# Wheel Odometry with Deep Learning-Based Error Prediction Model for Vehicle Localization
## 5 Results and Discussion
### Tests on the Dataset
#### 5.1.1 Tests in Challenging Driving Conditions  
Motorway  
The test results of the motorway scenario are displayed in Table 6 and Figure 3. It can be seen that the four metrics of Transformer-DC and Transformer-NDC were equal and were lower than those of LSTM and WhONet. Compared with LSTM and WhONet, both Transformer models showed 76% and 52% error reductions in the max metric, 83% and 69% error reductions in the \(\upmu\) metric, and 92% and 85% error reductions in the min metric, respectively, demonstrating better positioning reliability and positioning accuracy. All the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & \(N\) & \(d_{model}\) & \(d_{ff}\) & \(h\) & _Dropout_ & max & min & \(\mu\) & \(\sigma\) \\ \hline baseline & 6 & 512 & 32 & 8 & 0 & 0.36 & 0.03 & 0.09 & 0.07 \\ \hline \multirow{2}{*}{A} & \multirow{6}{*}{} & & 4 & 4 & 0.42 & 0.03 & 0.12 & 0.06 \\  & & & 16 & & 0.33 & 0.03 & 0.09 & 0.07 \\ \hline \multirow{2}{*}{B} & 4 & & & & 0.38 & 0.03 & 0.12 & 0.06 \\  & 8 & & & & 0.42 & 0.03 & 0.09 & 0.08 \\ \hline \multirow{2}{*}{C} & \multirow{2}{*}{} & 1024 & & & 0.51 & 0.03 & 0.09 & 0.10 \\  & & 256 & & & 0.51 & 0.03 & 0.09 & 0.10 \\ \hline \multirow{2}{*}{D} & \multirow{6}{*}{} & 16 & & 0.43 & 0.03 & 0.11 & 0.06 \\  & & 64 & & 0.85 & 0.03 & 0.25 & 0.20 \\ \hline \multirow{2}{*}{E} & \multirow{6}{*}{} & 0.1 & 1.13 & 0.04 & 0.14 & 0.20 \\  & & & 0.2 & 0.94 & 0.04 & 0.20 & 0.18 \\ \hline \end{tabular}
\end{table} 
Table 5: Parameter adjustment process of Transformer-NDC (parameter values not listed are the same as the corresponding parameter values of the baseline model). The test results for the wet road scenario are shown in Table 8 and Figure 5. Both Transformer-DC and Transformer-NDC performed approximately the same on the three data subsets. Compared to LSTM, the two proposed models show considerable perfor \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**IO-VNB Dataset**} & \multirow{2}{*}{**Performance Metrics**} & \multicolumn{4}{c}{**Model Error (m)**} \\ \cline{3-6}  & & \multicolumn{4}{c}{**CRSE**} \\ \cline{3-6}  & & **LSTM** & **WhONet** & **Transformer-NDC** & **Transformer-DC** \\ \hline \multirow{4}{*}{V-Vw6} & max & 1.45 & 0.57 & 0.68 & 0.68 \\  & min & 0.34 & 0.11 & 0.04 & 0.03 \\  & \(\mu\) & 0.84 & 0.36 & 0.12 & 0.12 \\  & \(\sigma\) & 0.29 & 0.09 & 0.10 & 0.10 \\ \hline \multirow{4}{*}{V-Vw7} & max & 1.93 & 0.61 & 0.62 & 0.64 \\  & min & 0.29 & 0.08 & 0.04 & 0.04 \\  & \(\mu\) & 1.14 & 0.36 & 0.12 & 0.12 \\  & \(\sigma\) & 0.46 & 0.13 & 0.11 & 0.11 \\ \hline \multirow{4}{*}{V-Vw8} & max & 1.91 & 0.57 & 0.46 & 0.48 \\  & min & 0.43 & 0.11 & 0.03 & 0.03 \\ \cline{1-1}  & \(\mu\) & 1.19 & 0.37 & 0.12 & 0.12 \\ \cline{1-1}  & \(\sigma\) & 0.44 & 0.12 & 0.09 & 0.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Test results for the driving condition with sharp cornering and successive left and right turns. Figure 4: Test results for the driving condition with sharp cornering and successive left and right turns. (**a**) V-Vw6; (**b**) V-Vw7; (**c**) V-Vw8. Quick Changes in Vehicle's Acceleration  
Table 9 and Figure 6 demonstrate the test results for the driving condition with quick changes in the vehicle's acceleration. Both Transformer-DC and Transformer-NDC had almost the same performance on the two data subsets. On the V-Vfb02e dataset, compared to LSTM, the two proposed models show 57%, 94%, 86%, and 72% improvements on the four metrics; compared to WhONet, the two proposed models show 55%, 82%, 82%, and 78% improvements on the four metrics. On the V-Vta12 dataset, compared to LSTM, the two proposed models show 54%, 92%, 83%, and 64% improvements on the four metrics; compared to WhONet, the two proposed models show 54%, 64%, 74%, and 59% improvements on the four metrics. In summary, the proposed models significantly improved the reliability, highest possible accuracy, average accuracy, and stability compared to LSTM and WhONet in this driving condition.