## 1 Introduction  
Automotive energy saving, environmental protection, and safety technologies are the core aspects of the world's automotive technology innovation, and automotive active safety control systems are essential for the future survival and development of automotive enterprises [1]. As one of the new energy vehicles, distributed-drive electric vehicles have become an important direction for electric vehicle development because of their unique advantages and huge development potential in power configuration, transmission structure, handling performance, and energy utilization. Obtaining key operating parameters for distributed-drive electric vehicles is essential to achieving system control, such as the longitudinal velocity, lateral velocity, and yaw rate of the vehicle, etc. However, such key information cannot be directly measured by sensors and other equipment. On the one hand, sensors measuring these parameters are influenced by environmental factors and are too demanding for installation conditions; on the other hand, the presence of non-Gaussian noise in real environments deteriorates the general estimation algorithms. Therefore, it is necessary to use on-board sensors in combination with appropriate algorithms for the estimation and identification of vehicle status [2, 3]. The Kalman filter (KF) algorithm is mostly used in practical estimation. [PERSON], [PERSON] et al. established a KF and recursive least squares method for adaptive observers to accurately estimate the vehicle driving state, but the algorithm design is complicated and has limitations because KF cannot adapt to nonlinear models and the amount of calculation of the least squares algorithm increases gradually with iterative operation [4]. [PERSON] et al. introduced limited memory filtering and random weighting theory in the extended Kalman filter (EKF) for algorithm adaptability. Using the limited memory filter allowsadjusting the weights for old and new data, thus reducing the estimation error caused by inaccurate models, and random weighting theory improves the accuracy of the algorithm by introducing random weighting factors to increase the utilization of new measurements in the filtering system. However, the linearization process of EKF performs Taylor expansion and then rounds off the second-order and higher terms, thus generating truncation errors as well as requiring the computation of a cumbersome Jacobian matrix, which can lead to accuracy degradation and filter scattering under high-dimensional systems [5]. [PERSON] and [PERSON] et al. presented the unscented Kalman filter (UKF) for this issue, which selects sigma sample points based on the Gaussian distribution property, does not need to compute complex Jacobi matrices, does not require linearization of the state equation, does not have truncation error, and offers more accurate and efficient performance [6]. [PERSON] et al. combined [PERSON]'s method with the UKF. By introducing the Huber cost function for real-time correction of measurement noise, the effect of irregular errors and noise is effectively suppressed while obtaining higher observation accuracy [7]. When selecting the sigma sample points of UKF, the average value at the center carries more weight, and its accuracy is very important, while UKF may diverge or decrease in accuracy in high-dimensional state spaces [8]. To solve this issue, [PERSON] and [PERSON] came up with the CKF, which is cubature transformation-based. The CKF is insensitive to dimensional increase and uses the ball cube rule to select the cubature points [9], which overcomes the deficiency that the UKF is not applicable to high-dimensional systems. [PERSON] et al. proposed a robust CKF (RCKF) that corrects the covariance matrix \(P_{\text{zz}}\) from the measurement noise using [PERSON]'s m-estimation method to eliminate outliers, leading to a more stable and robust estimate [10]. [PERSON] et al.