Vehicle Velocity Estimation based on Data fusion by Kalman Filtering for ABS

Melika Amiri Graduate student in electrical engineering, Islamic Azad

university, Science and Research Tehran, Iran

Melika _ 64@yahoo.com

Abstract: During the braking process, because of difference between the wheel velocity and the linear vehicle velocity, the slip occurred and it is made vehicle to lose steering control and the friction force, which stops the vehicle, is greatly reduced. To solve this problem, the Antilock Break System (ABS) was proposed, which monitors the wheel velocity and the vehicle velocity to detect and control the slip. The main stage in slip evaluation is vehicle velocity estimation and there are several methods for it, where each one has its advantages and drawbacks. In this paper, an analytical and practical solution to estimate the accurate vehicle velocity estimation based on the data fusion algorithms and during the breaking process is developed. Finally, simulation results show the effectiveness of the new methodology.

Keywords: Antilock Break System, Slip Control, Vehicle Velocity Estimation, Datafusion.

I. INTRODUCTION

The main objective of an Antilock Brake System (ABS) is to prevent wheels from locking up and slipping during the braking. Wheel locking up often happens when braking on a wet and slippery road or during a severe braking. During wheel lockup, vehicle loses steering control and reduces the friction force. In normal drive condition, the vehicle velocity is almost same as the wheel velocity. The speedometer calculates and displays the vehicle speed by measuring the wheel rotation velocity and multiplying it with the nominal wheel radius. However, when a wheel becomes locked and slips, the vehicle velocity and the wheel velocity are quite different. In ABS, the wheel slip, A, is defmed to indicate the difference between the wheel velocity and the vehicle velocity.

V-rOJ A= -

v ( 1 )

where v is the actual vehicle velocity over the ground, OJ is the wheel angular velocity and r is the rolling radius (wheel and tire). In normal driving, v = OJr and therefore A = O. In

Bijan Moaveni Assistant Professor, School of Railway Engineering

Electrical Railway, Iran University of Science Technology Tehran, Iran

B _ moavani@iust.ac.ir

severe braking, it is common to have OJ = 0 while v*-O , thus A = 1, which is called wheel lockup [1].

The ABS producers companies only utilize the wheel angular speed from the wheel speed sensors and they don't like to use other sensors to measure the vehicle longitudinal speed. So, it is important to estimate the vehicle longitudinal velocity and wheel angular speed using only measured wheel angular speed for the advanced slip control maneuver of ABS. In recent years, many efforts have been focused on the issue of the vehicle velocity estimation such as linear and nonlinear Adaptive filters, Kalman filer and etc., that each of them have advantages and drawbacks [1,2,3,4,5].

In the 2000s, Adaptive filter [1], as a simple and efficient method introduced that the estimation is solely based on the wheel velocity measurements without any additional information on the vehicle acceleration. This adaptive nonlinear filter method based on the characteristics of the wheel velocities and knowledge of the ABS operation and a heuristic assumption is made. This methodology estimates the vehicle longitude velocity by using of the available data from wheel speed and the ABS operation. The contributors show that the wheel velocities periodically reflect the actual vehicle velocity. But, since the road surface conditions and the vehicle deceleration are unknown to begin with, the estimation error seems inevitable when the ABS is first applied. Although, in results of nonlinear Adaptive filter experiments mentioned that primer error is inevitable, but as in this article can be seen, this problem is one of the drawbacks of the method and unfortunately, there is a lot of distortions and fluctuations in vehicle velocity estimation [6].

Another main method in velocity estimation of vehicles is Kalman filtering method. Although, this method can provide more accurate estimation and convergent to real velocity, but there is a high transient error [2],[6].

In this paper, by studying and analyzing the performance of Kalman filter and nonlinear Adaptive filter to estimate linear velocity, a new solution is presented to reduce fluctuations and distortion, without complex calculations and the problems of the previous methods. In other words, this paper presents proper structure of data fusion with the ability to improve the estimation of vehicle velocity.

978-1-4673-1148-9112/$3l.00 2012 IEEE 1495

II. VEHICLE DYNAMIC BASED ON THE LUGRE MODEL

One of the current models on vehicle dynamic, with considering the friction is LuGre model where all researchers and engineers use it as a powerful model in all of the speed estimation methods [7]. The LuGre model can describe the nonlinear friction characteristics, which is required between two level contacts. Many researchers have used this model because it has a simple structure to be implemented in the design of the controller and can represent most of the friction characteristics. A quarter-vehicle model with the average lumped LuGre dynamic tire friction model was adopted to design the observer as shown in Fig. 1.

v m

Figure l . A quarter-vehicle model [2]

The equations of the quarter-vehicle based on the LuGre model are [8]:

(Jo IVr I i =-v -8 ---z r h (vr ) J OJ = -rFx -uT

(2)

where z is the LuGre friction internal state, vr = V -rO) is the relative velocity, 8 is an unknown parameter of the tire/road condition, which can suitably describe the road characteristics. Also Ils is the normalized static friction coefficient, Ilc is the normalized Coulomb friction, v s is the Stribeck relative velocity, uT is the braking torque, J is the rotational inertia of quarter vehicle mass and m is the vehicle mass. Also, the braking force can be expressed as a follow:

where (Jo is the nonnalized rubber longitudinal lumped stiffness, (Jl is the nonnalized rubber longitudinal lumped damping, (J2 the nonnalized viscous relative damping, Fn is the rolling resistance and (Jv is rolling resistance coefficient.

III. VELOCITY ESTIMATION

In this section, we briefly review the mam methods m vehicle velocity estimation.

A. Adaptive Nonlinear filter In this method, the velocity estimation is solely based on

the wheel velocity measurements. In nonnal drive condition, the vehicle velocity is ahnost same as the wheel velocity and in designing filter, the input of filter is wheel angular speed multiplies with the nominal wheel radius and the output is linear vehicle velocity. However, during the wheel lockup or near lockup situation, this relationship no longer holds.

In [1], a nonlinear filter as (5) was presented.

v'(t) = -Rgsign(v (t)-rm(t))

y (t = 0) = Y o

(5)

In (5), met) is the input and vet) is the output. Rg is an

adjustment parameter of filter sensitivity and Yo is the initial value of the speed while braking. The output vet) will converge to the input rm(t) in steady state. The change of vet) is limited by Rg. When vet) represents the actual vehicle

velocity, the change of v(t) reflects the road surface condition. In implementations, the value of Rg, which limits the change

of v(t). is continuously updated. It makes the nonlinear filter adaptive to the road surface changes. An initial value of the parameter Rg , is selected to reflect the maximum vehicle deceleration.

B. Kalman Filter Approach The Kahnan Filter (KF) is one of the most widely used

methods for tracking and estimation due to its optimality, tractability and robustness. KF is a recursive predicted filter

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based on state techniques and recurrent algorithms. In fact, this filter is the collection of mathematical equations to estimate effective state for a dynamic system. The performance of dynamic system can disrupt with some white noises. For a linear noisy system as below

XK+I =AKXK+WK ZK+I =HK+IXK+I +VK+I

We have KF equations as (7) [10].

A A

XK+I1K =AKXK1K T

PK +IIK = AK PK +IIK AK + Q

(6)

KK+I =PK+IIKHk+I(HK+IPK+IIKHk+1 +RK+1)-1

XK+IIK+I =XK+11K +KK+I(ZK+I-HK+IXK+IIK) PK+IIK+I = (1-KK+IH K+I)PK+I1K

(7)

IV. VEHICLE VELOCITY ESTIMATION USING DATA FUSION STRATEGY

Data fusion is a research area that is growing rapidly due to the fact that it provides means for combining pieces of information coming from different sources/sensors, resulting in ameliorated overall system performance (improved decision making, increased detection capabilities, diminished number of false alarms, improved reliability in various situations at hand) with respect to separate sensors/sources[ll]. Different data fusion methods have been developed in order to optimize the overall system output in a variety of applications. There are a lot of various methods for multi sensor data fusion that using Kalman filter in the data fusion process [12]. In this section, a new method to estimate the vehicle velocity based on the data fusion are presented.

A. Series Fusion In this method, we use the speeds of two wheels of vehicle

as the inputs to the data fusion algorithm. In order to, estimated speed from Adaptive filter ( va ) as the initial conditions of vehicle velocity in the first Kalman filter and the estimated speed from the first Kalman filter (VI) as initial conditions of second KF as series is used. Note that the simple block diagram of this method is shown in Figure 2.

First wheel

" Measurement V Fusion

Figure 4. block diagram of measurement fusion

v. SIMULATION RESULTS In all simulations, LuGre model and following parameters

are used [8]:

m =1701.1kg,r =0.323m,8=1.

TABLE I. VEHICLE PARAMETERS[9]

Parameter Value Unit Parameter Value Unit

(Jo 40 [Ijm] f..Lc 0.5 [-]

(Jl 4.9487 [s / m ] f..L.,. 0.9 [ -]

(J2 0.0018 [s/m] Vs 12.5 [m/s]

parameter of Kalman filter are as below[2]: W k ,V k are Gaussian white noises that added to equations.

Q = diag([10-6 10-6 10-4 D,

Po =diag ([10-6 10-6 10-6D,

;0 =[0 vi va l E[Wk]=[O 0 of.

R = 1, Vo = 22.5 ,

r= 0.35 m,

In simulation of Adaptive filter, we used a quarter-vehicle LuGre model and all parameters as defined in section 2. Here, the value of R g = 6 is adjusted. Figure 5 shows the real and estimated speeds during a braking process, while we use of ABS. It is obvious that the estimated velocity is convergent to the real speed, but there are a lot of distortions and fluctuations. For more accurate investigation, Figure 6 shows the estimation error.

For Kalman filtering strategy, in the simulation a quarter -vehicle LuGre model is considered. Simulation results are shown in figure 7. Figure 8 shows the corresponding estimation error and clearly the value of error in early moments is much and after a few seconds has a swing around zero. But, in simulation of data fusion, we use the half-vehicle LuGre model. Simulation result of series fusion method is existed on figures 9 and 10. Figure 9, shows the good result of estimation and the estimated velocity convergent to real speed well. Also,

figure 10 shows that the amount of estimation error is too small.

Tn figure 11, the simulation result of mean filter method to estimate the vehicle velocity is demonstrated. The figure shows the converging estimated to the real speed. as the result and this method to be ok for vehicle velocity estimation without considering the value of error in early moments. With considering Fig 12, the value of error in early moments is seen. The error of series in comparison with mean filter error is very little. The applied calculations in this method are easy and this the main advantage of the mean filter approach, while it has much error than series fusion method.

Figure 13 shows the speed estimation of measurement fusion method which converges to the real speed except of early moments. Figure 14 prove that error in early moments is large. It is worth noting that in the simulation, we consider the different speeds from two wheels.

To analyze the simulations result, in table 2 the mean square of estimation errors for all estimation methods are introduced. The results show that the series fusion approach has the best performance.

] .f (.) o a:l :>

adaptiwfilter

time (Sec)

Figure 5. real speed and estimated speed with Adaptive filter

Figure 6. error diagram in Adaptive filter

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KF with r = 0.323

--""l

time(sec)

Figure 7. curve of real and estimated speed with KF

o

o

l \1\, o

_-_ --- ---

-0.15

-0.20::---C----cc1O--c,5c--c20:-2"c5- 30Cc----cc35--c40:--c45:-50 time(soc)

Figure 8. error diagram in KF

- \llat,

tIs]

F ignre 9. speed estimation of series fusion method

tIs]

Figure 10. error diagram of series fusion

awrage !user

->hat1

- >hat

Figure 11. speed estimation vhat with mean filter method

c L ---o---ce-Cc--e,,,ec, --=-,e-, ---cc"---c"c--l,, timers",,)

Figure 12. error diagram of mean filter method

v,

Figure 13. Speed estimation of measurement fusion

I '5 20 25 30 35 40 45 50

Fignre 14. error diagram of measurement fusion

TABLE II. MEAN SQUARE ERROR (MSE) OF ESTIMATION METHOD

Method MSE Series fusion 7.2xI0-R

Measurement fusion 2.08

Mean filter method l .01 Adaptive filter 0.1755 Kalman filter 5. 32

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VI. CONCLUSION

In this paper, we present a new velocity estimation approach based on the data fusion theory. Here, we introduce the three novel structures to access the high accuracy in vehicle velocity estimation. By analyzing and comparing the results, series fusion method has the best operation in all methods. This method solves the the problems like distortion and fluctuations of Adaptive filter and primer error of Kalman filter.

REFERENCES

[1] Fangjun Jiang , Zhiqiang Gao, "An Adaptive Nonlinear Filter Approach to the Vehicle velocity Estimation for ABS"IEEE Transaction on Automtic control,pp.490-495,Sep.2000.

[2] Deng Kun, Li Kaijun, and Xia Qunsheng ,"Application of Unscented Kalman Filter for the State Estimation of Anti-lock Braking System, "IEEE,Tshinghua University,Sep. 2006.

[3] Kazuyuki Kobayashi et al, "Estimation of Absolute Vehicle Speed using Fuzzy Logic Rule-Based Kalman Filter", Proceedings of the American Control Conference, Seattle, Washington, June 1995, p 3086-3090.

[4] Tianjun zhu, Hongyan Zheng, "Aplication ofUnscented Kalman Filter to Vehicle State Estimation"ISECS International Colloquim on Computing Communiccation,Control and Management ,2008

[5] ADaiB,U.Kiencke, "Estimation of vehicle Speed Fuzzy-Estimation in comparison with Kalman-Filtering",IEEE,University of Karlsruhe,Institude for zindustrial Information System, 1995

[6] Amiri melika, "designing of optimum filtering structure in order to linear speed estimation of vehicle for ABS" thesis of MA, Islamic azad university science and research, 2011,p 22-35

[7] Han Me Kim , Seong Ik Han and Jong Shik Kim, "Precision position control of servo systems using adaptive back-stepping and recurrent fuzzy neural networks", Journal of Mechanical Science and Teclmology 23 (2009) 3059-3070.

[8] Jingang Yit, Luis Alvarezt, Xavier Claeysf, Roberto Horowitzq and Carlos Canudas de Wit, " Emergency Braking Control with an Observer-based Dynamic Tire/road Friction Model and Wheel Angular Velocity information ," Proceedings of the American Control Conference Arlington, VA June 25-27, 2001.

[9] Carlosc Anudast E Wit, C Dynamic Tire Friction Models for Vehicle Traction Control," Proceedings of the 38th Conference on Decision & Control Phoenix, Arizona USA December 1999.

[10] AH. Jazwinski, " Stochastic Processes and Filtering Theory" Academic Press New York, 1970.

[11] Dr.IR.Nadaa Milisavljevic, "Sensor and Data fusion "books in Croatia, fist published February 2009

[12] 1. R. Raol, Multi-sensor data fusion with MATLAB, Taylor and Francis, 2009.

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