## 6 Analysis of Experimental Data  
Our recovery system was tested on a lake at the xinanjiang experimental field of the institute of acoustics, Chinese Academy of Sciences in December 2018. AUV sensed the position of DS by using the ultra short baseline (USBL) system and camera. The intersection of the extension line of AUV initial heading and the center of DS is the initial target point. AUV reached the target point by line-of-sight (LOS) guidance, and tracked the center line of DS. More detailed descriptions are given in Reference [36]. The experimental results are shown in Figure 17.  
We use these experimental data to verify the effectiveness of the proposed algorithm. Firstly, the method 1 and method 2 are applied to collect the measurement error data of acoustic sensor. Then the VAE-GMM algorithm is applied to estimate the overall distribution of measurement error data. Finally, the SVR algorithm is used to fit the relationship between the sttstistical characteristics of measurement error data and its coreresponding working distance. After data pre-processing, SLAM algorithm is applied to estimate the positions of AUV and DS. The actual measurement error in the experiment and the corresponding to estimated statistical characteristics are partly shown in Table 3. The data analysis results are shown in Figures 18-21. Figures 18 and 20 show the deviation between the estimated position and true position of AUV sensed by IMU. We can know that the position of AUV estimated by SLAM algorithm is close to the position sensed by IMU. It is applicable if without IMU. In Figures 19 and 21, the blue line shows the deviation between the position of DS estimated by SLAM and true position of DS sensed by IMU. The red line shows the deviation between the positon of DS directly estimated by the measurement of sensor and true position. We can know that the localization precision of the SLAM algorithm is higher than that of the original data. When the initial distance between AUV and DS is larger than the maximum operating distance corresponding to measurement error data, the above method can still be used. This is because the SVR method has the ability of prediction after training. In the experiment of AUV homing to the M-DS mentioned above, the initial distance between AUV and M-DS was about 207 m. Assuming that we only use measurement error data with the maximum working distance less than 150 m, the experimental data analysis results are as follows: \begin{table}
\begin{tabular}{c c c c c} \hline  & **1** & **2** & **3** & **4** \\ \hline
**actual error(x)** & \(-26.0954\) & \(-20.3664\) & \(-15.4389\) & \(-15.8233\) \\
**estimated mean(x)** & \(-20.4985\) & \(-19.3341\) & \(-18.0703\) & \(-11.6306\) \\
**estimated variance(x)** & \(52.5201\) & \(65.73\) & \(68.5750\) & \(34.4198\) \\
**actual error(y)** & \(20.8992\) & \(16.0174\) & \(14.7687\) & \(9.1035\) \\
**estimated mean(y)** & \(16.2934\) & \(15.9007\) & \(15.0819\) & \(10.1747\) \\
**estimated variance(y)** & \(9.5113\) & \(12.0081\) & \(12.3802\) & \(14.8358\) \\
**actual error(x)** & \(-6.9282\) & \(-4.1194\) & \(-1.1224\) & \(0.5263\) \\
**estimated mean(x)** & \(-3.9893\) & \(-3.8044\) & \(-2.6581\) & \(0.0927\) \\
**estimated variance(x)** & \(5.9733\) & \(2.5934\) & \(0.9619\) & \(0.4035\) \\
**actual error(y)** & \(1.4114\) & \(1.5264\) & \(0.0763\) & \(-0.9784\) \\
**estimated mean(y)** & \(2.8238\) & \(2.6493\) & \(2.0045\) & \(0.5360\) \\
**estimated variance(y)** & \(3.4287\) & \(3.4820\) & \(1.2557\) & \(0.9381\) \\ \hline \end{tabular}
\end{table} 
Table 3: Actual measurement error and estimated statistical characteristics. Figure 17: (**a**) Trajectory of AUV recorded by IMU in AUV homing to the F-DS. (**b**) Trajectories of AUV and mobile docking station (M-DS) recorded by IMU in AUV homing to M-DS. Figure 19: Deviation between estimated position and true position of F-DS recorded by IMU in AUV homing to the F-DS are illustrated by that in (**a**) X direction and (**b**) Y direction.