## 1 Introduction  
Hybrid electric vehicles have been widely accepted by the industry and the market as green vehicles with fewer emissions [1]. There are some advantages in energy savings and clean transporting. Some research data show that hybrid electric vehicles can mean energy savings of more than 30% and can reduce CO\({}_{2}\) emissions by 15%, compared to traditional vehicles [2]. Energy efficiency can be further improved in the hybrid electric vehicle power train for EVs using in-wheel motors, since there are no mechanical transmission, differential or redundant drive shafts [3]. Moreover, with in-wheel motors,the total torque demand can be distributed to each wheel independently. Intelligent methods for optimal torque distribution are capable of savings of more than 20% in energy consumption. In addition, flexible regenerative braking algorithms with in-wheel motors could further enhance the energy efficiency of EVs [4]. In this regard, consistently improving the performance of EVs equipped with in-wheel motors by applying novel control methods is still very critical and necessary for saving energy and providing clean transportation. The method can decrease traffic accidents and reduce casualties and economic loss [5]. In a vehicle stability measurement system, GPS can be used to detect performance. It can also be used as a sensor to provide real-time information for a vehicle dynamics stability control system [6]. Now, GPS has been applied in vehicle dynamics stability testing instruments, but the study of the GPS/INS combination for the vehicle stability test remains to be improved [7]. There are strong complementarities between GPS and INS. GPS has some disadvantages [8]. For example, a receiver antenna may be blocked temporarily or it may lose position data due to a signal interruption. INS can provide position, velocity and azimuth information without an external reference resource, but the system has accumulated error. It cannot give high-accuracy positioning information for a long time because of gyroscope drift error [9]. Errors of INS are mainly random drift errors, which cannot be compensated. GPS has such advantages as high positioning accuracy and no accumulated error. The two kinds of systems, used in combination, can compensate for each other and give full play to their strengths [10]. GPS measurement is stable, but the refresh rate (1-10 Hz) is relatively low. The GPS/INS integrated navigation system is a kind of composite that has unique advantages in terms of autonomy and bandwidth frequency. The Kalman filter is commonly used to fuse GPS/INS data [11]. [PERSON] [12] has done exploratory studies in reducing failure risk in an integrated vehicle health maintenance system using a fuzzy multi-sensor data fusion Kalman filter approach for IVHMS (integrated vehicle health maintenance system). [PERSON] _et al._[9] at American University estimated three key vehicle parameters, such as the tire-slip ratio, sideslip angle and tire sideslip angle based on the GPS speed measuring method. They used the combination between the GPS speed sensor and the high frequency inertial measurement unit (low update rate accelerometer). A tire cornering stiffness update algorithm was used to improve the Kalman filter. They provided an accurate estimation of vehicle state parameters. In Canada, the Center of Mobile Multisensor Research at Calgary University studied how to suppress the errors and to improve precision in detail [13]. They introduced a navigation system with a velocity update scheme that could predict and reduce the error accumulation when there is a loss in GPS signals. [PERSON] _et al._[14] at Stanford University proposed a method to estimate the key parameters of vehicle stability, based on the fusion of vehicle-grade inertial sensors and the GPS receiver. The method can improve the accuracy of estimation for vehicle state parameters considering the influence of pitch and roll, as well as sensor bias errors. Vehicle sideslip angle and yaw rate are two important parameters for vehicle stability [15].