An improved estimation method for vehicle velocity of distributed drive electric vehicle

: In this paper, Simulink and Carsim are combined to study the velocity estimation of distributed drive electric vehicles. Firstly, the minimum co-simulation system is established to complete the design and debugging of the algorithm. Then, a new algorithm combining unscented Kalman filter and strong tracking filter is proposed based on the vehicle estimation model. The accuracy and real-time performance of the velocity estimation algorithm are validated by simulation under snake-shaped driving conditions with different road adhesion coefficients. Finally, an experimental test is carried out to verify the effectiveness of the proposed algorithm in estimating vehicle velocity.


Introduction
The advanced electronic control systems such as electronic stability program (ESP) and acceleration slip regulation (ASR) have been widely used in modern vehicles. One of the necessary conditions for the effective operation of these systems is the state signals of vehicles could be acquired in real-time during driving [1][2].Therefore, how to evaluate the vehicle state parameters accurately and in real-time, including the longitudinal vehicle velocity and lateral velocity, has become a research hotspot [3]. Especially, the development of distributed drive electric vehicles (DDEVs) provides a good convenience for vehicle state parameters estimation.
The methods of vehicle state parameter observation include kinematics-based methods and dynamics-based methods. In kinematics-based methods, the target state variables could be calculated through kinematics relationships between some signals acquired by on-board sensors. In [4][5], the authors extracted the linear speed of wheels directly from the wheel speed sensors, and obtained the estimated value of longitudinal velocity after noise removal. In [6][7][8], the estimated value of lateral velocity was obtained from the relationship between yaw rate and the change rate of lateral velocity. Such methods do not depend on the vehicle models, but require high accuracy of sensors. In addition, the estimation errors are easily affected by wheel slip ratio and road conditions.

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Full list of author information is available at the end of the article The dynamics-based methods describe the vehicle state through some dynamic models, and then use estimation algorithm to estimate target state variables. Kalman filter theory has been widely used in estimation algorithm. In [9][10][11], the single-track and dual-track vehicle models were used as state estimation models. The dual-track vehicle model has high accuracy because it considers the effect of longitudinal driving force on the basis of the single-track model, but its estimation effects are limited by the accuracy of the model of tire forces. In [12], the estimation of velocity was realized by the unscented kalman filter (UKF) based on the three-degree-of-freedom(3-DOF) vehicle model. In [13], the dugoff tire model was added to the vehicle model, and then the extended kalman filter (EKF) was used to estimate the state parameters. Guo et al. [14] proposed an EKF method based on field programmable gate array (FPGA), which improved the estimation accuracy of longitudinal velocity. The effects of these methods depend on the accuracy of vehicle model. Moreover, the real-time tracking ability of the estimation algorithm needs to be improved in the process of drastic velocity change, such as double line-shifting condition and serpentine condition.
In view of improving the accuracy and real-time tracking ability of the velocity estimation method, a combination of strong tracking filter algorithm and UKF is designed based on a simulink/Carsim co-simulation platform for DDEVs. The overall structure of the observation method is shown in Figure 1. Then, a seven-degree-offreedom dynamic model and HSRI tire model are established to calculate the observed state variables, which are then transferred to the velocity estimation algorithm to complete the velocity estimation. Finally, the simulation and experimental tests are carried out to verify the estimation accuracy and real-time tracking performance of the proposed algorithm. Table 1 shows the specifications of the variables and parameters used for the simulations and experimental test.
The minimum co-simulation system 7-DOF vehicle dynamics model Figure 1. The overall structure of the observation method

The minimum co-simulation system
In this paper, Carsim and Simulink are combined to establish the minimum simulation system for velocity estimation. In Carsim the driver model can be directly set to analyze the influence of different driving behaviour on vehicle. At the same time, it can reflect the vehicle's response to different road conditions and air conditions in real time, and reflect the driving state of vehicle [15][16][17]. However, the electric vehicle models have not yet been developed in Carsim , so it is necessary to add the in-wheel motors to its vehicle models.

Model of the in-wheel motor
In [18], the voltage balance equation of in-wheel motor is: The equation of motion is: where: m ω is the angular velocity of in-wheel motor, m J is the moment of inertia, L T is the load torque. B is viscous friction coefficient

Vehicle velocity tracking model
In order to observe the velocity of DDEVs, a velocity tracking model is designed, as shown in Figure 2. In this model, a PID controller is applied. The input of the controller is the difference between the target velocity c V and the current velocity s V . The output signal of the controller is c u . Then the constraints are added to c u to prevent the driving torque from exceeding the maximum torque provided by motor, so, c u is converted to

The combination of simulation software
In order to realize the distributed driving, the torque signals of the four in-wheel motors are used as inputs to the vehicle model, and its outputs are the state parameters such as the steering wheel angle, the wheel speed and yaw rate, which will be used in the estimation algorithm The S-Function module of Simulink is used to realize the communication between the Carsim and the vehicle model.

7-DOF Vehicle Dynamics Model
During the modeling process, the roll motion and pitch motion of the vehicle are ignored, the front track width is considered to be equal to the rear, and the vertical motion of the suspension system is also not considered. Then, the 7-DOF vehicle model [5] shown in Figure 3 is constructed, and its 7-DOF include longitudinal motion, lateral motion and yaw motion, as well as four wheel rotations.
The dynamic equation of wheel rotation is as follows: represent the longitudinal forces of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel respectively, represent the lateral forces of those wheels.

HSRI tire model
The Institute of Highway Safety, Michigan University, USA, has conducted a large number of experiments on the nonlinear characteristics of the tires during vehicle driving, and obtained a semi-empirical tire model with high fitting precision, which is usually called the HSRI tire model. [20] Compared with the magic formula tire model, [21] the calculation amount of this model is less. The expressions are as follows: where µ 、 peak µ are the adhesion coefficient and peak adhesion coefficient, s A is the shape coefficient of tire, 1 C is the longitudinal stiffness of tire, 2 C is the lateral stiffness of tire, H is a function between parameters.
There is a hysteresis effect in the generation of the lateral force, so the relaxation length τ is introduced to describe the transient characteristics. [22] Then the tire dynamic lateral force can be expressed by the following formula: is the lateral force of the tire model under quasi-static condition.
The construction of the HSRI tire model requires the motion parameters such as α 、 s λ 、 z F . The calculation formula of α in [23] are as follows: The vertical loads of each wheel are affected by the longitudinal acceleration, the lateral acceleration and the height of COG. The calculation formula is: The wheel slip ratio during driving is as follows:

velocity Estimation Principle
The dynamic system of vehicle is a nonlinear dynamic Gaussian system. The state equations of the system can be expressed as follows: where f represents the function of the state equation, h is the observation equation function of the dynamic system, ) t ( W is the process excitation noise, and it is a Gaussian white noise. When implementing unscented transformation for Equation (24), the following result can be obtained:  (26) and (27), can be derived from the 7DOF dynamic model and HRSI tire model.
The state variables observed by the observer are longitudinal velocity, lateral velocity, lateral force of four wheels and yaw rate. The state variables measured by the observer are longitudinal acceleration, lateral acceleration and yaw rate. Therefore, q and w can be used to represent the observed state variables and the measured state variables respectively in the velocity estimation method. Their expressions are as follows: In the velocity estimation method, the driving torque, motor speed and front wheel angle can be easily measured. Therefore, the input variables are defined as u , and its expression is as follows: T   u  u  u  u  u  u  u  u  u  T  T  T  T   9  8  7  6  5  4  3  2  1  4  3  2  1  4  3  2 The above formula is simplified by the vehicle estimation model (7 DOF model and HSRI tire model), which results in:   The traditional UKF method has the problems of insufficient adaptive ability and poor robustness when the vehicle state changes sharply and the system model mismatches. [24] Therefore, the strong tracking filtering(STF) theory [25,26]is introduced to UKF to improve the performance of the estimation algorithm.

Algorithm steps
Step 1: Selection of sampling points and initialization of the mean and covariance. a). Selecting 2n+1 sampling points to form a sigma point set, and letting X 、 P respectively represent the mean and covariance of the sampling points.
] c). Calculating the Sigma point set: Step 2: Calculation of the predicted values of mean and covariance. a).Calculating the one-step predictions of 2n+1 Sigma point set.
Step 3: Combination of STF and UKF a) Updating the predictions of mean and covariance by introducing multiple fading sub-optimal factors.
(47) b). By calculating the errors of the predictions of mean and covariance, and the following result can be obtained.
Step 4: Calculation of the predicted error matrix a). The predictions of mean error matrix and covariance error matrix are shown in equations (49) and (50) respectively.
where ρ is the forgetting factor, . By calculating the predictions of mean and covariance based on the STF and UKF, and the following equations can be obtained.
Step 5: Calculation of the gain matrix and update of the system status a). The Kalman filter gain matrix can be expressed as : ). The state update and the covariance update are shown in Equations (54) and (55).

Simulation and Analysis
In order to evaluate the proposed estimation method, the strong tracking filtering algorithm (UKF+STF in figures) and the unscented kalman filter algorithm (UKF in figures) are simulated under different road adhesion coefficients. The 'actual value' in figures represent the variable values output by Carsim. Table 2 shows the values of the vehicle used for the simulations and experimental test. The simulation tests for the snake-shaped driving are carried out, in which the vehicle speed is constant at 50km/h and the road adhesion coefficients are set to 0.3 and 0.8 respectively. Figure 4 and Figure 5 show the simulation results of longitudinal velocity and lateral velocity under high and low adhesion coefficients respectively. respectively. In addition, the UKF method fluctuates sharply during the period of 6.5s~7.0s, 8.0s~8.7s, 8.9s~9.8s. The reason is that the UKF method cannot track the change of vehicle velocity in real time during steering. After introducing STF into estimation method, the estimation of lateral velocity remains stable and the estimation error is kept within 3%; In the estimation of longitudinal velocity, the fluctuation period of UKF method is 5.67s~8.34s, and the maximum error is 0.06km/h. However, the STF method has maintained good tracking ability, and kept the error within 0.02 km/h.
When the vehicle is driving on the road surface with adhesion coefficient of 0.3, the maximum and minimum values of the actual lateral velocity are 0.45 km/h and -0.47 km/h. The values estimated by UKF are 0.49km/h and -0.52 km/h, while the values estimated by the proposed method are 0.47 km/h and -0.48 km/h, which reduces the errors by 0.02 km/h and 0.04 km/h respectively. In addition, the UKF method fluctuates sharply during the period of 7.85s~8.47s. The estimated lateral velocity of the STF method follows the actual value closely, and the error is controlled within 0.015 km/h. The longitudinal velocity estimated by UKF method fluctuates sharply from 4.23s to 8.57s, and the maximum error is 0.07 km/h in this phase, which indicates that this method is not stable enough in estimating the velocity under the low-adherence road. However, the proposed estimation method has excellent performance and the error has been kept within 0.02km/h.
The simulation results show that the proposed method can track the change of vehicle velocity in real time under different road adhesion conditions, and the accuracy and anti-interference ability of this method are better than UKF method.

Test Platform Structure
The test prototype car was refitted into distributed electric drive form. Motor parameters are shown in Table 3. The HC'12.MPC0555 control panel that supports the automatic generation of Simulink code is used as the vehicle controller. The steering angle of the vehicle is measured by the steering parameter measuring instrument (Figure 6-a). The current required to control the motor is measured by the signal collection device (Figure 6-b).
The four-wheel speed signals are obtained by four wheel speed sensors mounted at the wheel (Figure 6-c).
As shown in Figure 6-d, the state parameters such as longitudinal velocity and lateral velocity during vehicle driving are measured by the attitude orientation navigator (model: XW-ADU5630), which are used as the actual value and compared with the estimated velocity of the algorithm to verify the validity and accuracy of the vehicle velocity observer. Figure 6. Signal collection device and its installation form

Validation process
The test site is dry asphalt pavement (adhesion coefficient is 0.8). Considering the limitation of site size and safety, the test path is set to S-shaped and the vehicle speed is controlled at about 50 km/h. The validity of the vehicle velocity observer is verified by comparing the estimated value of the velocity observer with the actual value measured by the state measurement system. Figure 7 shows the steering wheel angle signal of the experimental vehicle. The current signals of four in-wheel motors are shown in Figure 8.

Currents(A)
The left-front motor The right-front motor The left-rear motor The right-rear motor

Results analysis
It is clear that the actual value of longitudinal velocity is 49.98 km/h on average, while the average longitudinal velocity estimated by the velocity observer is 50.02 km/h. The average error during the whole process is 0.024km/h, and the maximum error is 0.03km/h; In the lateral velocity estimation, the average error is 0.016km/h, and the maximum error is 0.022km/h. Apparently, the estimations of the longitudinal velocity and lateral velocity are much closer to the actual values extracted from the state measurement system, which indicates that the velocity observer has a high estimation accuracy and shows that the observer has real-time tracking ability for the process of frequent direction change of vehicle. In addition, the errors at the peak in the figures are relatively large, which is due to the non-linear tire characteristics during vehicle steering, resulting in the deviation of the velocity estimation model in calculating tire force.

Conclusion
Based on the minimum co-simulation system, this paper proposes an algorithm combining UKF and STF to estimate the velocity of DDEVs, which takes the 7-DOF dynamic model and HSRI tire model as estimation models. Compared with the UKF method, the experimental and simulation results illustrate the accuracy and robustness of the proposed algorithm. The vehicle estimation model contains the vehicle dynamics model and the tire force calculation model, which means that it is difficult to distinguish their contributions to the estimation error. It is recommended that the data-driven intelligent tire model be further developed in order to estimate vehicle parameters more accurately.