## 3 Experiments and Results
### Data Processing  
The experimental model prediction uses the real drift position data returned by the Ultrashort Baseline (USBL) positioning system and sensor mounted on the AUV and the real-time meteorological data obtained by the National Marine Data Science Center [33] and the National Meteorological Science Data Center [34]. However, some ocean factors such as waves and currents that affect the AUV drift track cannot be directly obtained by the observed data. There is a need to establish a complete data set based on the reanalysis data of current and wave from satellite data [35; 36; 37]. The process of establishing the current database is shown in Figure 9.  
Firstly, the wind current database near the date of the event is constructed to obtain the reanalysis data from near the date of the event [38]. The fixed current data are compared with the analysis data of the current over the years, and the difference is taken as the sum of other current influencing factors near the date. Then, the synthesis of other ocean-current influencing factors is added to the wind current database constructed near the date of the incident, and that is the real ocean current database of the surface layer on the date of the incident. The calculation of wind current is based on the empirical formula obtained by the Polish Maritime University [39] as Equation (17):  
\[V_{wc}=\left(0.230446+0.0070957V_{w}\right)^{2}\pm 0.17 \tag{17}\]  
The value range of the wind current is obtained through wind speed \(V_{w}\) and the maximum value is taken as the value of the wind current. The direction of the wind current is obtained from the following equation, to obtain the direction \(c\) of the wind current as Equation (18):  
\[c=-35.338+3587.78/V_{w} \tag{18}\]  
In the data set of this paper, the drift time of the crashed AUV is from 13:00 on 3 November 2019 to 18:00 on 8 November 2019, and the data collection site is the Wolfberry scene spot. The maximum depth of the AUV diving is 800 m, the real-time wind speed is 11 m/s, and the wind direction is northwest wind. The actual AUV drift track is shown in Figure 10.  
We use the four indicators shown in the following formula to evaluate the prediction accuracy of our proposed prediction model.  
* Mean square error (MSE) describes the mean square error between the predicted and actual values in three dimensions: \[\text{MSE}=\sqrt{\frac{\sum_{k=1}^{n}\left(y_{k}-\hat{y}_{k}\right)^{2}}{N}}\] (19)  
Figure 9: Ocean current database creation process.  
\[y_{k}=\sqrt{\left(l_{1}-l_{2}\right)^{2}+\left(\varphi_{1}-\varphi_{2}\right)^{2}+ \left(d_{1}-d_{2}\right)^{2}} \tag{20}\]
* Root means square error (RMSE) is the square root of the difference between the predicted value and the actual value in three dimensions: \[\text{RMSE}=\sqrt{\text{MSE}}\] (21)
* Mean absolute error (MAE) is the average of the absolute differences between the predicted and actual values. \[\text{MAE}=\frac{1}{m}\sum_{i=1}^{m}\lvert y_{k}-\hat{y_{k}}\rvert\] (22)
* Relative error (RE) reflects the deviation of the measured value from the true value and can better reflect the credibility of the measurement: \[\text{RE}=\frac{y_{k}}{y_{k}}-y_{k}\cdot 100\%\] (23) where \(N\) is the number of predicted data, \(y_{k}\) is the measured AUV drift track, \(y_{k}^{*}\) is the predicted drift track, \(l\) is the longitude of the track, \(\varphi\) is the latitude of the track, and \(d\) is the depth of the track.