## 2 Materials and Methods
### Data Analysis
#### 2.2.1 Data Processing
* Step 3: Estimate the position of intersection points \(\psi_{\text{{\emph{Inter}}}}\) between \(\theta_{OS}\) and \(\theta_{\text{TS}}\) using the \"navfix\" program in MATLAB 2008 (Mathworks, Natick, MA, United States). Then, let \(\hat{\psi}_{\text{OS}}\) be the position of OS at \(\psi_{\text{CSP}}\). * Step 4: Calculate the travel time \(TT_{OS}\) of the OS from \(\psi_{OS}\) to \(\hat{\psi}_{\text{OS}}\) using \(\
u_{\text{OS}}\). * Step 5: Calculate the position \(\hat{\psi}_{\text{TS}}\) of the TS at \(TT_{OS}\) using \(\theta_{\text{TS}}\). * Step 6: Calculate \(dCPA(t)\) between \(\hat{\psi}_{\text{OS}}\) and \(\hat{\psi}_{\text{TS}}\) at time \(t\). * Step 7: Iterate Steps 1 to 6 to \(t=T\) (\(T\) is simulation time) and finish. For sequence data creation, the four behavior features mentioned above were used. The performance levels of the device control \(PL_{DOB}\) and the route control \(PL_{RCB}\) were calculated as  
\[PL_{DOB}(n) = \frac{1}{T}\sum_{t=0}^{T}\Bigl{(}DOB_{Rud}(n,t)+DOB_{Eng}(n,t) \Bigr{)}, \tag{2}\] \[PL_{RCB}(n) = \frac{1}{T}\sum_{t=0}^{T}(RCB_{Dev}(n,t)+RCB_{dCPA}(n,t)), \tag{3}\]  
respectively, where \(n\) is the participant number, with \(n=1,2,3,\cdots N\) (\(N=100\)); \(t\) is the simulation time that varies for each participant; \(DCB_{Rud}\) is the detected binary value of the device control behavior for rudder use; \(DCB_{Eng}\) is the detected binary value of the device control behavior for engine usage; \(RCB_{Dev}\) is the detected binary value of the route control behavior with respect to the controlled deviation; and \(RCB_{dCPA}\) is the detected binary value of the route control behavior for the controlled dCPA. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Behavior** & **Feature** & **Rule** & **Value** & **Description** \\ \hline \multirow{4}{*}{Device Control} & \multirow{2}{*}{Rudder Use} & \(oRA(t)<RA_{ref}\) & 0 & \(oRA(t)\): Ordered rudder angle at time \(t\) \\  & & \(oRA(t)\geq RA_{ref}\) & 1 & \(RA_{ref}\): Reference angle of \(\pm 5^{\circ}\) \\ \cline{2-5}  & Engine Use & \(oEP(t)<EP_{ref}\) & 0 & \(oEP(t)\): Used engine power at time \(t\) \\  & & \(oEP(t)\geq EP_{ref}\) & 1 & \(EP_{ref}\): Reference power of 10.13 MW \\ \hline \multirow{4}{*}{Route Control} & Controlled & \(Dev(t)<Dev_{ref}\) & 0 & \(Dev(t)\): Deviation1 at time \(t\) \\  & Deviation & \(Dev(t)\geq Dev_{ref}\) & 1 & \(Dev_{ref}\): Reference distance of 361.6 m \\ \cline{1-1} \cline{2-5}  & Controlled dCPA & \(dCPA(t)<dCPA_{ref}\) & 0 & \(dCPA(t)\): dCPA2 at time \(t\) \\ \cline{1-1}  & dCPA(t) \(\geq dCPA_{ref}\) & 1 & \(dCPA_{ref}\): Reference distance of 361.6 m \\ \hline \hline \end{tabular}  
* Calculated deviation using Equation (1); 2 Calculated distance of the closest point of approaches (dCPA) using Equation (2).  
\end{table} 
Table 6: Rules for the detection of four maneuvering behavior features. In the above Equations (2) and (3), all four variables were applied during the simulation time \(t\). However, interactions between the four variables and the maximum value of simulation time \(t\) are raised as issues, and will be discussed in Section 4. The performance level calculated by Equations (2) or (3) has a value between 0 and 1. A value of 1 means that the navigator's device control and route control techniques are at a higher level compared to zero. Using the calculated performance levels for 100 participants, behavior sequences with symbols \(v=\{\text{Poor, Average, Excellent}\}\) were created, using the rules of symbolic performance levels in Table 7. Then, the sequence data were constructed by allocating the success \(O_{Success}\) and the failure \(O_{Fail}\) of collision avoidance into the following \(2\times N\) (\(N\) is the sequence length) matrices:  
\[O_{Success}=\left[ \begin{array}{c}O_{DCB|Success}\\ O_{RCB|Success}\end{array} \right]\text{and }O_{Fail}=\left[ \begin{array}{c}O_{DCB|Fail}\\ O_{RCB|Fail}\end{array}