## 2 Review of Low Frequency Ultrasonic Communication-based Audio Markers
### LFU-Based Object Detection  
Figure 4 shows a block diagram of the LFU-based object detection method using LFU images. A speaker periodically produces a low frequency pulsed ultrasound from 18 to 20 kHz. In this paper, a linear frequency modulated (LFM) chirp is utilized [21], where the chirp length and repetition time are set to 512 and 4096 samples at a sampling rate of 48 kHz, respectively. While periodically reproducing the low frequency pulsed ultrasound, a microphone simultaneously captures the chirps and ambient sound, which are then filtered with a matched filter to clarify the pulsed LFU. Next, the filtered signal is segmented into consecutive frames of 4096 samples. Then, a Hanning window of a length of 256 samples, with a 50% overlap, is applied to each frame, which produces 31 sub-frames for a frame. Finally, a 256-point short-time Fourier transform (STFT) is applied to each sub-frame to obtain a spectrogram image.  
Let \(I(\mathbf{p},n)\) be a spectrogram image at a pixel \(\mathbf{p}\) and a sub-frame \(n\). Each input spectrogram image is subtracted by the background image, so that:  
\[\hat{F}^{2}(\mathbf{p},n)=I^{2}(\mathbf{p},n)-\hat{B}^{2}(\mathbf{p}),\;n=1,2,\cdots,31 \tag{8}\]  
where \(\hat{B}(\mathbf{p})\) is the initial background image estimated by assuming that there is no object within the initial \(N(=31)\) sub-frames [22], so that:  
\[\hat{B}(\mathbf{p})=\frac{1}{N}\sum_{n=0}^{N-1}I(\mathbf{p},n) \tag{9}\]  
Next, Equation (8) can be written in the product form of:  
\[\hat{F}^{2}(\mathbf{p},n)=H^{2}(\mathbf{p},n)I^{2}(\mathbf{p},n) \tag{10}\]  
where \(H(\mathbf{p},n)\) is a suppression function [23], defined as:  
Figure 4: Block diagram of the LFU-based object detection method in the proposed system.  
Figure 3: Procedure of the proposed user-aware audio marker system using the LFU-based object detection and communication.  
\[H(\mathbf{p},n)=\sqrt{1-\frac{\hat{B}^{2}(\mathbf{p})}{I^{2}(\mathbf{p},n)}}=\sqrt{\frac{\gamma( \mathbf{p},n)-1}{\gamma(\mathbf{p},n)}} \tag{11}\]  
Note here that \(0\leq H(\mathbf{p},n)\leq 1\)[23], and \(\gamma(\mathbf{p},n)=I^{2}(\mathbf{p},n)/\hat{B}^{2}(\mathbf{p})\) is the _a posteriori_ SNR.  
When an object is absent (hypothesis \(H_{0}\)), spectrogram images include only the background, i.e., \(H_{0}:I(\mathbf{p},n)=B(\mathbf{p})\); on the other hand, when an object is present (hypothesis \(H_{1}\)), spectrogram images include the foreground and background, i.e., \(H_{1}:I(\mathbf{p},n)=F(\mathbf{p},n)+B(\mathbf{p})\). The likelihood ratio for a pixel point \(\mathbf{p}\) and \(n\)-th sub-frame can be expressed as [23]:  
\[\Lambda(\mathbf{p},n)=\frac{1}{1+\xi(\mathbf{p},n)}\exp\left(\frac{\gamma(\mathbf{p},n)\xi (\mathbf{p},n)}{1+\xi(\mathbf{p},n)}\right) \tag{12}\]  
where \(\xi(\mathbf{p},n)=\hat{F}^{2}(\mathbf{p},n)/\hat{B}^{2}(\mathbf{p})\) is the _a priori_ SNR. The decision rule is established from the log likelihood ratio [23], so that:  
\[\log\Lambda(n)=\sum_{\mathbf{p}\subset\mathbf{B}}\log\Lambda(\mathbf{p},n)\begin{array}{c} \overset{H_{1}}{>}\\ \overset{<}{H_{0}}\end{array}\eta \tag{13}\]  
where \(\mathbf{B}\) implies the area in which a low frequency ultrasound can be reached. In particular, when an object is detected, \(\log\Lambda(n)\) is also used to scale the LFU transmission signal, which will be explained in the next subsection. Otherwise, the background images are updated as:  
\[\hat{B}(\mathbf{p})=\alpha\hat{B}(\mathbf{p})+(1-\alpha)I(\mathbf{p},n) \tag{14}\]  
where \(\alpha\) is set to 0.7 through exhaustive experiments.