at position B. The images on the left in Figure 9 show the captured images in the FDTD simulation obtained by reproducing the PCS model. The images on the right indicate the energy maps expressed by the convolution signal of Equation (10) and the impulse response obtained by the FDTD simulation, respectively. In Figure 9, the reflections propagating from the intruder to the microphone array according to each alpha are similar. The image results show that the magnitude of the wavefront formed by the edge boundary increases as the absorption coefficient of the edge boundary decreases. As a result, the overlap of the reflection formed behind the intruder also increases. In other words, as the reflected sound formed at the boundary becomes significantly louder than the reflected sound produced by the intruder, the spatial effect increases such that the overlapped signal is larger than the intruder's signal. Therefore, the simulation indicated that the error of position estimation increases with the boundary characteristics of the control space. The simulation results are summarized in Table 1, in which the errors in parentheses represent the angular and distance errors. Figure 9: Simulation results of the active localization method according to the change in absorption coefficient \(\alpha\): (**a**) \(\alpha\) = 0.9; (**b**) \(\alpha\) = 0.7; (**c**) \(\alpha\) = 0.5; (**d**) \(\alpha\) = 0.3. The square marker is the actual position and the cross marker is the estimated position. As Table 1 shows, the distance error was affected more by the reflectance of the boundary than by the angular error. There was a 5\({}^{\circ}\) error only at the angle at which the sound absorption was below 40% (\(\alpha\times 100\%\)) at the D position. From a distance error point of view, some scenarios failed to detect an intruder. In other words, when the diameter (0.3 m) of the circle considered as the intruder and the predicted distance were combined, the estimated distance exceeded the control space of 2 m \(\times\) 3 m. The results of \(\alpha\) being less than 0.6 at position A and less than 0.5 at position D were the result of detection failure. In addition, when the distance error was viewed in terms of error magnitude, a large error of 0.5 m or more, at \(\alpha<0.5\) at position B was observed. Therefore, we confirmed through the simulation that the approach proposed in this paper operates at \(\alpha\geq 0.7\), for which no angular error exists and the distance error is less than 19%. In the next section, we describe the relational equation that predicts the environment in which the active localization method operates through the RT20 and EDT of the acoustic parameters. This is because verifying the operation of the proposed method based on the boundary reflectance in a general reverberant environment is very difficult. Relationship Analysis of Acoustic Parameters and Absorption Coefficients to Propose Operating Conditions  
In this section, the conditions under which the active localization method operates in a reverberant space are explained using the relationship between the acoustic parameters and the absorption coefficient discussed in the previous section. The proposed approach predicts the position of a silent intruder based on the sound reflected from the intruder, and this phenomenon occurs within a short time; therefore, the pattern of early reflection is very important. If the maximum distance of the active localization system is estimated to be 3 m, the sound source generated by a loudspeaker moves for approximately 17.54 ms when the round-trip distance of the sound source is 6 m and the speed of sound is 342 m/s. In other words, the phenomenon occurring within 18 ms should be analyzed. Therefore, the EDT and RT20 of the acoustic parameters were used to analyze the control space.