## 2 Implementation of Active Localization: Signal Model, Processing, and Feasibility Test
### Proposed Algorithm Based on Steered Response Power with Moving Average  
In this section, the approach of an algorithm using the steered response power (SRP) is addressed. SRP is a sound source localization technique, and it is known as a robust localization technique in reverberant environments [32; 33]. \[\mathrm{P_{k}}(\theta)\equiv\int_{\mathrm{kT}}^{(k+1)T}\!\!\left|\sum_{m=1}^{ \mathrm{M}}\mathrm{w_{m}s_{m}(t-\hat{\tau}_{m}(\theta))}\right|^{2}\mathrm{dt} \tag{5}\]\[\hat{\theta}_{\rm s}=\underset{\theta}{\rm argmax}P_{\rm k}(\theta) \tag{6}\]  
where \(P_{\rm k}(\theta)\) is the power value of the classical SRP, \(\theta\) is the steered angle, \(\hat{\theta}_{\rm s}\) is the look direction, \(s_{\rm m}\) is the microphone signal, \(\hat{\tau}_{\rm m}\) is the delay of each microphone, \(W_{\rm m}\) is the weight, \(M\) is the number of microphones, \(m\) is the microphone index, \(k\) is the block index, and \(T\) is the length of some finite-length block signals. Equations (5) and (6) are the classical SRP using a microphone array, Equation (5) indicates the integrated output of the steered beamformer, and Equation (6) indicates the direction of the sound source. The proposed active localization estimates the position of a silent person as an angle and a distance in the horizontal plane of a linear microphone array (Figure 3). In other words, the proposed algorithm should represent a two-dimensional plane. In [34; 35], the generalized cross-correlation-phase transform (GCC-PHAT) was used to represent the spatial energy map. However, since the PHAT method revealed that the sound source can be determined well under low noise [36], the localization performance in the two dimensions is not robust. The proposed algorithm uses the reflection to estimate the position; thus, the signal-to-noise ratio (SNR) is not high. Therefore, the energy map is expressed by applying the delay and sum beamformer to the classical SRP and a moving average to the power of the steered block signal. Accordingly, Equations (5) and (6) are modified as Equations (7) and (9) to represent the energy map on the horizontal plane of the linear microphone array. \[P(t,\theta_{\rm d})\equiv\frac{1}{N_{\rm L}}\sum_{n_{\rm L}=0}^{N_{\rm L}-1}w_ {\rm l}\left|\sum_{m=1}^{M}r_{\rm m}^{\rm effect}(t-n_{\rm L}-\hat{\tau}_{\rm m }(\theta_{\rm d}))\right|^{2}\quad t=\ t_{\rm ref},t_{\rm ref}+1,\cdots,t_{\rm ref }+T-1 \tag{7}\]  
\[P(\hat{t}_{\rm s},\hat{\theta}_{\rm s})=\underset{t\in\theta_{\rm d}}{\rm argmax }P(t,\theta_{\rm d}) \tag{8}\]  
\[\hat{r}_{\rm s}=\frac{(\hat{t}_{\rm s}-t_{\rm ref})\times c}{2\times f_{\rm s}} \tag{9}\]  
where \(P(t,\theta_{\rm d})\) is the energy map of the SRP, \(\theta_{\rm d}\) is the set of desired angles, \(N_{\rm L}\) is the length of the moving average, \(P(\hat{t}_{\rm s},\hat{\theta}_{\rm s})\) denotes the position results, \(\hat{t}_{\rm s}\) is the index of the reflected time sample, \(\hat{t}_{\rm s}\) is the estimated distance between the maximum point and the origin, \(t_{\rm ref}\) is the index of the peak point generated signal (the origin), \(\hat{\theta}_{\rm s}\) is the estimated angle, \(c\) is the speed of sound, and \(f_{\rm s}\) is the sampling frequency. Figure 4 shows the measured signals of the A position in the experimental configuration when the boundary absorption coefficient of a room is equal to 0.625. In Equation (7), the length of the block signals (T) is set as the maximum distance that the signal can reciprocate in the target room. The estimated distance of an intruder is calculated using Equation (9) through the time information corresponding to the peak of the sound field variation. Figure 3: Example of an application of the proposed active localization method to a room. In this study, the input value of the SRP used the changed signal between the reference signal and the measured signal.