## 4 Result Verification
Next, quantitative statistical analysis was used to calculate the average estimation error and mean square error of the two algorithms under variable speed sinusoidal steering conditions. The results are shown in Table 2. According to the comparison data of the dual index evaluation system presented in Table 2, in the simulation scenario of variable speed sinusoidal steering, the estimation results under the C-SIR algorithm show an increasing error in the dynamic estimation of longitudinal tire force. Without considering noise and interference, the average error of the longitudinal tire force estimation value remains at the level of 2.3588, while the mean square error quantification index, which characterizes the fluctuation of the error, reaches 1.2069. In the same situation, the average estimation error and mean square error under the CFF-SIR algorithm are 1.1684 and 0.5311, respectively, which are significantly lower than the estimation results under the C-SIR algorithm overall. In addition, when considering noise, the average estimation error and mean square error under the C-SIR algorithm are 2.8692 and 1.7646, respectively, while the average estimation error and mean square error under the CFF-SIR algorithm are 1.2639 and 0.8682, respectively. When considering interference, the average estimation error and mean square error under the CFF-SIR algorithm are 2.9902 and 1.5006, respectively, while the average estimation error and mean square error under the CFF-SIR algorithm are 1.3417 and 0.5934, respectively. The comparative data confirms that the algorithm improvement not only significantly  
Figure 8: Estimation results of longitudinal tire force under sinusoidal steering condition. (**a**) Without noise and interference effects, (**b**) with noise effects, (**c**) with interference effects. improves the accuracy of the estimation results but also effectively controls the degree of deviation of the estimation results throughout the day, highlighting the applicability of the CFF-SIR algorithm in complex scenarios. On the basis of verification on the joint simulation platform, further use of chassis dynamometer test data would verify the longitudinal tire force estimation effect. During the model validation process, using an independent dataset for validation is crucial to ensuring the reliability of the model. By isolating training data from validation data, the simulation model can objectively evaluate its generalization ability by simulating unknown scenarios that it may face in the future. When the model performs well on the training data, it indicates that the model may have only excessively captured the noise or specific patterns in the training set, rather than truly representing the patterns behind the data. And independent datasets can force models to confront the complexity of the real world. Therefore, an independent dataset from chassis dynamometer testing was used to validate the longitudinal force estimation model. The D2P MotoHawk rapid prototyping system is a development environment that integrates standard ECU hardware and Matlab/Simulink(R2014a) software, providing a complete solution for motor drive control. The platform directly adopts mature ECU hardware architecture, saving users the workload of developing hardware on their own. During the experiment, using the vehicle dynamics model constructed by MotoHawk, researchers were able to simulate the complete driving conditions of the vehicle from stationary acceleration to constant speed under different throttle opening conditions. The experimental system is equipped with multiple measuring devices: current/voltage sensors installed at the hub motor monitor the electrical parameters of the controller input in real time; the speed measurement is achieved using the gear pulse counting method; the tire force data is collected and processed by a professional chassis dynamometer system. All measurement data and control instructions are transmitted and stored through the CAN bus, with the Vehicle SPY tool specifically responsible for recording bus data.