## 2 Implementation of Active Localization: Signal Model, Processing, and Feasibility Test  
### Signal Model and Definition of Sound Field Variation  
The implementation of active localization to estimate the position of a silent intruder requires a reflected sound generated by a silent intruder. We define the sound field variation as the difference between the sound field before intrusion and the sound field after intrusion. Therefore, the proposed active localization based on the sound field variation can be tested using two steps. The first step is to measure the sound field in a targeted security space using an active approach with a loudspeaker and a microphone array. The second step is to obtain the position of the silent intruder by acquiring the signals of the sound field variation based on a comparison between the signal of the sound field before intrusion (the reference sound field) and after intrusion (the event sound field). Figure 2 shows the scheme of sound field variation and, as an example, shows some of the reflections. Because the proposed active localization method uses the time signals from a direct sound to the early reflections and we assume that the silent intruder affects the specific reflection locally, we define the decomposition of room impulse responses as in Equations (1) and (2). Equations (1) and (2) represent the decomposition of the room impulse response (RIR) of the reference and intruder scenarios in the time domain, respectively. \[\mathrm{h_{ref}}=\mathrm{h_{s}}+\mathrm{h_{r1}}+\cdots+\mathrm{h_{rn}}+ \mathrm{h_{ reverberation}} \tag{1}\]  
Figure 2: Scheme of sound field variation between (**a**) a reference scenario and (**b**) an event scenario: (**a**) Early reflection of room impulse response in a reference scenario without an intruder; (**b**) early reflection of room impulse response in an event scenario with an intruder. \[\mathrm{h_{event}}=\mathrm{h_{s}}+\alpha_{1}\mathrm{h_{r1}}+\cdots+\alpha_{n} \mathrm{h_{rn}}+\mathrm{h_{person}}+\mathrm{h_{reverberation}} \tag{2}\]  
where \(\mathrm{h_{ref}}\) is the RIR of a reference scenario, \(\mathrm{h_{event}}\) is the RIR of an event scenario, \(\mathrm{h_{rn}}\) represents the early reflections of each scenario, \(\mathrm{h_{person}}\) is the new response generated by a person, \(\mathrm{h_{reverberation}}\) is the late reverberation of the room impulse response, and \(\alpha_{n}\) represents the attenuation coefficients. Methods to estimate the room shape or locate a sound source by analyzing the echo components of the RIR have been proposed [28; 29; 30]. However, because these methods are performed assuming that the RIR is known, the problem of measuring RIR every time an intruder moves in a scenario exists, and they have the disadvantage of being slow systems. Therefore, in this study, the signal modeling was represented by the viewpoint of the echo decomposition of the RIR, but the signal generated by the loudspeaker was determined using the Gaussian-modulated sinusoidal pulse in Equation (10) to analyze the changed sound field before and after the intrusion, and the extraction of the changed echo component was performed using Equation (3). If the silent intruder affects the reflection \(\mathrm{h_{rn}}\) of the RIR locally, the sum of early reflections in an event scenario is approximate to the sum of early reflections in a reference scenario, i.e., \(\alpha_{1}\approx\alpha_{2}\approx\cdots\approx\alpha_{n}\approx 1\). Therefore, Equation (2) can be rewritten as Equation (3). \[\mathrm{h_{event}}=\mathrm{h_{ref}}+\mathrm{h_{person}}+\mathrm{error} \tag{3}\]  
The sound field variation can be calculated using Equation (4).