## 2 Materials and Methods
### Features of AUV Performance and AUV-Based Side-Scan Sonar Operations
#### 2.1.1 AUV Performance Features
Once submerged, it switches to the Doppler Velocity Log (DVL) for calculating velocity and direction relative to the seafloor. This dual approach ensures that as long as the AUV remains within the DVK's operational range, it can maintain precise positioning, even when satellite signals are unavailable [27]. Nevertheless, one limitation of this mode is its reliance on the AUV to remain within the operational constraints of the DVL. The fixed-point mode includes a time-bound safeguard mechanism, necessitating the AUV to reach its predetermined destination within a specified timeframe. Failure to do so will promptly activate a surfacing alarm. When conducting surveys along a predetermined trajectory, the desired outcome is to align the AUV's path with the planned survey line. However, the underwater environment may impact the AUV's navigation, leading to deviations from the planned line, as depicted in Figure 3.  
In this diagram, \(A\) and \(B\) denote the starting and ending points of a specific measuring line in fixed point navigation mode. \(C\) and \(C_{1}\) represent positions corresponding to two  
Figure 3: Fixed point mode yaw. different yaw situations. Distances from the point to the planned measuring line are indicated by \(CD\) and \(C_{1}D\). The heading angle is denoted as \(t\), and its calculation formula is as follows:  
\[t=arc\tan\frac{y_{B}-y_{C}}{x_{B}-x_{C}} \tag{1}\]  
Here, \((x_{B}\),\(y_{B})\) and \((x_{C}\),\(y_{C})\) refer to the coordinates of point \(B\) and point \(C\), respectively, under the Mercator projection. The calculation formula for \(CD\) and \(C_{1}D\) is as follows:  
\[d=-\frac{(y_{A}-y_{B})x_{C}+(x_{B}-x_{A})y_{C}+(x_{A}y_{B}-x_{B}y_{A})}{\sqrt{ (y_{A}-y_{B})^{2}+(x_{B}-x_{A})^{2}}} \tag{2}\]  
Here, \((x_{A}\),\(y_{A})\) denotes the coordinate of point \(A\) under the Mercator projection. \(d\) represents the distance value, with \(CD\) being a positive value and \(C_{1}D\) being a negative value. The AUV line correction algorithm is a dynamic correction algorithm, and its formula is as follows:  
\[t^{\prime}=t+d \tag{3}\]  
Here, \(t^{\prime}\) represents the heading of the AUV during dynamic correction. It is worth noting that a limit is set for d, preventing it from exceeding \(\pm 5^{\circ}\). This limitation is in place to avoid large-angle turns by the AUV. In this specific mode, the AUV's movement is dictated by preset time and direction parameters. This approach depends on the initial satellite-based positioning, usually determined before submersion. Once the AUV is submerged, there is no requirement for the DVL to continuously track the seafloor. This allows AUV's flexibility to operate at depths exceeding the measuring range of the DVL. However, its pronounced dependence on inertial navigation data has been found to result in inaccurate positioning [28]. When planning continuous survey lines, the timing for changing direction must be meticulously calculated. This mode is particularly vulnerable to external factors, such as water currents, which can introduce deviations in the submersible's position. Figure 4 illustrates the fixed-point and fixed-direction motion control modes for visual reference. AUV Underwater Motion Control Modes in the Vertical Plane  
Constant-Altitude Mode  
It is designed to maintain the AUV at a predetermined depth above the seafloor, but the submersible's movements are influenced by seafloor topography. As underwater  
Figure 4: Fixed-point and fixed-direction motion control modes. (**a**) Fixed-point modes. (**b**) Fixed-direction modes. depths vary, the separation between the vehicle and the seafloor is determined either by the DVL or single-beam systems. This mode incorporates an altitude maintenance alarm mechanism, whereby the AUV will resurface if it deviates from a specified altitude for an extended duration. The principle revolves around the height measurement equipment which measures the distance to the seabed at a fixed working frequency, typically 2 Hz.