## 5 Conclusions and Future Work  
This study presented and compared two algorithms, UKF and MHE, for the vehicle longitudinal velocity, lateral velocity, yaw rate, and tire lateral force estimating of DDEVs. Even though today some of these vehicle states can be directly measured by optical sensors or GPS sensors, some practical issues such as cost, accuracy, and reliability inhibit production vehicles from using these sensors at present or in the near future. In contrast, our proposed estimation algorithms are designed based on the information fusion combining feedback signals of electric motors and the existing standard sensor unit equipped in today's typical vehicles. In some vehicle stability controller studies such as [40; 41; 42; 43],  
Figure 13: Estimation performance comparison using UKF and MHE with longitudinal velocity incorrectly initialized. (The red dashed line is estimated by MHE; the black dotted line is estimated by UKF; and the continuous blue line is the reference value). **(a)** Estimated lateral tire force FL under initial guess of longitudinal speed 120 km/h; **(b)** Estimated lateral tire force FL under initial guess of longitudinal speed 80 km/h; **(c)** Estimated lateral tire force RL under initial guess of longitudinal speed 120 km/h; **(d)** Estimated lateral tire force RL under initial guess of longitudinal speed 80 km/h; **(e)** Estimated lateral tire force FR under initial guess of longitudinal speed 120 km/h; **(f)** Estimated lateral tire force FR under initial guess of longitudinal speed 80 km/h; **(g)** Estimated lateral tire force RR under initial guess of longitudinal speed 120 km/h; **(h)** Estimated lateral tire force RR under initial guess of longitudinal speed 80 km/h. it can replace expensive optical or GPS sensors as a cost-efficient way of providing accurate vehicle state information including velocities, yaw rate, sideslip angle, and tire lateral forces. In this article, the mathematical vehicle model was established based on 3-DOFs planar vehicle model with a simplified \"Pacejka 2002\" tire model. Computer simulations are conducted under the emergency DLC test in the co-environment of CarSim and Simulink to evaluate the performance of designed estimators. It is supposed to be persuasive, since during this maneuver vehicle states show large variation. Based on the analysis of the simulation results, our findings are summarized as follows. 1. The estimation results for vehicle states including the longitudinal velocity, lateral velocity, yaw rate, and lateral tire forces, by both UKF and MHE, are satisfactory. 2. Compared with UKF, MHE has better estimation accuracy, especially under serious nonlinear situations. 3. MHE has faster convergence ability and is more robust against an incorrect initial estimate of the longitudinal velocity. As a future research topic, estimation on rolling movement will be taken into consideration, which is of great significance for the rollover prevention control. Furthermore, our prototype vehicle is currently in the design and manufacturing stage. Field tests need to be carried out in the future to verify the proposed estimation algorithms. The work as supported by the BCV project (Berlin City Vehicle Project) of the Technical University of Berlin. The authors would like to thank the China Scholarship Council (CSC) for providing the financial support (201306030007) for [PERSON] to pursue his Ph.D. degree at TU Berlin. We acknowledge support by the German Research Foundation and the Open Access Publication Funds of Technische Universitat Berlin. [PERSON] and [PERSON] proposed the conception and design of this study. [PERSON] provided the resources and software. [PERSON] built the vehicle model and tire model and designed the unscented Kalman filter. [PERSON] designed the moving horizon estimator. [PERSON] and [PERSON] carried out the simulations. All authors conducted the data analysis, discussed the results, and contributed to writing and reviewing the manuscript.