# Wheel Odometry with Deep Learning-Based Error Prediction Model for Vehicle Localization
###### Abstract
proposed an off-line iterative estimation algorithm in [12] and an online estimation method in [13] in which Kalman filter and the least squares algorithm are performed in an iterative loop for wheel circumference estimation of autonomous vehicles to improve wheel odometry's accuracy. They further estimated the wheel circumferences recursively to improve the wheel speed estimation with a nonlinear least squares method in [14]. The study [15] calibrated the parameters of the wheel odometry model with Gauss-Newton regression and Kalman filter. [PERSON] et al. [16] presented a method able to accurately calibrate the model parameters by using a Rauch-Tung-Striebel smoothing scheme which enables to obtain state estimates close to the ground truth. In summary, these studies used traditional state estimation methods to improve wheel odometry's accuracy. However, these methods rely on precise parameter adjustment, which lacks adaptability to various driving conditions. On the other hand, the wheels are affected by many factors of road conditions and their own parameters so that it is difficult to obtain an accurate model under the action of multiple factors using traditional state estimation methods. Deep learning is a data-driven approach that can learn complex nonlinear properties and uncertainty from data. Researchers have proposed deep learning-based techniques to discover the error drift characteristics of IMUs over time for better GPS/INS combined navigation solutions [17; 18; 19; 20]. Several deep learning techniques have also been applied to wheel odometry: an LSTM model was proposed to learn the uncertainty of wheel odometry in [21], and a WhONet model was proposed in [22], which further improved the performance compared to the LSTM model. The transformer model [23] emerged in the field of natural language processing (NLP), and it was first used for machine translation tasks to achieve SOTA effects. A transformer model can fully utilize the GPU resources for parallel computation to accelerate the training speed. Compared with traditional models such as RNN and LSTM that deal with time series, transformer models do not rely on past hidden states to capture the dependence on previous information but learns the association of information at each moment in a time series as a whole, avoiding the risk of losing past information and reducing the performance degradation caused by long-term dependence. This study aims to explore a new low-cost localization method that combines wheel odometry and deep learning techniques. The main contributions of this paper are as follows:  
1. A transformer-based error prediction model is developed to learn the measurement uncertainty of wheel odometry, and the end-to-end correspondence from the wheel speed to the travel distance error is established. Tests on a publicly available dataset and an experimental vehicle are performed to verify that the proposed model can accurately predict the output error of wheel odometry and improve the accuracy, stability, and reliability compared to LSTM and WhONet under various driving conditions. In addition, the model trained using the public dataset is transferred to the experimental vehicle to verify the model's generalization capability and the improved positioning performance of dead reckoning by combining the model. 2. Driving condition characteristics, including features describing road types, road conditions, and vehicle driving operations, are considered. Models with different inputs are developed and compared, one with and the other without driving condition characteristics. The tests demonstrate that the model that considers driving characteristics has better adaptability to longer GNSS outage driving conditions.