## 1 Introduction
To address the issue of increased data inaccuracy at low sampling rates, a robust recursive algorithm and a reconstructed longitudinal dynamics model were combined to reduce estimation bias. In addition, the generalization ability of the model is crucial, and data-driven models need to adapt to different vehicle models, operating conditions, and environmental conditions. To improve generalization ability, researchers use techniques such as multi-source data fusion and transfer learning to enable the model to maintain good performance under different data distributions. Furthermore, vehicle parameter identification and state estimation typically require real-time performance to meet the requirements of vehicle control and safety systems [26; 27; 28]. Therefore, researchers continuously optimize algorithm structures and computational efficiency, using lightweight neural network architectures and improved Kalman filtering algorithms, etc., to reduce computational complexity and improve model running speed. The fusion of data-driven and model-based identification algorithms has demonstrated many significant advantages [29; 30; 31; 32; 33]. The fusion of the two cleverly compensates for the errors of using them separately, thereby improving the accuracy of vehicle state estimation [34; 35; 36; 37]. [PERSON], [PERSON] et al. [19] proposed an estimator for intelligent tire force soft measurement and built tire force estimation models under different sensor target configurations based on radial basis function neural networks, significantly improving the parameter sensitivity and generalization performance of the model. In terms of enhancing generalization ability, fusion algorithms reduce reliance on a large amount of comprehensive and high-quality training data and utilize prior knowledge of the model to supplement and derive data, enabling the algorithm to maintain good estimation performance even in conditions where data is scarce or insufficiently covered [38; 39; 40]. This enables the algorithm to better adapt to different vehicles and complex real-world conditions, greatly improving its generalization ability. In terms of improving computational efficiency, model-based methods provide prior information and constraints for parameter searches in data-driven algorithms, narrowing down the search scope and reducing computational complexity [41; 42]. Meanwhile, by integrating with model-based methods, physical models can be used to describe the dynamics of some vehicles, simplifying the structure and input-output relationship of data-driven models and reducing the complexity and computational burden of the models. In terms of enhancing physical interpretability, the model-based part integrates the physical laws and dynamic characteristics of the vehicle into the algorithm, making it have clear physical meaning and interpretability. The data-driven part is also constrained and guided by physical laws after fusion, avoiding unreasonable estimation results that violate physical reality, thereby enhancing the credibility and interpretability of the algorithm [43; 44]. In response to the above challenges, this study focuses on the longitudinal tire force estimation problem of 4 WIDEV and proposes a longitudinal force estimation framework that combines data-driven and modified recursive subspace identification algorithms, aiming to balance the interpretability of the mechanism model with the dynamic adaptability of the data-driven algorithm. The research contribution of this paper can be summarized as follows. (1) An electric drive wheel model is constructed, driven data is collected based on the chassis dynamometer experimental platform, and research on a tire longitudinal force estimation method based on a modified recursive subspace identification algorithm is conducted.