## 1 Introduction  
Safety and energy conservation are two eternal themes for automotive design [1]. Over the past few decades, active safety control has become one of the most effective accident avoidance technologies [2]. Anti-lock braking system (ABS), traction control system (TCS) and electronic stability program (ESP), etc., all key components of the active safety control system [3], rely heavily on accurate knowledge of vehicle states such as vehicle velocity, yaw rate, side-slip angle, tire forces and so on. Furthermore, vehicle state information is crucial not only for safety but also for the energy management system of electric vehicles [4]. Generally speaking, vehicles with standard stability control systems are normally equipped with a steering wheel angle sensor and inertial sensors (INS, including longitudinal and lateral acceleration sensor, yaw rate sensor). As the research subject in this article, distributed drive electric vehicle (DDEV) is an electric vehicle with four independently controllable motorized wheels. This kind of power configuration provides us with many remarkable advantages, such as short transmission chain and high transmission efficiency, precise torque generation, and easy implementation of torque vectoring. More importantly, for our study, DDEV is able to provide us with the accurate torque and rotational speed information of each wheel from the feedback signals of four individual motors [5]. However, the other vehicle dynamics states are still difficult to measure or cannot be measured economically [6]. Notable attempts have been made to work out different estimation approaches. Currently, existing state estimation algorithms are classified into three categories: \"non-model-based\", \"kinematic-model-based\" (KMB) and \"dynamic-model-based\" (DMB) approaches. \"Non-model-based\" approaches mainly include fuzzy logic, support vector machine and artificial neural network, etc. [7; 8; 9; 10], where a vehicle is regarded as a black box and the nonlinear relationship between inputs and outputs is mapped based on a mass of training data. The accuracy of these methods strongly depends on the quality and quantity of the training data. Meanwhile, without vehicle models, this method is difficult to give out a convincing mathematical explanation of the mapping relationship [11]. As for the KMB approach, it does not contain the physical parameters of the vehicle, and therefore this kinematic approach is not affected by parametric uncertainties. [PERSON] and [PERSON] [12] developed a preliminary estimation of the yaw rate using kinematic relationships, and subsequently fed this initial estimate into a nonlinear observer to generate the final estimate of yaw rate. [PERSON] and [PERSON] [13] proposed a vehicle lateral velocity estimator using both physical and kinematic modeling. As for the kinematic part, the estimator has been shown to provide satisfactory performance. However, the drawbacks of the KMB approaches are also apparent. This method only works when the yaw rate is non-zero, because the kinematic model is unobservable when the yaw rate is zero. Additionally, the estimates produced by the kinematic approach are more noisy than those produced by the dynamic-model-based approach [13]. Unlike the aforementioned methods, DMB approaches include specific and detailed vehicle mathematical models as well as physical parameters such as mass, yaw moment inertia, COG (center of gravity) position and so on. The DMB estimation design can be carried out using sliding mode observer [14; 15; 16], Luenberger observer [17; 18], Kalman filter (KF) and its extensions, and moving horizon estimation (MHE), etc. We will provide a more detailed review of the latter two approaches. The Kalman filter [19] is widely applied for linear system estimation under the assumption of Gaussian-distributed state and measurement noise. In the nonlinear case of automobile field, the extended Kalman filter (EKF) [20; 21; 22] and unscented Kalman filter (UKF) [23; 24; 25; 26] take up a large percentage.