## 1 Introduction  
With the intellectualizing of vehicles, the active safety control system becomes particularly important in ensuring human-vehicle safety. As an important component of this system, the vehicle stability controller can effectively prevent vehicles from sharp steering, sideslip, and overturn when additional yaw moment is needed (e.g., Active steering, anti-collision upon emergency, path planning, tracking control), and thus is critical in guaranteeing human-vehicle safety [1; 2; 3; 4; 5]. Despite the many studies on vehicle stability control, modeling of the vehicle, which is a highly nonlinear system, cannot accurately or quantitatively describe the disturbance caused by parameter perturbation, external environment, and other factors during real-world driving. The sideslip angle, a key parameter of vehicle stability control, cannot be directly determined by sensors given the consideration of costs and thus, is estimated by building observers based on multi-information fusion [6; 7; 8; 9; 10]. If a vehicle model cannot well reflect the real vehicle status or if the measured sideslip angle is largely different from the real value, the vehicle stability control quality will be lowered and vehicle instability cannot be effectively avoided. Determination of the sideslip angle is the basis to develop stability control algorithms. In this field, Kalman filtering and its suboptimal filtering algorithms can well estimate the status of nonlinear systems and thus are widely applied [11]. When the model errors caused by inaccurate estimation of road surface friction are compensated by using sideslip angle speed feedback, the sideslip angle can be computed by combining the variable-structure extended Kalman filtering [12]. Based on the status constraints during estimation, the constrained unscented Kalman filtering was used to determine the sideslip angle by considering the measured noise and nonlinearity of the system [13]. An unscented Kalman filter based on the ANFIS observer was proposed and used to introduce the measurable parameters of the vehicle sensor into the unscented Kalman filter, which thereby computed the sideslip angle [14]. A body sideslip angle adaptive dynamic calibrated variable structure observer based on unscented Kalman filtering was proposed and used to compensate the model uncertainty by using the parameter adaptive unscented Kalman observer. Then the variable structure observer was used to compensate the errors in the strongly nonlinear zone, and thereby the sideslip angle was determined [15]. Based on the Rational tire model, the tire characteristics under different driving conditions were described by online estimation and updating tire parameters, and the sideslip angle was estimated using the extended Kalman filtering algorithm [16]. A novel sideslip angle algorithm integrating deep neural network and nonlinear Kalman filtering was proposed and used to estimate sideslip angle [17]. The above algorithms based on Kalman filtering and its suboptimal filtering algorithms can be well used to estimate the vehicle sideslip angle, but the unscented Kalman filtering algorithms are limited by the low effectiveness for highly nonlinear systems. Moreover, extended Kalman filtering needs to calculate estimating the Jacobian matrix, which is very complex computationally. The adaptive double-layer unscented Kalman filter (ADUKF), because of high filtering precision, is applicable to the status estimation of highly nonlinear systems [18], and thus was selected here to compute vehicle sideslip angle. During the design and development of vehicle stability control algorithms, it is needed to build a dynamic model which can reflect the real vehicles. However, the existing vehicle models cannot accurately represent real vehicles, owing to parameter perturbation, environmental complexity and variability, simplification of modeling, and other factors.