## 2 Research Content and Methodology
### Methodology
#### 2.2.1 Precision Measurement Optimization Model  
The Precision Measurement Optimization Model (PMOM) is designed to optimize measurement accuracy and efficiency. It is suitable for seabed topographies that are inclined planes, ensuring the efficient provision of high-precision data during the measurement process. Applicable marine conditions: Within a water body where the seabed slope is a smooth inclined plane (assumed to be deeper in the west and shallower in the east), the east-west and north-south length of the sea area, the water depth \(D\) measured at the center of the sea area, the seabed slope \(\alpha\), and the opening angle \(\theta\) of the multibeam transducer are known. The possible positions of the seabed slope relative to the horizontal plane are illustrated in Figure 4. Since the intersection of the seabed slope with the horizontal or sea surface may affect subsequent calculations of water depth, it is assumed that the projection of the seabed slope on the horizontal plane can cover the entire sea area, as shown in Figure 4b,c. Due to the unique topography of this sea area, high-precision measurements are necessary to obtain detailed information about the sea area. For such regions, the PMOM can design a set of survey lines that fully cover the entire area to be measured, with adjacent stripes overlapping between 10% and 20%, fulfilling the requirement for the shortest total measurement length. This optimizes the model's capability to address inaccuracies in measurements within such areas. The following are the implementation steps for the model. Firstly, determining the survey line path is critical for achieving efficient measurement and minimizing the total length of the survey lines. The angle \(\beta\) formed by the projection of the survey line direction with the seabed slope's normal on the horizontal plane can be controlled by fixing or changing \(\beta\). According to the principle that the shortest distance between two points is a straight line, the total length of curved survey lines will inevitably be greater than that of straight lines. Therefore, to achieve high efficiency and accuracy in measurements, it is advisable to fix \(\beta\) for each survey line so that the lines are straight. As the water depth increases, both the coverage width \(W\) and the overlap rate \(\eta\) of the multibeam system increase. Therefore, the survey lines of this model start from the westernmost  
Figure 4: Within a defined and limited area, the angle between the seabed slope and the horizontal plane is known, but the relative positional relationship between the two planes remains unknown. Therefore, there are three possible relational configurations of these planes under this circumstance: (**a**) the seabed slope does not completely cover the horizontal plane of the rectangular sea area; (**b**) the seabed slope just completely covers the horizontal plane of the rectangular sea area; (**c**) the seabed slope completely covers the horizontal plane of the rectangular sea area. edge of the simulated maritime area as straight lines, laid out sequentially in the direction of increasing sea floor elevation. This arrangement maximizes the utilization rate of the coverage width in deep-sea areas, effectively reducing the total length of the survey lines. The next crucial step is to maximize the coverage width \(W\) of the survey lines, as this directly impacts the required number of survey lines and the total length of the survey lines. To minimize the total survey line length, we derive the relationship between the coverage width \(W\) and the survey line direction \(\beta\) using the mathematical model and trigonometric functions illustrated in Figure 5[22]. Calculating the optimal survey line direction \(\beta\) that maximizes the coverage width is essential. This step is critical because choosing the best \(\beta\) value affects the efficiency of coverage and determines the economy and accuracy of the entire measurement operation.