# Wheel Odometry with Deep Learning-Based Error Prediction Model for Vehicle Localization
## 6 Conclusions  
In this study, a Transformer-based wheel odometry error prediction model is established to accurately predict the accumulated and changing travel distance errors during vehicle driving so as to improve the positioning performance of wheel odometry. The study and its findings can be summarized as follows:  
1. Two different Transformer error prediction models are designed. Both models contain four-wheel wheel speed as the input. One considers the driving condition features, which contain multiple features describing different road types, road conditions, and driving operations, as the input, and the other does not. 2. The performance of the proposed model is evaluated and compared with LSTM and WhONet under challenging driving conditions and longer-term GNSS outage driving conditions. The results demonstrate that the proposed model has higher accuracy, stability, and reliability under various challenging driving conditions and longer-term GNSS outage driving conditions. Specifically, the model performs up to 96%, 94%, 97%, and 95% better than LSTM and up to 84%, 95%, 92%, and 78% better than WhONet on the max, min, mean, and standard deviation metrics under various challenging conditions. In addition, Transformer-NDC performs up to 51%, 84%, 71%, and 60% better than WhONet on the max, min, mean, and standard deviation metrics under longer-term GNSS outage driving conditions. Although the Transformer models with and without the driving condition characteristics achieve approximately the same performance under challenging driving conditions, Transformer-DC, which considers the driving condition characteristics, can better adapt to driving conditions with longer-term GNSS outage than Transformer-NDC and improve the model's overall performance. 3. Tests on an experimental vehicle are conducted to verify the model's generalization capability and the improved dead reckoning positioning performance by combining the model. In particular, a model trained on a public dataset is directly applied to the experimental vehicle, and the model's performance on the experimental vehicle is compared with that on a data subset with the similar driving condition. The results show that although the model's performance declines slightly, the mean and standard deviation of the model's errors are only 0.6 m and 0.2 m, which demonstrates that the model is still effective at predicting the odometry error and improving the accuracy and stability of localization. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Performance Metrics (m)** & **Dead Reckoning** & **Dead Reckoning with Transformer Model** \\ \hline max & 4.01 & 2.99 \\ min & 0.06 & 0 \\ \(\mu\) & 1.58 & 1.34 \\ \(\sigma\) & 0.84 & 0.74 \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Comparison between original dead reckoning and dead reckoning with Transformer model. This study explored the possibility of applying the Transformer model to wheel odometry, providing a new solution for the application of deep learning to localization. Although the test on the experimental vehicle validated the model's generalization capability and provides a basis for the application and generalization of the model to multiple vehicle types, in future work, more study is needed to further develop and explore related techniques to enhance the generalization of the Transformer model to multiple vehicle types and to improve the model accuracy after transferring so that the efficiency of model utilization can be improved, in addition, the related techniques to improve the performance of the Transformer model and the use of other deep-learning models to localization can be studied. Conceptualization, H.D. ; data curation, K.H. ; investigation, K.H. ; methodology, K.H. ; project administration, N.X. and K.G. ; resources, H.D. and N.X. ; software, K.H. ; supervision, K.G. ; validation, K.H. ; writing--original draft, K.H. ; writing--review and editing, K.H. All authors have read and agreed to the published version of the manuscript.