## 1 Introduction  
With the rapid development of electric vehicle technology, the in-wheel motor, as a distributed drive component, is more and more widely used. The real-time and accurate acquisition of the vehicle driving state and road adhesion coefficient is also an urgent requirement for achieving active safety control. Due to the high cost of GPS, INS, and road-imaging technology, they are impossible to popularize in the automobile control process within a short time. Therefore, the real-time and accurate estimation of the vehicle driving state and road adhesion information based on distributed drive theory, combined with low-cost sensors, has become a research hotspot concerning the active safety control of in-wheel motor vehicles [1; 2; 3]. The Kalman filter algorithm has the advantage of recursive iteration, which can effectively suppress noise and improve the system accuracy. An extended Kalman filter (EKF) and unscented Kalman filter (UKF) are developed based on the classical Kalman filter algorithm. The Kalman filter method is widely used in the field of vehicle state estimation and road adhesion coefficient estimation [4; 5; 6]. [PERSON] et al. proposed a double radial basis function and extended Kalman filter (DRBF-EKF) method, which can adaptively adjust the network structure [7]. The radial basis function (RBF) neural network structure is improved via a \(k\)-means algorithm, and the EKF is used for noise filtering to improve the estimation accuracy, so as to realize the dynamic joint estimation of the vehicle sideslip angle and road adhesion coefficient. [PERSON] et al. combined the EKF with the limited memory filter to improve the stability and anti-interference properties of the filter, which can effectively estimate the road adhesion coefficient [8]. [PERSON] et al. proposed the method of a parallel UKF. A UKF that can adapt to a strong nonlinear system was used to estimate the vehicle inertia parameters, and a state-parameter joint observation system based on a vehicular parallel double UKF was designed, so that the vehicle still showed a high observation accuracy under heavy-load loading conditions [9]. In order to effectively solve the nonlinear problem in vehicle dynamics, a double unscented Kalman filter (DUKF) was run in parallel, to estimate the vehicle state and other parameters at the same time, and this achieved good results [10]. The EKF truncates the Taylor expansion of a nonlinear function by first-order linearization, ignoring other higher-order terms, and thereby transforming the nonlinear problem into a linear problem. The EKF algorithm may cause filtering divergence when the neglected high-order terms in the Taylor expansion result in significant errors; in addition, because the Jacobian matrix is required in the linearization process of the EKF, the cumbersome calculation process makes the method relatively difficult to implement. The UKF is an algorithm based on the combination of unscented transformation and Kalman filtering. This algorithm mainly uses the idea of the Kalman filter, but when subsequently solving the predicted value and measured value of the target, it needs to apply the sampling point for the calculation. The UKF approximates the n-dimensional target sampling points by designing weighted points, calculates the propagation of these weighted points through the nonlinear function, and obtains the updated filtering value through the nonlinear state equation, to conduct target tracking. The UKF effectively overcomes the EKF's shortcomings of a low estimation accuracy and poor stability. However, it is difficult to ensure the positive definiteness of the state estimation covariance matrix in the calculation process of the UKF, and it is necessary to select a suitable set of parameters in order to obtain the ideal estimation results. The cubature Kalman filter (CKF) is a new nonlinear Gaussian filtering method proposed by Canadian scholars in 2009 [11; 12], which has been widely used in the field of vehicle control [13; 14; 15; 16].