# Wheel Odometry with Deep Learning-Based Error Prediction Model for Vehicle Localization
## 5 Results and Discussion
### Tests on the Dataset
#### 5.1.2 Tests in Longer GNSS Outage Driving Conditions  
Since WhONet has better performance than LSTM, as shown in Tables 6-11, in this section, the proposed model was compared further with WhONet to evaluate their performance over four longer-term GNSS outages of 30 s, 60 s, 120 s, and 180 s using the corresponding data subsets in Table 4, and the evaluation results are shown in Tables 12-15. Test results on the 30 s GNSS outage driving condition are displayed in Table 12 and Figure 9. The results show that Transformer-NDC demonstrated significantly better performance than the WhONet model. Specifically, the errors on the four metrics were reduced by up to 50%, 81%, 66%, and 60%, respectively, demonstrating that the Transformer model has higher accuracy and better stability and reliability than the WhONet model in this driving condition. In addition, the performance of Transformer-DC on the max metric is improved compared to Transformer-NDC, which proves that considering the driving condition characteristics boosts the model's  
Table 13 and Figure 10 illustrate the test results under the 60 s GNSS outage driving condition. It can be seen that compared with the WhONet model, Transformer-NDC improved the performance enormously. Specifically, the errors were reduced on the four metrics greatly by up to 25%, 82%, 66%, and 42% on the V-Vfb02a and V-Vfb02b data subsets; on the V-Vfb3 data subset, although the errors on the max and \(\mu\) metrics were slightly increased, the mean error was decreased tremendously by 62%. Additionally, Transformer-DC improved the performance on the four metrics by up to 32%, 82%, 67%, and 23% on the three datasets compared with the WhONet model, and it reduced the maximum error by up to 33% compared to Transformer-NDC. In summary, the proposed models have higher accuracy and better stability and reliability in error prediction compared to WhONet, and considering the driving condition characteristics can enhance the model's reliability. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**IO-VNB Dataset**} & \multirow{2}{*}{**Performance Metrics**} & \multicolumn{3}{c}{**Model Error (m)**} \\ \cline{3-5}  & & \multicolumn{3}{c}{**CRSE**} \\ \cline{3-5}  & & **WhONet** & **Transformer-NDC** & **Transformer-DC** \\ \hline \multirow{3}{*}{V-Vtb3} & max & 2.29 & 2.54 & 1.71 \\  & min & 0.29 & 0.16 & 0.12 \\  & \(\mu\) & 1.31 & 0.50 & 0.47 \\  & \(\sigma\) & 0.25 & 0.34 & 0.27 \\ \hline \multirow{3}{*}{V-Vfb02a} & max & 9.62 & 7.24 & 6.55 \\  & min & 0.87 & 0.19 & 0.19 \\ \cline{1-1}  & \(\mu\) & 2.02 & 0.68 & 0.68 \\ \cline{1-1}  & \(\sigma\) & 1.11 & 0.64 & 0.86 \\ \hline \multirow{3}{*}{V-Vfb02b} & max & 2.94 & 2.41 & 2.40 \\  & min & 1.10 & 0.20 & 0.20 \\ \cline{1-1}  & \(\mu\) & 2.08 & 0.71 & 0.69 \\ \cline{1-1}  & \(\sigma\) & 0.48 & 0.38 & 0.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Results under the 60 s GNSS outage driving condition. Figure 9: Test results under the 30 s GNSS outage driving condition. (**a**) V-Vtb3; (**b**) V-Vfb02a; (**c**) V-Vfb02b. The test results under the 120 s GNSS outage driving condition are listed in Table 14 and Figure 11. Compared with the WhONet model, except for the slight increment on the \(\sigma\) metric on the V-Vtb3 data subset, both Transformer models improved the performance on the four metrics. Specifically, Transformer-NDC reduced the errors on the four metrics by up to 50%, 81%, 67%, and 35%, respectively, and the Transformer-DC reduced the errors on the four metrics by up to 50%, 84%, 71%, and 35%, respectively, proving that the proposed models have higher accuracy and better stability and reliability compared with the WhONet model in this driving condition. In addition, the values on the four metrics of Transformer-DC are reduced compared to Transformer-NDC, demonstrating that considering the driving condition characteristics improves the model's accuracy, stability, and reliability.