###### Abstract
In extreme operating conditions, the estimation method based on the nonlinear vehicle dynamics model has a high estimation accuracy [9]. [PERSON] et al., based on the Takagi-Sugeno (T-S) fuzzy model to describe the lateral force of tires, design a T-S fuzzy observer to estimate the vehicle roll state, and use the linear matrix inequalities (LMIs) criterion to prove the observer's stability to solve the nonlinear problem of lateral force of vehicle under large lateral deflection angle working condition [10]. To solve the problem of inertial parameter changes such as the center of gravity position when the vehicle load changes, [PERSON] et al., proposed an algorithm based on smart tires combined with a nonlinear vehicle dynamics model to estimate tire loads and vehicle parameters, which has a higher sampling rate and better robustness in estimating tire loads [11]. [PERSON] et al. proposed an integrated control method for lateral dynamics, combining nonlinear vehicle state and parameter estimation with a second-order differential Kalman filter to build a nonlinear vehicle model capable of accurately estimating the peak pavement adhesion coefficient as well as the sideslip angle under extreme operating conditions [12]. In recent years, more nonlinear estimation algorithms have been used in the field of vehicles. Among them are various Kalman filter derivative algorithms, such as extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF). When the vehicle model is complex, the EKF algorithm has trouble solving complex Jacobian matrices, while the UKF algorithm has high computational complexity. CKF is a Gaussian weighted integral approximation algorithm based on the third-order spherical-phase diameter volume rule proposed by Canadian scholars [PERSON] and [PERSON] in recent years. The square root cubature Kalman filter (SCKF) is an improved algorithm based on the CKF that uses square root approximation recursion to effectively reduce the algorithm's computational complexity while ensuring accuracy, stability, and real-time performance [13,14]. To design the vehicle state observer, which is based on the Kalman filter algorithm, it is essential to have a more accurate mathematical model as well as statistical properties of the known noise; otherwise, the prediction results will have large errors and even divergence in severe cases [15]. [PERSON] et al., used a weighted adaptive sliding window algorithm to adaptively adjust the measurement and process noise matrices of the SCKF algorithm, which has more improved accuracy and robustness than the conventional method [16]. [PERSON] et al. used an adaptive fusion of the estimated and integrated values to accurately estimate the vehicle sideslip angle by considering the sensor's unknown color noise and correcting the integration term [17]. Most literature addressing the problem of statistical noise uncertainty employs adaptive corrections to measure and process noise in order to make accurate predictions. The interacting multiple model Kalman filter method has been widely used in the field of target tracking and extended to many fields such as vehicle state estimation [18; 19]. [PERSON] et al. based work on the framework of an interacting multiple model approach to update the probability of target state estimation and motion model by distance-rate measurement. Combined with SCKF algorithm to cope with the nonlinearity of the measurement equation, the designed IMM-SCKF algorithm has good performance in maneuvering target tracking [20]. [PERSON] et al. designed SCKF with different error covariance matrices based on an interacting multiple model framework in order to solve the uncertainty of the error covariance of the navigation system in vehicle dynamics state estimation, and the results show that the IMM-SCKF algorithm has better accuracy compared with the traditional method [21]. In order to adapt to different vehicle-road system models, [PERSON] et al.