# Wheel Odometry with Deep Learning-Based Error Prediction Model for Vehicle Localization
## 5 Results and Discussion
### Tests on the Experimental Vehicle  
In this section, Transformer-NDC is taken as an example, and the model's generalization capability and improved dead reckoning performance based on wheel odometry combined with the model was verified on the experimental vehicle, which is shown in Figure 13. RTK equipment was loaded on the vehicle to provide centimeter-level-accuracy GPS coordinates that can be used as true values to verify the localization accuracy. Figure 12: Test results under the 180 s GNSS outage driving condition. (**a**) V-Vtb3; (**b**) V-Vfb02a; (**c**) V-Vfb02b. To verify the generalization capability of the model, the model trained on the public dataset was directly applied to this experimental vehicle. The experiment was conducted in a region of Changchun, and the model's performance on the real vehicle data was compared with that on the V-Vta8 dataset under similar driving conditions, as is shown in Table 16. It can be seen that the corresponding maximum and mean metrics of CRSE increase after the model transfers, but not much, and there is a slight decrease in the minimum and standard deviation, so the model still has good model prediction function after the model is transferred. The vehicle driving route during the experiment is shown in Figure 14, and the RTK-GPS coordinates, the positioning coordinates obtained by dead reckoning alone, and the positioning coordinates obtained by dead reckoning combined with the odometry error prediction model were recorded. It can be seen from the enlarged parts in the figure that the green curve and the blue curve overlap approximately in most cases, which is due to the fact that the vehicle driving along the lane is the most dominant driving behavior, and the odometry output error mainly affects the longitudinal positioning error of the vehicle, which cannot be directly reflected in this figure. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Performance Metrics**} & \multicolumn{2}{c}{**Model Error (m)**} \\  & **CMSE** \\  & **V-Vta8** & **Experimental Vehicle** \\ \hline max & 1.02 & 1.46 \\ min & 0.05 & 0.02 \\ \(\mu\) & 0.33 & 0.60 \\ \(\sigma\) & 0.21 & 0.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Error comparison of the experimental vehicle and the corresponding data subset. Figure 14: Localization trajectory comparison. Figure 13: Experimental vehicle. Figure 15 compares the error of the original dead reckoning with the error of the dead reckoning after compensation using the error prediction model proposed in this paper. In Figure 15b,c, the error after compensation using the error prediction model is significantly lower compared to the original dead reckoning, and in Figure 5a, although the error of the original dead reckoning is relatively lower than the error after combining with the prediction model compensation between the first 1000 points and the 4500 th to 5000 th points, which is caused by the deep learning-based model's uncertainty, both are small and less than 0.5 m, and the error after combining with the prediction model compensation is lower than the original dead reckoning at other points most of the time. It is thus proven that the proposed error prediction model can effectively compensate for the output error of the wheel odometry in the x and y directions and overall, thus improving the accuracy of the dead reckoning and the performance of the positioning system. Table 17 compares the performance indexes of the original dead reckoning error and the error after error compensation with the model. It can be seen that the maximum value of the positioning error is significantly reduced, and the mean and standard deviation of the error are also reduced after the error is compensated for by the error prediction model,  
Figure 15: Error of the dead reckoning and the dead reckoning with the Transformer model relative to the real trajectory. (**a**) Error in the x coordinate; (**b**) Error in the y coordinate; (**c**) The total error.