# Modeling Human Encounter Situation Awareness Results Using Support Vector Machine Models
## 2 Materials and Methods
### Risk of Collision
#### 2.2.1 Collision Risk Index  
In this study, an index was used to calculate the risk of collision. Several indicators have been reported for calculating the risk of collision, but we used the index reported in the study of [PERSON] et al. (7). It is because collision risk indexes reported in other studies define head-on and crossing using different values, and weights are applied accordingly. Therefore, it was judged inappropriate for our study. The parameters required for calculating indexes applied in our study are DCPA, TCPA, distance (\(d\)), relative bearing (\(\psi_{r}\)), and speed ratio (\(K\)). The variables of the two ships, OS and TS, are described to define the parameters encountered in the collision situation. The two ships in Figure 2 are assumed to move on the Earth-fixed coordinate system. Here, the coordinates of the OS are \(P_{o}(x_{o},y_{o})\), the velocity is \(V_{o}\), the course is \(\psi_{o}\), the coordinates of the TS are \(P_{t}(x_{t},y_{t})\), the velocity is \(V_{t}\), and the course is \(\psi_{t}\). Moreover, Az is the azimuth of the OS and TS. When the OS navigates in its course \(\psi_{o}\), its relative velocity components are on the X axis, Y axis (\(\Delta X,\Delta Y\)), respectively, and its relationship with the TS is calculated as follows (24). \[ \begin{array}{l}\Delta X=V_{t}sin\psi_{t}-V_{o}sin\psi_{o}\\ \Delta Y=V_{t}cos\psi_{t}-V_{o}cos\psi_{o}\end{array}  \tag{1}\]  
\[ \begin{array}{l}V_{r}=\sqrt{\Delta X^{2}+\Delta Y^{2}}\end{array}  \tag{2}\]  
\[\psi_{r}=\arctan\frac{\Delta X}{\Delta Y} \tag{3}\]  
Here, \(V_{r}\) means relative speed, and \(\psi_{r}\) means relative direction. When knowing the three parameters (OS's coordinates converted into radians (\(\varphi_{o}\), \(\lambda_{o}\)), distance to the TS (\(d\)), and bearing to the TS (\(Az\))), the coordinates of the TS (\(\varphi_{t}\), \(\lambda_{t}\)) were obtained using rhumb line calculation (25; 26). The latitude of the TS converted into \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Relative** & **Heading (OS)** & **Heading (TS)** & **Encounter** & **Range of** \\  & **Bearing** & & & **Angle** & **Head-on (\({}^{\circ}\))** \\ \hline (16) & ✓ & ✓ & ✓ & & 337.5–022.5 \\ (17) & ✓ & ✓ & ✓ & ✓ & 348.75–011.25 \\ (19) & ✓ & ✓ & ✓ & & 345–015 \\ (20) & ✓ & ✓ & ✓ & ✓ & 355–005 \\ (18) & ✓ & ✓ & ✓ & ✓ & 348.75–011.25 \\ \hline \hline \end{tabular} where the Range of Head-on refers to the area value determined as a Head-on situation if TS exists in the range based on the relative bearing of the OS.  
\end{table} 
Table 1: Variables and parameters used in the classification of encounter situations. radians (\(\varphi_{t}\)) is described in Equation (5), where the angular distance (\(\phi\)) is calculated from Equation (4). \[\phi=d/R \tag{4}\]  
\[\varphi_{t}=\varphi_{o}+\phi\cdot\cos Az \tag{5}\]  
The longitude of the TS converted into radians (\(\lambda_{t}\)) is obtained by adding the longitudinal difference between the OS and the TS (\(\Delta\lambda\)). The calculation of \(\Delta\lambda\) uses the projected latitude difference described in Equations (6) and (7). The constant \(\delta\) is derived using the inverse Gudermannian function, which provides the height of the Mercator projection of a given latitude. \[\delta=ln(tan(\pi/4\,+\,\varphi_{t}/2)/tan(\pi/4\,+\,\varphi_{o}/2)) \tag{6}\]  
As for the projected latitude difference (\(q\)), different values were used when there was a latitude difference and when there was no latitude difference using the constant \(\delta\). For the computations, \(10e^{-12}\) was used as a number close to zero. \[\varphi_{t}=\varphi_{o}+\phi\cdot\cos Az \tag{7}\]  
\[\Delta\lambda=\phi\cdot\sin Az/q \tag{8}\]  
The longitude of the TS converted into radians (\(\lambda_{t}\)) is derived by adding a longitudinal difference to the \(\lambda_{o}\). \[\lambda_{t}=\lambda_{o}+\Delta\lambda \tag{9}\]  
where \(R\) is the radius of the Earth (3440 nautical miles).