## 3 Data Pre-Processing  
The working medium of an acoustic sensor is sea water. The ocean is a very complex acoustic medium, whose complexity is mainly reflected in different acoustic propagation rules with the change of sea area and season. Due to the viscosity and heat conductivity of seawater, some of the sound energy is absorbed by seawater. Air bubbles, suspended particles, uneven water masses, plankton, and uneven boundaries in seawater can cause acoustic signal scattering. The above phenomenons will  
Figure 1: The recovery system consists of **(a)** AUV-\(I1\) and **(b)** AUV-\(I\) with DS. Figure 2: The overview of our recovery system. cause the energy loss of the signal from the source in the process of transmission. In addition, due to the non-uniform sound velocity in sea water, the sound line will be refracted, so the acoustic source signal may not reach the receiving point at a long distance. On the other hand, due to the existence of a large number of scatterers and uneven interfaces in the ocean, when the acoustic source emits sound waves, it will encounter these scatterers and generate scattered waves, which will interfere with the reception of acoustic signals. In conclusion, due to the working medium and working principle of the acoustic sensor, the measurement results of the acoustic sensor will have certain errors, and the farther the working distance is, the greater the interference will be and the greater the error will be. Table 1 shows the navigation data of our recovery system in a sea trial. \((x_{AUV},y_{AUV})\) and \((x_{DS},y_{DS})\) are the positions of AUV and DS measured by IMU. These positions are true as the IMU used by our AUV has very high precision. \((x_{DS},y_{DS})\) are the true distance between AUV and DS in \(X\) and \(Y\) direction of observation coordinate system. \(Z_{x}\) and \(Z_{y}\) are the measurements of acoustic sensor of AUV. We define measurement error as follows:  
\[ \begin{cases}e_{x}=Dis_{x}-z_{x}\\ e_{y}=Dis_{y}-z_{y}\end{cases}  \tag{1}\]  
The Figure 3 shows all measurement errors of this trail. One of the premises of the SLAM algorithm is to know the statistical characteristics of the measurement error. In order to better describe the statistical characteristics of the measurement error, it is assumed that the error consists of two parts, namely, system error and random error, that is, \(w=\varepsilon+\epsilon\). In the formula, w represents the measurement error. \(\varepsilon\) represents the system error. \(\epsilon\) is \begin{table}
\begin{tabular}{c c c c c} \hline  & **1** & **2** & **3** & **4** \\ \hline \((x_{AUV},y_{AUV})\) & \([800.0205,300.0763]\) & \([730.6679,249.8969]\) & \([680.1911,184.9589]\) & \([650.2868,145.8485]\) \\ \((x_{DS},y_{DS})\) & \([665.9183,178.3197]\) & \([629.7143,123.7123]\) & \([601.9309,83.1256]\) & \([584.3957,58.0357]\) \\ \(Dis_{x}\) & \(-39.9557\) & \(-10.3142\) & \(-5.6934\) & \(-3.4857\) \\ \(Dis_{y}\) & \(176.6203\) & \(161.2694\) & \(128.3054\) & \(109.6431\) \\ \(Z_{x}\) & \(-28.3\) & \(-1.5\) & \(-0.9\) & \(1.1\) \\ \(Z_{y}\) & \(160.9\) & \(151.6\) & \(120.5\) & \(101.7\) \\ \((x_{AUV},y_{AUV})\) & \([600.0220,75.7450]\) & \([550.1815,7.1173]\) & \([525.1551,-25.3517]\) & \([500.7651,-59.2965]\) \\ \((x_{DS},y_{DS})\) & \([555.0595,16.7112]\) & \([525.5794,-26.8272]\) & \([512.2178,-40.1101]\) & \([498.4322,-61.5103]\) \\ \(Dis_{x}\) & \(-2.9681\) & \(-0.6816\) & \(-2.1319\) & \(-0.6412\) \\ \(Dis_{y}\) & \(74.1472\) & \(41.9169\) & \(19.5100\) & \(3.1515\) \\ \(Z_{x}\) & \(0\) & \(-1.3\) & \(0\) & \(-0.4\) \\ \(Z_{y}\) & \(67.8\) & \(36.2\) & \(20.9\) & \(4.7\) \\ \hline \end{tabular}
\end{table} 
Table 1: Navigation data of our recovery system. Figure 3: The measurement errors in the process of Autonomous Underwater Vehicle (AUV) docking with fixed docking station (F-DS). random error and follows the zero-mean Gaussian distribution. \(\epsilon\sim N(0,\sigma^{2})\), where \(\sigma^{2}\) is the variance of random error.