## 3 Risk Identification during Navigation
### Ship's Position Dead Reckoning  
When the ship enters the next segment of the traffic lane in TSS waters, the general direction of traffic flow changes and the ship will continue to sail in the general direction of traffic flow in the following segment. Ships often travel at sea speed in the Chengshantou TSS due to the broader navigable waters and fewer obstacles. Sea speed denotes that the revolution speed of the main engine is constant and cannot be changed in a short time. As a result, this paper assumes that the weather is fine, and the ship is sailing at sea speed. Dead reckoning of the OS's and TS's positions is carried out based on the OS's and TS' present information. Rapid data updates and cyclic calculations are used to correct ship position dead reckoning errors and achieve a self-adaptive judgment. The course-altering process when performing ship position dead reckoning is, therefore, ignored. When the TS's course is nearly identical to the recommended traffic flow direction of the traffic lane to which it belongs, the TS's position is determined using the traffic flow direction and the TS's speed. The specific implementation method is as follows. 1. Determine the ship's position in the channel. For any convex quadrilateral segment abcd, if the sum of the triangle areas \(\text{S}_{1},\text{S}_{2},\text{S}_{3},\text{S}_{4}\) formed by the line connecting the ship's center of gravity to the four vertices of the convex quadrilateral abcd is equal to the area \((\mathrm{S_{abcd}})\) of the quadrilateral abcd, the ship can be judged to be within the convex quadrilateral segment. The illustration is as per Figure 4.  
Check whether the ship is sailing in the general direction of traffic flow. If the difference between the course and the recommended traffic flow direction of a segment is less than \(10^{\circ}\), it is assumed that the ship is sailing along the channel, as shown in Equation (10). If the course difference is greater than \(10^{\circ}\), it is assumed that the ship is not sailing along the general direction of traffic flow, as shown in Equation (11). \[\left(X_{t}^{j},Y_{t}^{j}\right)\in O_{s}\boldsymbol{\xi}|TC_{j}-\varphi_{s}| <10^{\circ} \tag{10}\]  
\[\{(X_{t}^{j},Y_{t}^{j})\
otin\sum_{s=1}^{16}O_{s}\}||\{(X_{t}^{j},Y_{t}^{j}) \in O_{s}\boldsymbol{\xi}|TC_{j}-\varphi_{s}|\geq 10^{\circ}\} \tag{11}\]  
where \(\varphi_{s}\) indicates the recommended traffic flow direction for the segment where the ship is positioned, \(\varphi_{s+1}\) represents the recommended traffic flow direction for the next segment, \(\left(X_{t}^{j},Y_{t}^{j}\right)\) is the coordinate of the \(j\)-th TS at the moment \(t\), \(TC_{j}\) is the course of the \(j\)-th TS, and \(TC_{o}\) is the course of the OS. The method for dead reckoning the ship's position in different situations  
Based on the judgment conclusions in steps 1 and 2, the ship's current speed, course, and position, the ship's positions after a period of time can be calculated. The ship's position when the OS and TSs proceed in the appropriate traffic lane in the general direction of traffic flow for that lane is dead reckoning through Equation (12). The positions of OS or TSs, which are in the traffic lane but not along the general direction of traffic flow, can be dead reckoned by Equations (13) and (14), respectively. The ship's position when the ship is not in the TSS traffic lane is dead reckoned through Equation (14). \[\left\{ \begin{array}{l}\left\{X_{t}^{j}=X_{o}^{j}+v_{j}*t*\sin\left(TC_{j} \right),\;t\in[0,T]\\ Y_{t}^{j}=Y_{o}^{k}+v_{j}*t*\cos\left(TC_{j}\right),\;t\in[0,T]\\ \left\{X_{t}^{j}=x_{T}+v_{j}*(t-T)*\sin\left(\varphi_{s+1}\right),t\in[T,1800] \\ Y_{t}^{j}=y_{T}+v_{j}*(t-T)*\cos\left(\varphi_{s+1}\right),t\in[T,1800]\end{array} \right.\right. \tag{12}\]  
\[\left\{