# 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
\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{4}{*}{V-Vtb3} & max & 4.01 & 3.64 & 2.80 \\  & min & 1.75 & 0.34 & 0.30 \\  & \(\mu\) & 2.62 & 0.99 & 0.95 \\  & \(\sigma\) & 0.19 & 0.61 & 0.49 \\ \hline \multirow{4}{*}{V-Vfb02a} & max & 11.75 & 7.56 & 7.30 \\  & min & 2.05 & 0.49 & 0.38 \\ \cline{1-1}  & \(\mu\) & 4.07 & 1.35 & 1.19 \\ \cline{1-1}  & \(\sigma\) & 1.41 & 1.16 & 1.08 \\ \hline \multirow{4}{*}{V-Vfb02b} & max & 5.76 & 2.88 & 2.86 \\  & min & 2.52 & 0.48 & 0.41 \\ \cline{1-1}  & \(\mu\) & 4.15 & 1.42 & 1.38 \\ \cline{1-1}  & \(\sigma\) & 0.88 & 0.57 & 0.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Results under the 120 s GNSS outage driving condition. Figure 10: Test results under the 60 s GNSS outage driving condition. (a) V-Vtb3; (b) V-Vfb02a; (c) V-Vfb02b. Table 15 and Figure 12 show the test results under the 180 s GNSS outage driving condition. Compared with WhONet, Transformer-NDC improved the performance on the max, min, and \(\mu\) metrics by up to \(51\%,79\%\), and \(66\%\), respectively, exhibiting that the Transformer model has higher accuracy and better reliability than the WhONet model in this driving condition. By considering the driving condition characteristics, Transformer-DC reduced the error on the four metrics on the V-Vtb3 and V-Vfb02a data subsets and the error on the max and \(\mu\) metrics on the V-Vfb02b data subset, which proves that considering the driving condition characteristics improves the model's accuracy, stability, and reliability. In conclusion, the proposed Transformer models can accurately predict odometry errors under different longer GNSS outage driving conditions and have higher accuracy, stability, and reliability than the WhONet model. Additionally, Transformer-DC, which considers the driving condition characteristics, can better adapt to different driving conditions than Transformer-NDC, and this improves the model's overall performance. From the tests in Section 5.1, it can seen that whether considering the driving condition characteristics or not, the proposed Transformer model can predict odometry errors with higher accuracy, stability, and reliability than LSTM and WhONet under various driving conditions including challenging and longer GNSS outage driving conditions, which may cause the wheel odometry output to become unpredictable and to accumulate errors. The results showcase the superiority of the model and its great potential in terms of improving positioning performance. Although the Transformer models with and without the driving condition characteristics can perform roughly equally well under challenging driving conditions, the Transformer model's overall performance can be improved under longer GNSS outage driving conditions by considering the driving condition characteristics. It can be inferred that considering the driving condition characteristics can improve the reliability and stability of long-term prediction by enhancing the adaptability to various driving conditions, while this is not so evident in short-term prediction.