## 3 Proposed Model and Experiment Setup
### Mathematical Calculation
The link budget parameters can be expressed by Equation (9) through to (11) [11]:  
\[RSS=P_{t}+G(h_{t})+G(h_{r})-P_{L}HD-L \tag{9}\]  
\[\mathrm{d}\ [\mathrm{km}]=2\ \mathrm{E_{r}}[\cos^{-1}(\frac{\mathrm{E_{r}}}{ \mathrm{E_{r}}+\mathrm{h_{t}}}*\cos(\theta))-\theta] \tag{2}\]0  
\[\mathrm{d}\ [\mathrm{km}]=2\ \mathrm{E_{r}}[\cos^{-1}(\frac{\mathrm{E_{r}}}{ \mathrm{E_{r}}+\mathrm{h_{t}}}*\cos(\theta))-\theta] \tag{2}\]1  
where RSS denotes the received signal strength, \(P_{t}\) denotes the transmitter power, \(G(h_{t})\) denotes the transmitter antenna height gain, \(G(h_{t})\) denotes the receiver antenna height gain, \(L\) denotes the connector and cable loss, \(N\) denotes the noise figure, \(I\) denotes the interference, \(B\) denotes the bandwidth, \(SINR\) denotes the signal-to-interference-ratio, and \(T\) denotes the throughput (b/s). The position of the drone is assumed to be at the centre of the image because the GPS module is placed above the camera. Therefore, the coverage of an image can be estimated using the camera's field of view (FOV), as shown in Figure 5, while the target's GPS coordinates can be calculated as per (12) to (19) [44]. Notably, the coverage of an image from an aerial perspective can be estimated using the camera's field of view (FOV). This makes it possible to obtain an FOV with 180 degrees of peripheral vision. This is why it is presented as a rectangular shape. \[\mathrm{d}\ [\mathrm{km}]=2\ \mathrm{E_{r}}[\cos^{-1}(\frac{\mathrm{E_{r}}}{ \mathrm{E_{r}}+\mathrm{h_{t}}}*\cos(\theta))-\theta] \tag{2}\]2  
\[\mathrm{d}\ [\mathrm{km}]=2\ \mathrm{E_{r}}[\cos^{-1}(\frac{\mathrm{E_{r}}}{ \mathrm{E_{r}}+\mathrm{h_{t}}}*\cos(\theta))-\theta] \tag{2}\]3  
\[\mathrm{d}\ [\mathrm{km}]=2\ \mathrm{E_{r}}[\cos^{-1}(\frac{\mathrm{E_{r}}}{ \mathrm{E_{r}}+\mathrm{h_{t}}}*\cos(\theta))-\theta] \tag{2}\]4  
\[\mathrm{d}\ [\mathrm{km}]=2\ \mathrm{E_{r}}[\cos^{-1}(\frac{\mathrm{E_{r}}}{ \mathrm{E_{r}}+\mathrm{h_{t}}}*\cos(\theta))-\theta] \tag{2}\]5  
where a denotes the length of the area, FOV (x) denotes the horizontal FOV of the camera, b denotes the width of the area, FOV (y) denotes the vertical FOV of the camera, scale (x) denotes the linear relationship between the x pixels and the distance, and scale (y) denotes the linear relationship between the y pixels and the distance. A target is assumed to be located on the (x, y) pixel in the photograph, and the offset of the target from the centre of the picture is as per (16):  
\[\text{offset target}=\left[ \begin{array}{c}\text{scale }(\text{x})*\text{x}\\ \text{scale }(\text{y})*\text{y}\end{array} \right](\text{m}) \tag{16}\]  
Figure 5: A drone with a bride’s eye view of the vertical coordinates of GPS positions. As the GPS location of the image frame is referenced from the centre of the image, the GPS must be corrected. In this way, missing persons on the edges of the frame can be located more accurately. The pixel values are given to the software in x and y Cartesian coordinates, then multiplied by the distance per pixel in their respective directions. The x and y directions are then rotated depending on the heading of the drone using the rotation of matrix, as per (17):  
\[ \begin{array}{c}\mathrm{R}\ \ \mathrm{c}\\ \mathrm{w}\end{array} =\left[ \begin{array}{cc}\cos(\Psi)&-\sin(\Psi)\\ \sin(\Psi)&\cos(\Psi)\end{array} \right] \tag{17}\]  
where \(\psi\) denotes the angle of the drone. Consequently, the position offset in the world frame can be solved as per (18):  
\[\mathrm{P}=\mathrm{R}\ \ \mathrm{c}\\ \mathrm{w}\end{array}\mathrm{offset}\ \mathrm{target}=\left[ \begin{array}{c} \mathrm{Px}\\ \mathrm{Py}\end{array} \right] \tag{18}\]  
where P denotes the position offset in the world frame, \(\mathrm{Px}\) denotes the latitude, and Py denotes the longitude. \[\mathrm{GPS}\ \mathrm{target}=\mathrm{GPS}\ \mathrm{cam}+\left[ \begin{array}{c} \mathrm{Px}\\ \mathrm{\frac{Py}{Ty}}\end{array}