## 2 Implementation of Active Localization: Signal Model, Processing, and Feasibility Test
### Proposed Algorithm Based on Steered Response Power with Moving Average
In other words, the impulse response in Equation (3) was not directly predicted, but the sound field variation in the same reproduction signal was estimated by subtracting the reference signal from the measured microphone signal. We used a triangular moving average of 36 samples in the 48 kHz sampling rate, and the estimated distance was calculated as the product of time and sound speed. This averaging method empirically reduced the error variance of the estimated angle and distance in the proposed active localization. Figure 5 shows the block diagram used to implement the proposed method using the sound field variation and the SRP with a moving average. Figure 5a shows the steps to synchronize the measured signals. Figure 5b shows that the measured signals are stored as the reference signals if no event is detected, as depicted in Figure 5c, and Figure 5d indicates the proposed SRP to estimate the position of a silent person. In the signal synchronization step in Figure 5a, we set up the block diagram to minimize the time delay between the reference signal and event signal for each microphone. Thus, two steps were involved. The first was to reduce the quantization error by setting the clocks of the loudspeaker and microphone board identically in hardware. The second step, after measurement, was to verify and compensate for the time delay between tref of Equation (7) and the peak of the generated signal based on correlation. The event detection in Figure 5c was used to determine intrusion by selecting the threshold of sound field variation in [17]. In this study, we focused on the analysis of the SRP  
Figure 4: Example of measured signals: (**a**) Reference signals before intrusion; (**b**) event signals after intrusion; (**c**) sound field variation. Figure 5: Block diagram of the proposed active localization method: (**a**) Step to synchronize the measure signals; (**b**) Step for reference signals defined as measured signals if no event is detected; (**c**) Step for event detection; (**d**) Step for SRP using Equations (7)–(9). results in Figure 5d. In other words, we aimed to analyze the relationship between the variables (reverberation time and early decay time) in the control space and the signal processing results. The signal generated by the loudspeaker formed a sound field with a specific frequency band in a security area using the Gaussian-modulated sinusoidal pulse of Equation (10), and then the change to the sound field was measured using the microphone array. \[\mathrm{x(t)}=\mathrm{A}\mathrm{e}^{-\kappa\left(\mathrm{t-d}\right)^{2}} \cos(2\pi\mathrm{f}_{\mathrm{center}}(\mathrm{t-d})) \tag{10}\]  
where A is the magnitude of the signal, \(\kappa=\)5\(\pi^{2}\)b\({}^{2}\)f\({}_{\mathrm{center}}^{2}/\left(\mathrm{q}\cdot\ln(10)\right)\) is the envelope constant, b is the normalized bandwidth, q is the attenuation of the signal, f\({}_{\mathrm{center}}\) is the center frequency, and d is the time delay. In this study, the center frequency was fixed at 1 kHz, and the attenuation and normalized bandwidth of the sound source were set to 6 and 0.25, respectively. The center frequency was 1 kHz because the directivity pattern of the loudspeaker used in the experiment was cardioid at 1 kHz. When analyzing a short-period pure-tone signal as a frequency component, a discrete-time Fourier transform was used, and at least five periods were required to estimate the frequency components. Therefore, the attenuation and normalized bandwidth were selected to form five periods in the pulse sound (Figure 6).