## 2 Research Content and Methodology
### Methodology
#### 2.2.2 Complex Area Survey Line Optimization Model
To meet the actual measurement needs, we need to consider both the determination of the navigation direction and the overlap rate. According to Model 1, we are starting the survey lines from the edge of the maritime area and arranging them to increase seabed elevation results in the maximum coverage width \(W\). The next step is to consider the optimal overlap rate between each survey line to maximize measurement efficiency, determining the minimum number of survey lines the MBES system needs to survey the area fully. Given that the overlap rate \(\eta\) is defined under the assumption of flat seabed topography, when the seabed slope is finely segmented, a small section of the slope can be approximated as a flat surface, thus maintaining the definition of \(\eta=1-d/W\). We adopt the straight-line approximation concept [24] for each coverage width segment \(W\), where the overall optimal solution is composed of local optimal solutions. We first determine the starting position of the survey ship. As shown in Figure 9, based on Model 1, a vertex \(H_{1}\) of the curved marine area is selected as the starting coordinate because, at this point, the water is deeper, and both the coverage width and the overlap rate are greater. Next, we calculate the data for each key point in the model based on geometric relationships. The coordinates of point \(Z_{1}\) are calculated based on the multibeam's opening angle \(\theta\), corresponding to point \(H_{1}\). From this, we can determine the equation of the line \(H_{2}Z_{1}\) and traverse all data points to find the \(H_{2}\) point that satisfies this equation. If no data points satisfy the equation, we choose the point closest to the line \(H_{2}Z_{1}\) as \(H_{2}\). Figure 8: Import the single-beam bathymetric data of this maritime area into Python and create a schematic diagram of the seabed. In this diagram, the direction from west to east is designated as the x-axis, from south to north as the y-axis, and the sea depth is represented on the z-axis. Then, we calculate the length of the first coverage width \(W_{1}\), which is the Euclidean distance between \(H_{1}\) and \(H_{2}\). Then, we determine the coordinates of the next point \(Z_{2}\), based on the position of \(Z_{1}\) and \(d_{1}\). We then verify that all calculations meet the coverage width constraints and optimization goals to ensure the continuity and completeness of the multibeam coverage:  
\[\left\{ \begin{aligned} & W_{1}+\sum_{i=1}^{n}d_{i}^{\prime}\geq H_{1}H_{n }\\ &\eta\leq 20\%\end{aligned} \right. \tag{5}\]  
Based on the steps outlined and Equation (5), the minimum number of multibeam transmissions required can be determined. For a detailed derivation of the formulas, see Appendix B.2. Finally, by traversing all \(x\) values in the attachment, the minimum number of multibeam transmissions for different \(x\) values is determined. A survey line is formed by sequentially connecting each measurement point in the order of increasing \(x\) values, resulting in the projection of the optimal survey line array in the marine area. Then, we utilize the high-precision measurement model within the PMOM to complete subsequent surveys.