## 1 Introduction  
With the development of the automotive industry, performance optimization and safety control of vehicles have become increasingly important. Accurate vehicle parameters and status information are crucial for fields such as vehicle dynamics control, fault diagnosis, and intelligent driving. The mechanism model-based vehicle state estimation method is currently one of the most commonly used methods for soft sensing of vehicle states [1, 2]. However, the balance between modeling complexity and state estimation accuracy is an important issue in the design process of model-based observers [3; 4; 5]. On the one hand, although complex high-dimensional vehicle dynamics models can more accurately describe the vehicle state, there are problems such as difficulty in accurately measuring parameters, difficulty in model initialization and calibration, and heavy computational burden. In addition, some vehicle parameters have weak observability, which makes it difficult to achieve the expected calibration effect and limits their practical application [6; 7]. On the other hand, some studies simplify the model structure or use low-order models, such as vehicle dynamics models based on two or three degrees of freedom, for state estimation, which reduces computational complexity but sacrifices accuracy [8; 9]. Traditional physics model-based methods face problems such as large model errors and difficulty in accurately measuring parameters when facing complex and changing practical working conditions [10; 11; 12; 13]. However, data-driven methods provide a new approach to solve these problems. In data-driven methods, neural networks have attracted much attention due to their powerful nonlinear mapping and learning capabilities. For example, multi-layer perceptrons can compress time-series field measurement data to achieve long-term accurate prediction of vehicle states, while long short-term memory networks [14] are suitable for processing long-term dependencies in time-series data and can be used for estimating state variables such as vehicle yaw rate and center of mass sideslip angle. Support vector machine [15] is based on statistical learning theory, which analyzes and predicts data by finding the optimal classification hyperplane or regression function. It has certain applications in classification and regression problems in vehicle parameter identification and state estimation. Kalman filtering and its improved algorithms are also commonly used methods. The extended Kalman filter [16; 17; 18] estimates the state by linearizing nonlinear systems, but its accuracy is limited in strongly nonlinear systems; the unscented Kalman filter uses an unscented transform to approximate the probability density distribution, resulting in higher estimation accuracy for nonlinear systems. In addition, deep learning [19; 20] is gradually emerging in the fields of vehicle parameter identification and state estimation, which can automatically extract complex features from data and improve the accuracy and robustness of estimation. However, data-driven state estimation methods also face many challenges. Data is the foundation of data-driven methods, but in practical applications, data often has problems such as noise and missing values, which affect data quality [21; 22; 23]. To this end, researchers use data preprocessing techniques such as data cleaning, denoising, interpolation, etc., to improve data quality. At the same time, data augmentation techniques are used to simulate different working conditions or driving scenarios to generate more training data and expand the dataset [24; 25]. [PERSON], [PERSON] et al. [14] used long short-term memory neural networks to store high-fidelity data of sequence signals, and improved the control accuracy of self-balancing vehicles through neural network weight optimization. [PERSON], [PERSON] et al. [24] proposed a vehicle quality estimation scheme based on the multi-forgetting factor recursive least squares algorithm.