Vehicle Position Estimation

Using Vehicle Dynamic Model

Jaewoo Yoon1 and Byeongwoo Kim2,

1 44610 Graduate School of Electrical Engineering, University of Ulsan, 93 Daehak-ro,

Ulsan, Korea jewos0127@gmail.com

2 44610 School of Electrical Engineering, University of Ulsan, 93 Daehak-ro, Ulsan, Korea bywokim@ulsan.ac.kr

Abstract Accurate vehicle positioning information is essential reliable operation of advanced driver assistance systems (ADAS). Conventionally, fusing information by attaching an inertial measurement unit (IMU) to the outside of the vehicle with GPS is widely used for this purpose. However, because a linear tire model is used as the dynamic model for positioning estimation, most methods have low vehicle positioning accuracy during high speed driving. This paper proposes a position estimation algorithm that rectifies this problem. The proposed algorithm is equivalent to a high-precision DGPS but fuses information from the inexpensive GPS in the vehicle and vehicle status information acquired from modules such as electronic stability control (ESC) and electric power steering (EPS) via controller area network (CAN) communication and extended Kalman filter (EKF) without a special linearization process.

Keywords: advanced driver assistance system, localization, nonlinear tire model

1 Introduction

In recent years, studies on advanced driver assistance systems (ADASs) have been actively conducted by major automotive manufacturers in Korea and overseas [1]. For stable operation of ADAS, it is very important that timely and accurate vehicle position information is obtained. The most widely used method to obtain vehicle position information is the global positioning system (GPS). Using GPS information, the position, speed, and time of a vehicle can be acquired. However, using a GPS has some limitations in that satellite signals are often interrupted and the accuracy of positioning information is very low in downtown areas, mountainous regions, and tunnels. To overcome these limitations, a number of studies on information fusion technology, in which sensors such as inertial measurement units (IMUs) are attached to fuse various pieces of information, have been conducted [2-3].

Kalman filter (KF) and extended Kalman filter (EKF), which can be applied without special linearization even if nonlinear models are utilized, have been used to

Advanced Science and Technology Letters Vol.118 (Electrical and Electronic Engineering 2015), pp.32-36

http://dx.doi.org/10.14257/astl.2015.118.07

ISSN: 2287-1233 ASTL Copyright © 2015 SERSC

fuse information obtained from various sensors. In EKF models, various types of vehicle dynamic models are used. However, most existing vehicle models employ a linear tire model, which results in the models not being able to estimate the vehicle’s position accurately because they cannot accurately simulate a tire slip during high speed driving [2-3].

Most vehicles on the market in recent years come equipped with electronic stability control (ESC) and electric power steering (EPS) modules and their speed, acceleration, and steering angle can be acquired via controller area network (CAN) communication. Consequently, this paper proposes a position estimation algorithm that uses inexpensive satellite navigation systems and vehicle status information obtained via CNA communication. In addition, a very accurate position estimation algorithm that utilizes a nonlinear tire vehicle model is applied to the EKF algorithm. Finally, efficacy of the proposed algorithm was evaluated using the commercial automotive simulation model (ASM) program from dSPACE Company.

2 Vehicle Position Estimation Algorithm

2.1 Vehicle Dynamic Model

In this study, a bicycle model, which approximates both right and left wheels as a single wheel, was used as the vehicle dynamic model, as shown in Fig. 1. Eq. (1) shows the equation of motion of this vehicle dynamic model with three degrees of freedom, considering longitudinal, lateral, and yaw directions from the center of gravity.

rff

rff

rff

yryxf

z

xyyxy

yxyxx

FlFFlI

vFFFm

v

vFFFm

v

cossin1

cossin1

sincos1

(1)

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34 Copyright © 2015 SERSC

Fig. 1. Dynamic vehicle model

2.2 Nonlinear Tire Model

A tire is characterized by strong nonlinearity; therefore, it should be modeled using a simple physical model for accurate experimental results. Because it has very strong nonlinearity, it is modeled through repetitive experiments. Although various tire models have been proposed, this study employed a tire model proposed by Dugoff to calculate the force of the tire in the longitudinal and lateral directions [4]. Using a few variables, the Dugoff tire model yields a performance similar to the results of a real test. The Dugoff tire model can be expressed using Eqs. (2)–(4):

i

i

i

y

i

i

i

x

fCF

fCF

i

i

1

tan

1 (2)

where,

1,1

1,2

i

iii

iif

iff

ii

zi

i

CC

Fi

2222 tan2

1

(3)

C and

C are the respective tire stiffness in the longitudinal and lateral directions,

is the friction constant between tire and road surface, and i

and i

are the slip angle of the tire in the longitudinal and lateral directions, respectively.

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Copyright © 2015 SERSC 35

2.3. Position Estimation Algorithm

A vehicle’s position is estimated using the vehicle dynamic model, nonlinear tire model, and the EKF [5]. The equation of state in the EKF and the measurement equation is shown in Eq. (4):

Tyxk

vyvxx

TIMUyxGPSGPSk

IMUIMU

aayxz

(4)

3 Simulation and Results

A driving test was conducted at 72 km/h (20 m/s2) maximum speed on a 2510 m-long Hockenheimring track. To ensure a large tire slip, we set the acceleration in the longitudinal and lateral directions to a maximum of 5 m/s2. In addition, noise was added to the vehicle location, acceleration, and yaw information to create a test environment similar to that of real driving. The simulation results showed that the algorithm proposed in Fig. 2 estimated the reference signal more accurately than the GPS did. The location error at each axis was also found to be within ±1 m, as shown in Fig. 3.

Fig. 2. X-Y (east-north) vehicle position trajectory

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36 Copyright © 2015 SERSC

0 20 40 60 80 100 120 140 160 180-1.5

-1

-0.5

0

0.5

1

1.5

time [s]

X(E

ast)

Posi

tion

Erro

r [m

]

0 20 40 60 80 100 120 140 160 180-1.5

-1

-0.5

0

0.5

1

1.5

time [s]

Y(N

orth

) Pos

ition

Erro

r [m

]

(a) (b)

Fig. 3. Estimated vehicle position error: (a) X (east) position error, (b) Y (north) position error

4 Conclusion

In this paper, a vehicle position estimation algorithm was proposed for reliable operation of ADAS. The proposed algorithm estimates a vehicle’s position using the vehicle’s internal sensors, inexpensive satellite navigation devices, a vehicle dynamic model, a nonlinear tire model, and EKF. The results of simulations conducted via a commercial program using the proposed algorithm showed that the position errors for each axis were within ±1 m.

Acknowledgments. This research was supported by the MSIP(Ministry of

Science, ICT and Future Planning), Korea, under the C-ITRC(Convergence

Information Technology Research Center) (IITP-2015-H8601-15-1005) supervised by

the IITP(Institute for Information & communications Technology Promotion).

Following are results of a study on the "Leaders INdustry-university Cooperation"

Project, supported by the Ministry of Education (MOE).

References

1. An, K.H., Lee, S.W., Han, W.Y., Son, J.C.: Technology trends of self-driving vehicles, Electronics and Telecommunications Trends, 24, 35–44 (2013).

2. Rezaei, S., Sengupta, R.: Kalman filter-based integration of DGPS and vehicle sensors for localization, IEEE International Conference on Mechatronics & Automation, vol. 1, pp. 455–460, Niagara Fall (2005).

3. Jo, K., Chu, K., Sunwoo, M.: Interacting multiple model filter-based sensor fusion of GPS with in-vehicle sensors for real-time vehicle positioning, IEEE Transactions on Intelligent Transportation System, 13 (1), 329–343 (2013)

4. Dugoff, H., Fancher, P.S., Segel, L.: An analysis of tire traction properties and their influence on vehicle dynamics performance. SAE, 700377 (1970)

5. Kalman, R.E.: A new approach to linear filtering and prediction problems. Trans. ASME-J. Basic Eng., 82, 35–45 (1960)

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