# Wheel Odometry with Deep Learning-Based Error Prediction Model for Vehicle Localization
###### Abstract  
Wheel odometry is a simple and low-cost localization technique that can be used for localization in GNSS-deprived environments; however, its measurement accuracy is affected by many factors, such as wheel slip, wear, and tire pressure changes, resulting in unpredictable and variable errors, which in turn affect positioning performance. To improve the localization performance of wheel odometry, this study developed a wheel odometry error prediction model based on a transformer neural network to learn the measurement uncertainty of wheel odometry and accurately predict the odometry error. Driving condition characteristics including features describing road types, road conditions, and vehicle driving operations were considered, and models both with and without driving condition characteristics were compared and analyzed. Tests were performed on a public dataset and an experimental vehicle. The experimental results demonstrate that the proposed model can predict the odometry error with higher accuracy, stability, and reliability than the LSTM and WHONet models under multiple challenging and longer GNSS outage driving conditions. At the same time, the transformer model's overall performance can be improved in longer GNSS outage driving conditions by considering the driving condition characteristics. Tests on the experimental vehicle demonstrate the model's generalization capability and the improved positioning performance of dead reckoning when using the proposed model. This study explored the possibility of applying a transformer model to wheel odometry and provides a new solution for using deep learning in localization. autonomous driving; localization; wheel odometry; deep learning; transformer model +
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IMU measurements are affected by multiple noises that are amplified during the multiple integrations of acceleration to displacement and angular velocity to attitude angle, grow exponentially, and accumulate over time. Wheel odometry measures the number of pulses per unit of time at the wheel through wheel encoders to calculate wheel speed and travel distance. Due to the necessity of an anti-lock brake system (ABS), wheel encoder sensors are mounted on the vehicle, making wheel odometry a localization technology that can be used universally. Compared to IMU's accelerometer sensors, wheel odometry requires fewer integration steps to determine the vehicle position, reducing errors in the integration process and providing a better positioning solution. Wheel odometry was initially widely used in mobile robotics and was then gradually applied to vehicles to complete localization tasks. [PERSON], [PERSON] et al. [8] improved the problem of poor estimation of vehicle attitude and IMU bias when GNSS signals are weak or down, which occurs in common GNSS/IMU fusion algorithms, by considering wheel odometry. [PERSON], [PERSON] et al. [9] complemented visual-inertial odometry with wheel odometry for automotive applications. In addition, wheel odometry can be the primary localization algorithm in some special cases, such as low light conditions, low speed driving, and parking scenes [10; 11]. The accuracy of wheel odometry-based localization is affected by many factors; on the one hand, it is affected by model parameters, such as tire diameter. Although these can be calibrated during installation, they can change dynamically when the vehicle is driven due to certain factors, such as wheel wear and load changes, which can affect the odometry output. On the other hand, the measurement accuracy of odometry is affected by wheel slip. In addition, unevenness on the road surface, such as bumps and potholes, interferes with the odometry results. Therefore, the output errors of wheel odometry have high uncertainty, and accurately predicting the wheel odometry error is key to improving wheel odometry-based localization accuracy. [PERSON], [PERSON] et al.