## 1 Introduction
[PERSON] [20] compared EKF and a higher gain observer, the results of which demonstrated that EKF has more robustness and accuracy. [PERSON] et al. [21] proposed the dual EKF, which has two Kalman filters running in parallel to estimate vehicle states and parameters simultaneously. However, the main drawback of the EKF is Jacobian matrices calculation, which requires costly computation. Moreover, EKF only employs the first-order Taylor expansion on a nonlinear system, which may lead to great error or even divergence of the filter if the model is seriously nonlinear. Addressing these issues, the UKF utilizes a deterministic sampling technique known as the unscented transform (UT) to pick a minimal set of sample points (called sigma points) around the mean, which is a derivative-free alternative to EKF and avoids the expensive update of the Jacobian matrix on each iteration. Meanwhile, UKF is able to achieve higher-order Taylor series expansion accuracy [27; 28]. Thus, UKF should be more suitable for vehicle state estimation application in consideration of the high nonlinearity of vehicle dynamics, particularly during critical conditions. [PERSON] and [PERSON] [23] developed a robust method to estimate the tire forces using UKF. Simulation results demonstrated a high convergence rate and good stability properties of the UKF estimator. Based on the piecewise linear tire model, [PERSON] et al. [24] achieved vehicle state estimation with UKF. [PERSON] et al. [25] constructed an UKF observer for the vehicle state using an advanced vertical tire load calculation method. Apart from the Kalman filter methods, MHE is another powerful method able to provide a good solution to nonlinear estimation systems. At each sampling time, MHE estimates the states or parameters by minimizing a cost function over the previous finite time horizon. In addition, constraints can be added to this optimization problem in a very natural way, which makes it possible for MHE to handle constrained processes very well [29]. [PERSON] [30] estimated the friction coefficient in autonomous driving using MHE. [PERSON] [31] proposed an MHE-nonlinear model predictive control (NMPC) framework to control field vehicles using an adaptive nonlinear kinematic model. In this study, to further explore the potential application of UKF and MHE, we compare their performance regarding to convergence, accuracy as well as robustness, for the DDEV state estimation. First of all, a 3-DOFs vehicle model is presented serving for the state estimation. The longitudinal tire force is calculated based on the wheel rotational equation, while the lateral tire force is obtained from a semi-empirical tire model. After that, the estimator designing based on UKF and MHE is described in detail. Simulations are carried out using a 27-DOFs high-fidelity CarSim vehicle model equipped with vehicle stability controller (VSC), which is believed to be accurate enough to inspect the precision of the presented approaches. Furthermore, the accidental error of estimated results is taken into account to test the robustness of the two estimation algorithms. Finally, simulation results are analyzed in terms of tracking accuracy and convergence behavior. The rest of this paper proceeds as follows. Section 2 gives the measurement, control and state vectors of a DDEV followed by a detailed modeling of a 3-DOFs vehicle state estimation model. Estimation algorithms and the implemented procedures are described in Section 3. The computer simulation is conducted under a double lane change (DLC) maneuver, the results of which are compared and analyzed in Section 4. Section 5 concludes the paper.