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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 13, NO. 1, MARCH 2012 329
Interacting Multiple Model Filter-Based Sensor
Fusion of GPS With In-Vehicle Sensors for
Real-Time Vehicle Positioning
Kichun Jo, Student Member, IEEE, Keounyup Chu, Student Member, IEEE, and Myoungho Sunwoo, Member, IEEE
Abstract—Vehicle position estimation for intelligent vehicles
requires not only highly accurate position information but reliable
and continuous information provision as well. A low-cost Global
Positioning System (GPS) receiver has widely been used for con-
ventional automotive applications, but it does not guarantee accu-
racy, reliability, or continuity of position data when GPS errors
occur. To mitigate GPS errors, numerous Bayesian filters based
on sensor fusion algorithms have been studied. The estimation
performance of Bayesian filters primarily relies on the choice of
process model. For this reason, the change in vehicle dynamics
with driving conditions should be addressed in the process model
of the Bayesian filters. This paper presents a positioning algorithm
based on an interacting multiple model (IMM) filter that inte-
grates low-cost GPS and in-vehicle sensors to adapt the vehicle
model to various driving conditions. The model set of the IMM
filter is composed of a kinematic vehicle model and a dynamic
vehicle model. The algorithm developed in this paper is verified
via intensive simulation and evaluated through experimentation
with a real-time embedded system. Experimental results show that
the performance of the positioning system is accurate and reliable
under a wide range of driving conditions.
Index Terms—Information fusion, interacting multiple mode
(IMM) filter, in-vehicle sensors, vehicle positioning.
I. INTRODUCTION
THE IMPORTANCE of accuracy and integrity in a po-
sitioning system has increasingly been emphasized for
intelligent transportation system (ITS) applications based on
position information, including advanced driver-assistance sys-
tems, electronic toll collection, intersection collision warnings,
and traffic control. Today, the satellite-based Global Positioning
System (GPS) is widely used for such applications because
Manuscript received October 13, 2010; revised June 29, 2011 and
September 16, 2011; accepted September 18, 2011. Date of publication
December 6, 2011; date of current version March 5, 2012. This work was
supported in part by the National Research Foundation of Korea funded by the
Korean government under Grant 2011-0017495, by the Ministry of Knowledge
Economy, by the Korea Institute for Advancement in Technology through the
Workforce Development Program in Strategic Technology, by the Ministry of
Education, Science, and Technology through the BK21 Program under Grant
201000000000173, and by the Industrial Strategy Technology Development
Program of the Ministry of Knowledge Economy under Grant 10039673. The
Associate Editor for this paper was M. Da Lio.
K. Jo and K. Chu are with the Automotive Control and Electronics
Laboratory (ACE Lab), Department of Automotive Engineering, Hanyang
University, Seoul 133-791, Korea (e-mail: jokihaha@hanyang.ac.kr; acehev@
hanyang.ac.kr).
M. Sunwoo is with the Department of Automotive Engineering, Hanyang
University, Seoul 133-791, Korea (e-mail: msunwoo@hanyang.ac.kr).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TITS.2011.2171033
the GPS receiver provides vehicle position and velocity data
in global coordinates. However, a standalone GPS receiver
cannot fulfill the positioning requirements of ITS applications
due to the occasional temporary loss of satellite connection
and signal errors. To provide continuous, accurate, and high
integrity position data, the positioning system should be aided
by additional sensors such as an inertial navigation system
(INS), vehicle motion sensors, digital road maps, cameras,
radar, or laser scanners [1].
The fusion of GPS data with data from INS is a common
solution for positioning systems due to the complementary
natures of these two types of sensors [1]–[9]. However, the in-
stallation of an INS requires extra cost and effort, and accurate
INS systems are too expensive for automotive applications. On
the other hand, passenger cars equipped with a vehicle stability
control system already utilize vehicle motion sensors such
as wheel speed sensors, a yaw rate sensor, an accelerometer,
and a steering sensor [10]–[12]. In addition, the accuracy and
reliability of these in-vehicle sensors are increasingly being
developed for multiple safety and comfort applications [13],
[14]. Therefore, the fusion of data from in-vehicle sensors with
GPS data becomes sufficiently accurate and reliable for the
vehicle positioning system without additional cost or sensor
installation. Information regarding the external vehicle environ-
ment from vision sensors, radar, and laser scanners can also be
used with the data from the positioning system by integrating
the information into a digital map that has highly accurate road
features [15]–[27].
Numerous Bayesian filter-based sensor fusion approaches
have been proposed for use with the positioning algorithm [28].
The extended Kalman filter (EKF) is the most widely used for
information fusion algorithms because nonlinear localization
problems can easily be solved using this filter [10]–[12], [29].
Although the EKF provides efficient and reliable performance
for practical applications, the linearization process can lead
to divergence in a highly nonlinear system. To prevent this
problem, advanced nonlinear filtering methods such as the par-
ticle filter were introduced [30]. However, this method requires
excessive computational power to be implemented in embedded
systems.
The performance of a positioning system depends not only
on the filter structure but also on the appropriate choice of
process model for the Bayesian filter. The roles of the process
models in positioning systems were investigated in [31], which
demonstrated significantly better performance for a positioning
algorithm that had a good process model compared with that of
1524-9050/$26.00 © 2011 IEEE
330 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 13, NO. 1, MARCH 2012
Fig. 1. Overall architecture of the IMM-based positioning system.
an algorithm with a poor process model, despite the use of the
same sensor suites and number of states in all algorithms.
The major problem is that it is very difficult to choose
an optimal model for all driving conditions. Higher-order ad-
vanced vehicle models that can account for various driving
conditions are not suitable for positioning systems because of
the unobservability of some of the parameters and the heavy
computing load in real-time embedded systems. To adapt the
vehicle model for application under variable driving conditions,
an innovation-based adaptive estimation technique such as an
input estimation method and a variable state dimension ap-
proach is proposed [32]. However, this method is complicated
and inefficient.
As an alternative, the multiple model (MM) approach was
proposed. This approach assumes that the system follows one
of a finite number of different models. The possible vehicle
driving patterns are represented by a set of models, and vehicle
state information is obtained by combining specific model
filters. Among several MM estimate methods, the interacting
MM (IMM) estimator is the most popular due to its high perfor-
mance and low computational power [32]–[34]. Therefore, the
IMM filter has been used for localization and tracking problems
in several studies [5], [8], [35]–[37]. In those studies, the MM
filters contributed to adapt the different maneuvering states.
The MM set that consists of maneuvering and nonmaneuvering
states originated from the object target tracking applications
that cannot directly inform the target maneuvering information
[34], [38]. However, the information of maneuvering conditions
of ego-vehicle can be obtained immediately from steering sen-
sors and wheel speed sensors. In the ego-vehicle positioning,
the estimation of vehicle motion aided by in-vehicle sensors
will improve the performance of positioning [39]. Therefore, in
this paper, dynamic vehicle characteristics such as lateral force
and tire slip angle are integrated into the MM set.
This paper presents an IMM filter-based positioning algo-
rithm that considers the variety of driving conditions in which a
vehicle can be operated. To adapt to changing vehicle dynamic
characteristics under various driving conditions, the MM set of
the IMM filter includes both kinematic and dynamic vehicle
models. While the kinematic vehicle model is appropriate for
low speeds and small wheel slip driving conditions such as
those in an intersection or parking lot, the dynamic vehicle
model is suitable for high speeds and large wheel slip con-
ditions, such as experienced in normal traffic and highway
conditions. The IMM filter weights the appropriate vehicle
model according to the driving conditions using a stochastic
process. Therefore, the IMM filter-based positioning system is
able to provide better accurate positional information than can
single model filter-based positioning algorithms under various
driving conditions.
The rest of this paper is organized as follows. Section II
discusses the overall system architecture. Next, the system
model set is defined in Section III. In Section IV, the IMM
filter is described. The simulation and experimental results are
presented in Sections V and VI, respectively, and conclusions
are offered in the final section.
II. SYSTEM ARCHITECTURE
Fig. 1 describes the overall architecture of the proposed
positioning system that is classified into a sensor part and a
positioning algorithm part. The sensor part is composed of a
group of in-vehicle sensors and a low-cost GPS receiver. Cur-
rently, many passenger cars are equipped with a vehicle stability
control system and a GPS-based in-car navigation system. The
essential components of the vehicle stability control system
include several vehicle motion sensors, such as a yaw rate
sensor, an accelerometer, wheel speed sensors, and a steering
angle sensor. The vehicle motion data from the sensors can
easily be obtained from in-vehicle sensor networks, such as
the controller area network (CAN). Therefore, the positioning
algorithm that estimates the vehicle position by combining the
vehicle motion data with GPS can immediately be implemented
in such passenger vehicles.
A low-cost GPS receiver that has widely been used for in-
car navigation applications allows for the determination of
global positioning and velocity estimates of a vehicle with a
bounded error. However, although a GPS can provide absolute
positional information, the measurement frequency is low and
discontinuous. Furthermore, signals from a GPS are affected by
JO et al.: IMMFILTER-BASED SENSOR FUSION OF GPSWITH IN-VEHICLE SENSORS 331
Fig. 2. Kinematic vehicle model. This model assumes no tire slip between the
wheels and the ground.
the external environment. In contrast, vehicle motion sensors
provide continuous measurements and are not affected by the
external environment; however, they are prone to integral errors
due to sensor drift. The complementary features of the two
types of sensors permit the positioning systems to achieve in-
creased update rates, accuracy, and integrity due to application
of the information fusion algorithm.
In the positioning algorithm, the IMM filter-based infor-
mation fusion algorithm calculates the position and heading
angle estimates by combining the data from GPS and in-vehicle
motion sensors. The vehicle model set of the IMM filter is
composed of a kinematic vehicle model and a dynamic vehicle
model. The kinematic vehicle model is based on the assumption
of no wheel slip. This model is suitable for low-speed and
low-slip driving conditions, such as those in an intersection or
a parking lot, because the process noise of the lateral force
of the vehicle does not affect the filter estimation process.
However, under high-speed and large wheel slip driving con-
ditions, the assumptions of the kinematic vehicle model break
down, resulting in poor estimation performance. Therefore, the
dynamic vehicle model, which considers lateral tire force and
vehicle moments, can be applied to these types of situations.
By combining estimates from individual model-based EKFs
using the interacting process of the IMM filter, the positioning
system improves the accuracies of positional and heading angle
information over a wide range of driving conditions.
III. VEHICLE MODEL SET
The performance of the IMM-based positioning algorithm
depends on the design and selection of the model set. For
superior performance, the model set should be able to represent
a wide range of vehicle motion patterns. In this paper, the
kinematic and dynamic vehicle models are used to represent
possible types of vehicle motion.
A. Kinematic Vehicle Model
The kinematic vehicle model was derived from the kinematic
relationships in a fundamental bicycle model, as shown in Fig. 2
[40]. In the bicycle model, the pairs of left and right wheels of
a vehicle are represented by single wheels. The front steering
angle is described by δ, and the center of gravity CG of the
vehicle is at point G. The distances from the CG to the front
and rear wheels are represented by lfand lr, respectively. In
addition, (X, Y )represents the location of the CG in the global
frame, ψdescribes the heading angle of the vehicle, and vG
represents the velocity at the CG, which produces a vehicle slip
angle β.
The kinematic vehicle model assumes that there is no tire
slip between the wheels and the ground; therefore, the velocity
vectors vFand vRat points Fand Rare in the direction of
the orientation of the front and rear wheels, respectively. This
assumption is reasonable for low-speed motion of the vehicle.
At low speeds, the lateral force that is generated by the tires can
be represented by the following centrifugal force equation:
Fy=mv2
G
rG
(1)
which varies with the quadratic of vehicle speed vG.Atlow-
speed driving conditions, since the lateral forces are very small
and negligible, the velocity vectors at each wheel are almost the
same as the direction of the tire.
The point Ois the instantaneous rotation center for the
vehicle and is defined by the intersection of lines OF and OR,
which are perpendicular to the orientation of the front and rear
wheels, respectively. The radius of the vehicle path rGcan be
obtained from the length of the line OG that connects the center
of gravity Gto the instantaneous rotation center O. The velocity
at Gis perpendicular to the line OG, and the direction of the
velocity at Gwith respect to the longitudinal axis of the vehicle
is represented by the vehicle slip angle β. The angle ψis defined
as the heading angle of the vehicle, and the term ψ+βis the
course angle of the vehicle.
By applying the sine rule to triangles OGF and OGR, the
following equations can be obtained:
sin(δ−β)
lf
=sin π
2−δ
rG
(2)
sin β
lr
=sin π
2
rG
.(3)
By rearranging (2) and (3)
sin δcos β−sin βcos δ
lf
=cos δ
rG
= tan δcos β−sin β=lf
rG
(4)
sin β=lr
rG
.(5)
Adding (4) and (5)
tan δcos β=lf+lr
rG
.(6)
If we assume that the radius of the vehicle path rGslowly
changes due to the low vehicle speed, then the rate of change of
332 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 13, NO. 1, MARCH 2012
Fig. 3. Dynamic vehicle model. This model assumes that the lateral force
acting on a tire is proportional to the tire slip angle.
orientation of the vehicle should be equal to the angular velocity
of the vehicle γas follows:
γ=˙
ψ=vG
rG
.(7)
Using (7), (6) can be rewritten as
˙
ψ=vG
lf+lr
cos(β) tan(δ).(8)
The vehicle slip angle βcan be calculated by subtracting (4)
from (5) as
β= tan−1lrtan δ
lf+lr.(9)
The global motion of the vehicle can be defined from the
course angle ψ+βand the vehicle velocity vGas
˙
X=vGcos(ψ+β)
˙
Y=vGsin(ψ+β).(10)
B. Dynamic Vehicle Model
The kinematic vehicle model is reasonable for low-speed
vehicle motion because the lateral force generated by the tires is
very small. In contrast, at higher speeds or with sharp steering,
the no-wheel-slip assumption breaks down due to the lateral
force. In this situation, the dynamic vehicle model should be
considered to determine the lateral velocity of the vehicle.
To account for vehicle slip and lateral velocity, we used a
dynamic vehicle model for lateral vehicle motion, as shown in
Fig. 3 [41], [42]. The following equation describes the lateral
dynamics of the bicycle model and was derived by summing
the forces and moments about the center of gravity, where
mand Izdescribe the vehicle mass and the yaw moment of
inertia, whereas γ,vx, and vyrepresent the yaw rate and vehicle
longitudinal and lateral velocities, respectively [40]:
Fy=Fyf +Fyr =may=m(˙vy+vxγ)
Mz=lfFyf −lrFyr =Iz¨
ψ. (11)
The dynamic vehicle model assumes that the lateral force
acting on a tire is proportional to the tire slip angle, as repre-
sented in (12). The tire slip angle can be defined as the angle
of the wheel velocity vector relative to the longitudinal wheel
axis, i.e.,
Fyf =2Cfαf≈2Cfβ+lf˙
ψ
vx
−δ
Fyr =2Crαr≈2Crβ−lr˙
ψ
vx(12)
where Cfand Crrepresent the front and rear tire cornering
stiffness, and the tire slip angles of the front and rear wheels are
represented by αfand αr, respectively.
We can calculate the overall vehicle motion of the dynamic
vehicle model using the following equation:
˙
β=−γ+2Cf
mvxδ−β−lfγ
vx+2Cr
mvx−β+lrγ
vx
˙γ=2Cflf
Izδ−β−lfγ
vx−2Crlr
Iz−β+lrγ
vx
˙
ψ=γ
˙
X=vGcos(ψ+β)
˙
Y=vGsin(ψ+β).(13)
IV. INTERRUPTING MULTIPLE MODEL FILTER STRUCTURE
The proposed IMM-based positioning system calculates the
model probabilities and integrates the EKF estimates of each
model using a stochastic process to adapt to a wide range
of driving conditions. Under high-speed and high-slip driving
conditions, the dynamic vehicle model-based filter is more
appropriate because it considers the lateral force and slip of
a vehicle. In contrast, under low-speed and low-slip driving
conditions, the kinematic vehicle model-based filter provides
better positioning performance because the slip angle of the tire
is sufficiently small to satisfy the kinematic model assumption.
In addition, since the lateral force of the vehicle is very small,
it can cause a numerical divergence problem for the dynamic
vehicle model EKF.
The overall process of the IMM filter for the proposed
positioning system is shown in Fig. 4. Using the stochastic
processes, the IMM filter weighs a suitable vehicle model for
the external driving conditions and estimates the position and
heading angle. The IMM filter is composed of four parts: in-
teracting, filtering, model probability updating, and estimation
fusion.
A. Interacting
Initially, the states from the previous step of each model are
combined with the mixing weight in the IMM filter. The mixing
weight can be written as
μj|i
k−1|k−1=1
ˆμi
k|k−1
πjiμj
k−1,i,j=1,2(14)
JO et al.: IMMFILTER-BASED SENSOR FUSION OF GPSWITH IN-VEHICLE SENSORS 333
Fig. 4. Process of the IMM filter.
where μj
k−1is the model probability of model jin the previous
step, and πji is the probability of a transition from model jto
model i. The mixing probabilities ˆμi
k|k−1are described as
ˆμi
k|k−1=
2
j=1
πjiμj
k−1i=1,2.(15)
The model transition of the IMM filter is governed by a
first-order Markov assumption that the current state variables
contain all the information needed to characterize the proba-
bility distribution for the next time step. The model transition
probability matrix πji describes the probability that the vehicle
model will make a transition from model state jto i. These
probabilities are assumed to be aprioriknown parameters and
can be represented as a probability transition matrix
πji =0.9803 0.0197
0.0066 0.9934 (16)
where the index number i,j=1 represents the kinematic
vehicle model, and the index number i,j=2 refers to the
dynamic vehicle model. These values were calculated using
a statistical method related to the sojourn times and sampling
interval of the real traffic condition [8], [43].
The initial mixing state ˜xi
k−1|k−1and the initial mixing
covariance ˜
Pi
k−1|k−1of model iare
˜xi
k−1|k−1=
2
j=1
ˆxj
k−1|k−1μj|i
k−1|k−1i=1,2(17)
˜
Pi
k−1|k−1=
2
j=1
μj|i
k−1|k−1
׈
Pj
k−1|k−1+ˆxj
k−1|k−1−˜xi
k−1|k−1
׈xj
k−1|k−1−˜xi
k−1|k−1T
i=1,2(18)
Fig. 5. EKF for each single model filter.
where ˆxj
k−1|k−1and ˆ
Pj
k−1|k−1are the state and covariance of
model jin the previous step, respectively.
B. Model-Matched Filtering
Using the initial mixing state and the covariance of the
interacting step, the EKF of each model predicts and updates
the model state and covariance. The overall operation of the
discrete EKF for model iis shown in Fig. 5 [44].
1) Prediction With the Process Model: In the prediction
step, the predicted state ˆxi
k|k−1and its covariance ˆ
Pi
k|k−1are
calculated. To obtain the predicted state and covariance at
time step k, the continuous process models for the kinematic
model (8)–(10) and the dynamic model (13) should be trans-
ferred into the discrete process model for numerical evaluation
and implementation of the filtering system on a digital micro-
processor. To execute the process model in real time, Euler’s
method, which is a first-order numerical process for solving a
differential equation, was used. Equation (19), shown below,
represents the approximation process of Euler’s method, i.e.,
˙x∼
=xk−xk−1
T
⇒xk∼
=xk−1+˙x·T(19)
334 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 13, NO. 1, MARCH 2012
where Trepresents the sampling period of the filtering system.
This approximation substitutes for all the derivatives that ap-
pear in the differential equation of the process model. Using
Euler’s approximation process, the discrete process models for
the kinematic vehicle model and the dynamic vehicle model are
defined as follows:
Discrete kinematic vehicle model equation:
x1
k=f1x1
k−1,u
k=⎡
⎢
⎢
⎢
⎢
⎢
⎣
vwhl
tan−1(lrtan(δSAS)/(lf+lr))
vk−1cos(βk−1) tan(δSAS)/(lf+lr)
ψk−1+Tγ
k−1
Xk−1+Tv
k−1cos(ψk−1+βk−1)
Yk−1+Tv
k−1sin(ψk−1+βk−1)
⎤
⎥
⎥
⎥
⎥
⎥
⎦
.
(20)
The discrete dynamic vehicle model equation is shown in (21)
at the bottom of the page.
The states of both vehicle models are represented as
xk=[vkβkγkψkXkYk]T(22)
and the model input is described as
uk=[vwhl δSAS]T(23)
where vwhl and δSAS describe the data from the wheel speed
sensor and the steering angle sensor, respectively. Using these
discrete process model equations, the next predicted state
ˆxi
k|k−1can be calculated as
ˆxi
k|k−1=fi˜xi
k−1|k−1,u
k,i=1,2(24)
where ˜xi
k−1|k−1refers to the initial mixing state in the interact-
ing step. The covariance of the predicted state ˆ
Pi
k|k−1can be
obtained as
ˆ
Pi
k|k−1=Fi
k˜
Pi
k−1|k−1Fi
kT+Gi
kQk−1Gi
kT,i=1,2
(25)
where Fi
krepresents the Jacobian of the nonlinear process
model
δfi
δx x=˜xi
k−1|k−1
=Fi
k,i=1,2(26)
Gi
kdescribes the gain matrix of the process noise, and Qk−1
is the covariance matrix of the process noise. The parameter
uncertainties of the kinematic and dynamic vehicle models are
assumed to be within the allowable range of the EKF process
noise.
For the implementation of the EKF of the discrete dynamic
vehicle model, stable conditions using Euler’s method should
be achieved. Although the continuous dynamic vehicle model
is stable, the discretized model might numerically be unsta-
ble due to the simple approximation of Euler’s method. In
particular, since the dynamic model contains the inverse of
vehicle speed 1/v, the solution of the difference equation could
numerically be unstable at low-speed conditions with a long
sampling period. This problem can be solved with a higher
order discretization method or fast sampling rate. However,
these solutions are undesirable for implementation of a real-
time embedded system. In contrast to the discrete dynamic
vehicle model, which has the numerical problem, the numerical
stability of the kinematic vehicle model is independent of the
vehicle speed and sampling period.
2) Measurement Update: In the update step, the EKF up-
dates the corrected state ˆxi
k|kand covariance ˆ
Pi
k|kusing mea-
surement data from the yaw rate sensor and the GPS receivers.
While the yaw rate sensor provides reliable vehicle yaw rate
information, which is independent of the external environment,
the data from the GPS receiver are affected by several external
noise sources such as lack of visible satellites, change in the
distribution of visible satellites, GPS signal blockage, and mul-
tipath. Therefore, variation in the noise characteristics of GPS
due to the external environment should be considered when
using the measurement update step of the EKF. In this paper,
a rule-based update method and a validation gate are applied
for the EKF to consider such noise changes.
Rule-based measurement update: If the GPS receiver was
not affected by external noise, then the measurement vector can
be represented as
zk=[vGPS γyawrate (β+ψ)GPS XGPS YGPS ]T
(27)
where vGPS and (β+ψ)GPS describe the velocity and course
angle, XGPS and YGPS represent the global positions from
the GPS receiver, respectively, and γyawra te is the yaw rate
from the in-vehicle sensor network. The sampling rate of the
in-vehicle sensor is faster than the sampling rate of the GPS
receiver, and it is synchronized to the execution rate of the
filtering algorithm. Therefore, the yaw rate data can always be
x2
k=f2x2
k−1,u
k
=
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
vwhl
βk−1+T−γk−1+2Cf
mvk−1δSAS −βk−1−lfγk−1
vk−1+2Cr
mvk−1−βk−1+lrγk−1
vk−1
γk−1+T2Cflf
IzδSAS −βk−1−lfγk−1
vk−1−2Crlr
Iz−βk−1+lrγk−1
vk−1
ψk−1+Tγ
k−1
Xk−1+Tv
k−1cos(ψk−1+βk−1)
Yk−1+Tv
k−1sin(ψk−1+βk−1)
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
(21)
JO et al.: IMMFILTER-BASED SENSOR FUSION OF GPSWITH IN-VEHICLE SENSORS 335
used for an element of the measurement vector. However, this
measurement vector cannot be used for all update steps because
the noise characteristics of GPS vary depending on the external
driving conditions.
Since the vehicle velocity vGPS and the course angle (β+
ψ)GPS, which were obtained from the GPS receiver, are based
on the Doppler effect, the noise variances of these outputs
depend on the vehicle speed [45]. At low speed less than a
certain threshold Vmin, the noise variance usually increases
significantly. Therefore, it is reasonable to ignore the GPS
velocity and course angle measurements at low speeds. The
low-speed condition can be determined by the wheel speed vwhl
from the in-vehicle sensor network, which is independent of
the GPS signal conditions. The measurement vector at the low-
speed condition can be represented as
zk=[γyawrate XGPS YGPS ]T.(28)
The condition of the GPS signal can be inferred by the
information from the GPS receiver, including the number of
satellites numOf Sat and the horizontal dilution of precision
hdop.IfnumOfSat drops below a certain threshold Nmin or
hdop exceeds a threshold Hmax, then all of the data from the
GPS receiver are neglected by the EKF. The thresholds Nmin
and Hmax are obtained experimentally. In addition, because the
execution rate of the filtering algorithm is usually faster than
the sampling rate of the GPS receiver, the EKF cannot update
the measurements of the GPS if the receiver was not sampled.
At these conditions, only yaw rate data are included in the
measurement vector according to
zk=[γyawrate ]T.(29)
All of the rule-based measurement update algorithms are
described in the following pseudocode:
01 IF gpsUpdate is true THEN
02 IF numOfSat < Nmin or hdop>H
max THEN
03 zk=[γyawrate ]T
04 H=[001000]
05 ELSE IF vwhl <V
min THEN
06 zk=[γyawrate XGPS YGPS ]T
07 H=⎡
⎣
001000
000010
000001
⎤
⎦
08 ELSE IF
09 zk=[vGPS γyawrate (β+ψ)GPS XGPS YGPS ]T
10 H=⎡
⎢
⎢
⎢
⎣
100000
001000
010100
000010
000001
⎤
⎥
⎥
⎥
⎦
11 END IF
12 ELSE IF
13 zk=[γyawrate ]T
14 H=[001000]
15 END IF
Validation gate: A validation gate describes a threshold
that is associated with the acceptability of the measurement
data. The validation gate can be calculated using the measure-
ment vector zk, the predicted state from the prediction step
ˆxi
k|k−1, and the associated covariance matrix Si
k, as represented
in the following:
˜
Vi
k(g2)=z:zk−H·ˆxi
k|k−1TSi
k−1
×zk−H·ˆxi
k|k−1≤g2
=z:vi
kTSi
k−1vi
k≤g2,i=1,2(30)
where vi
kis the innovation, and gis the number of sigma [46].
The associated covariance matrix Si
kcan be described as
Si
k=Hˆ
Pi
k|k−1HT+R. (31)
The validation gate is the ellipsoidal volume in the mea-
surement space, and if the measurement vector lies inside
the validation gate, then these values are considered to be
valid measurements. If the measurement vector lies outside the
validation gate due to sudden erroneous data from the GPS
receiver, then the filtering algorithm discards the value in the
update step.
After the measurement vector is chosen, the EKF updates the
corrected state ˆxi
k|kand covariance ˆ
Pi
k|kusing the following
equation:
ˆxi
k|k=ˆxi
k|k−1+Ki
kzk−Hˆxi
k|k−1
ˆ
Pi
k|k=I−Ki
kHˆ
Pi
k|k−1
Ki
k=ˆ
Pi
k|k−1HTSi
k−1.(32)
C. Mode Probability Update
The likelihood function of each mode iat time k, under the
Gaussian assumption, is given by
Λi
k=
exp −1
2νi
kTSi
k−1νi
k
2πSi
k
(33)
where νi
kand Si
kare the innovation and its covariance,
respectively.
The model probability update is calculated as follows:
μi
k=1
cΛi
k¯ci(34)
where cis the normalization constant for the mode probability
update
c=
2
j=1
Λj
k¯cj.(35)
336 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 13, NO. 1, MARCH 2012
TAB LE I
VEHICLE PARAMETERS
TAB LE II
SENSOR PROPERTIES
D. Estimation Fusion
According to the Gaussian mixture equation, the combined
state ˆxk|kand its covariance ˆ
Pk|kare calculated as
ˆxk|k=
2
i=1
μi
kˆxi
k|k(36)
ˆ
Pk|k=
2
i=1
μi
kˆ
Pi
k|k+ˆxi
k|k−ˆxk|kˆxi
k|k−ˆxk|kT.
(37)
V. S IMULATION
The proposed positioning algorithm was analyzed through
intensive simulation, the results of which are averages of
100 Monte Carlo simulations. The simulation was performed
using Carsim, a commercial software package for the simu-
lation of vehicle dynamics. The parameters of the simulated
vehicle model are shown in Table I, and the properties of the
equipment sensors are described in Table II. The uncertainty in
the model parameters and the noise of each sensor was assumed
to be Gaussian white noise. Positional information from a GPS
receiver was emulated by summing the position data from the
reference vehicle model and the assumed GPS noise, and the
in-vehicle sensors were similarly emulated. The wheel speed
sensor information and the steering angle sensor information
were used as inputs for the process model during the EKF
prediction step. The data from the yaw rate sensor and the GPS
receiver were used as measurements for the update step.
A. Characteristic of the Tire Slip Angle
The tire slip characteristics were analyzed using a steady-
state cornering test, performed under a constant steering angle
of two degrees and several constant velocity conditions. Fig. 6
shows the tire slip angles of the four wheels and the bicycle
model. The front and rear tire slip angles of the bicycle model
can be obtained as the average of the right and left tire slip
angles. According to Fig. 6, the faster vehicle velocity causes
larger slip angles in the front and rear tires under steady-state
cornering conditions.
B. Evaluation of the IMM Filter
The simulation was carried out under variable speed con-
ditions with a constant steering angle of two degrees. Fig. 7
represents the vehicle speeds in the simulation, including the
data of the emulated wheel speed sensor. To analyze the IMM
filter for several tire slip conditions, the vehicle speed varied
from 2.5 to 22.5 m/s. Fig. 8(a) describes the model probability
that was calculated using the IMM filter, and Fig. 8(b) shows
the Euclidean distance error of each single model EKF and
the IMM filter. Since the lateral tire slip was very small at
low-speed conditions, the kinematic vehicle model was used
to represent the vehicle motion. The performances of the IMM
filter and the kinematic vehicle model EKF were nearly equal,
and the IMM filter had less error than did the dynamic vehicle
model EKF estimate. At the high-speed condition, because
the lateral tire slip affects the vehicle dynamics, the model
probability of the dynamic vehicle model in the IMM filter
was greater than that of the kinematic vehicle model. This
result indicates that the dynamic vehicle model is more suitable
for high-slip driving conditions compared with the kinematic
vehicle model. In addition, the Euclidean distance error of the
IMM filter was almost the same as the error of the dynamic
vehicle model EKF.
VI. EXPERIMENT
The vehicle used to conduct the experiments was a small
SUV equipped with a vehicle stability control system, as shown
in Fig. 9. The vehicle motion data from the stability control
system could be obtained from the in-vehicle network CAN.
The noise specifications of the in-vehicle sensors are repre-
sented in Table III. The low-cost GPS receiver, SiRFstar III,
which combined a small ceramic patch antenna with a low-
power GPS chipset, was used for the measurements of the
positioning system. The update rate of the GPS receiver was
4 Hz, and the noise specifications of the GPS are described
in Table IV. The IMM-based positioning algorithm was im-
plemented in a real-time embedded system that contained a
32-bit real-time microcontroller unit (Freescale MPC5567).
The sampling rate of the implemented positioning algorithm
was 40 Hz. To evaluate the performance of the proposed
JO et al.: IMMFILTER-BASED SENSOR FUSION OF GPSWITH IN-VEHICLE SENSORS 337
Fig. 6. Tire slip angle under a constant steering angle of two degrees and several constant speeds.
Fig. 7. Variable vehicle speed simulation. The Euclidean distance errors and
the model probability for low-speed and small tire slip conditions.
Fig. 8. Model probability and Euclidean distance errors for various speed
conditions.
positioning system, an accurate localization system that inte-
grated two differential GPSs (DGPSs) with an INS was used
as a reference. In the case of DGPS blockage, the localization
system was evaluated through comparison with road data from
satellite maps.
The experimental evaluation was performed in two test envi-
ronments. The first region included several driving conditions,
such as parking lots, curved roads, and intersections. In this
region, the adaptation performance of the positioning algorithm
was evaluated. The second region had poor GPS conditions
since this area contained many tall buildings. The continuity
and reliability of the positioning system were confirmed in this
region.
A. Evaluation of the Positioning Algorithm in
Several Driving Environments
Fig. 10 represents a map of the test region used for the
evaluation of IMM filter adaptation performance. The re-
gion included several driving environments, such as parking
lots (1, 10), curved roads (2–4), and intersections (5–9). The
vehicle speed and steering input are described in Fig. 11. The
parking lots (1, 10) and intersections (5–9) represent the low-
speed and small tire slip condition, and the curved roads (2–3)
represent the high-speed and large tire slip condition.
Fig. 12 describes the model probability that was calculated
using the IMM filter. The model probability represents the
suitability of the vehicle model for the driving conditions.
On the small slip curved road, the model probability of the
kinematic vehicle model was larger than that of the dynamic
vehicle model. According to this result, the kinematic vehicle
model is more suitable for low-slip driving conditions than the
dynamic vehicle model. In contrast, in the large-slip curved
road, the model probability of the dynamic vehicle model was
greater than that of the kinematic vehicle model, indicating that
the dynamic vehicle model is more appropriate for high-slip
regions than the kinematic vehicle model.
Fig. 13 shows the detailed logged data of the positioning
system for each driving condition, where the red line repre-
sents the reference trajectory from the positioning system that
combined the two DGPSs with an INS. The brown dashed-
dotted line represents the filtering result of a single kinematic
vehicle model EKF, and the pink dashed line represents the
filtering results of a single dynamic vehicle model EKF. The
338 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 13, NO. 1, MARCH 2012
Fig. 9. Test vehicle equipped with a vehicle stability control system.
TABLE III
NOISE SPECIFICATIONS OF IN-VEHICLE SENSORS
TAB LE IV
NOISE SPECIFICATIONS OF GPS
blue line illustrates the results of the proposed positioning
system based on the IMM filter. Fig. 14 shows the Euclidean
distance error of each single model EKF and the IMM filter.
For the low-speed and small tire slip condition, the estimation
using a dynamic vehicle model had a numerical divergence
problem due to the small lateral force. Therefore, the results
of the dynamic model EKF had large distance errors, as shown
Fig. 10. Test region for the evaluation of the adaptation performance.
in Fig. 13(a) and (d). In this case, the IMM filter attributed
a large amount of weight to the kinematic vehicle model for
the estimation process. In contrast, for the high-speed and large
tire slip region, the estimation using a kinematic vehicle model
contained large distance errors due to the exclusion of the tire
slip angle, as shown in Fig. 13(b) and (c). In this case, the
IMM filter attributed more weight to the dynamic vehicle model
compared with that of the kinematic vehicle model.
JO et al.: IMMFILTER-BASED SENSOR FUSION OF GPSWITH IN-VEHICLE SENSORS 339
Fig. 11. Vehicle speed and steering input.
Fig. 12. Model probability of the IMM filter.
B. Bad GPS Conditions
Fig. 15 shows the map of the test region used for the
evaluation of the continuity and reliability of the positioning al-
gorithm. The green dash line represents the reference trajectory
from the satellite map, the blue line represents the proposed
positioning algorithm results, the red dots represent the low-
cost GPS positional data, and the boxes represent tall buildings.
Fig. 16 shows the number of satellites used for position esti-
mation using the GPS and the horizontal dilution of precision
(HDOP). Since the region included many tall buildings, the
GPS signal was frequently blocked, as shown in regions a and
b of Fig. 16.
To consider the GPS blockage and the poor GPS information,
a rule-based filter update method with a validation gate was
applied for the positioning algorithm. The algorithm did not
update the GPS measurements when the number of satellites
in used was less than or equal to four or when the HDOP was
greater than five. The validation gate was installed to detect and
reject drift errors due to the multipath GPS signal. Therefore,
the positioning algorithm was shown to provide continuous
and reliable position information even in a harsh GPS signal
environment.
VII. CONCLUSION
In this paper, we have described the development of a vehicle
positioning system that is robust to changes in driving condi-
tions for use in ITS applications. The developed positioning
algorithm integrates information from a low-cost GPS receiver
with that of in-vehicle sensors. Using in-vehicle sensors and
low-cost GPS, which are already installed in the vehicle stabil-
ity control system, along with an in-car navigation system, the
340 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 13, NO. 1, MARCH 2012
Fig. 13. Positioning system results for each driving condition.
Fig. 14. Euclidean distance errors for each single model EKF and for the IMM filter.
positioning algorithm can immediately be implemented in such
commercial vehicles.
The proposed IMM-based positioning system combines the
EKF estimates from both kinematic and dynamic vehicle mod-
els to allow it to adapt to variable driving conditions. Under
high-slip driving conditions, the estimate of the dynamic vehi-
cle model-based filter is emphasized by the IMM filter since it
considers lateral force. In contrast, for the low-speed and small
tire slip condition, the estimates of the kinematic vehicle model-
based filter are preferentially used for the IMM filter because
the process noise of the lateral vehicle velocity does not affect
the filter estimation process.
JO et al.: IMMFILTER-BASED SENSOR FUSION OF GPSWITH IN-VEHICLE SENSORS 341
Fig. 15. Test region for evaluation of continuity and reliability.
Fig. 16. Number of satellites used and the HDOP for the GPS receiver.
The thresholds Nmin and Hmax for the rule-based update algorithm are
both five.
We verified this positioning algorithm through simulations
and experiments. The purpose of the simulation was an analysis
of the relationship between the tire slip angle and each vehicle
model. While the estimation performance of the kinematic
vehicle model EKF was better than that of the dynamic vehicle
model EKF for the low tire slip condition, the dynamic vehicle
model EKF had better estimation performance for the large
tire slip condition. The experiments were performed in vari-
ous driving environments, such as parking lots, intersections,
curved roads, and in a region with bad GPS signal that was
surrounded by tall buildings. The experimental results showed
that the estimates of the developed algorithm were accurate and
reliable under the various driving conditions.
Due to the limitations of the two degrees-of-freedom bicycle
model, the estimation of vehicle position in a very steep sloped
driving environment and a large longitudinal tire slip condition
was prohibited. In future work, the authors plan to extend
the positioning algorithm to consider more dynamic states of
road slope and longitudinal tire slip. The limitation might be
compensated for by applying the longitudinal acceleration data
to the positioning algorithm. The integration of the accelerom-
eter and the wheel speed sensor in the positioning algorithm
will improve the estimation of vehicle speed, which is very
important for vehicle positioning [47].
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Kichun Jo (S’10) received the B.S. degree in me-
chanical engineering in 2008 from Hanyang Univer-
sity, Seoul, Korea, where he is currently working
toward the Ph.D. degree with the Automotive Con-
trol and Electronics Laboratory.
His main fields of interest are information fusion
theories and applications for vehicle localization and
tracking, controller design, and system integration of
intelligent vehicles. He has also worked on model-
based embedded software development for automo-
tive control systems.
Keounyup Chu (S’10) received the B.S. degree
in mechanical engineering and the M.S. and Ph.D.
degrees in automotive engineering from Hanyang
University, Seoul, Korea, in 2004, 2006, and 2011,
respectively.
He is currently with the Automotive Control and
Electronics Laboratory, Hanyang University. His re-
search activities include the design of intelligent
vehicles, real-time systems, distributed control sys-
tems, and in-vehicle networks. His current research
interests are in motion planning and collision mitiga-
tion. He has also worked on the development of an autonomous vehicle.
JO et al.: IMMFILTER-BASED SENSOR FUSION OF GPSWITH IN-VEHICLE SENSORS 343
Myoungho Sunwoo (M’81) received the B.S. degree
in electrical engineering from Hanyang University,
Seoul, Korea, in 1979, the M.S. degree in elec-
trical engineering from the University of Texas at
Austin in 1983, and the Ph.D. degree in system en-
gineering from Oakland University, Rochester, MI,
in 1990.
He joined General Motors Research (GMR) Lab-
oratories, Warren, MI, in 1985 and has been working
in the area of automotive electronics and control for
26 years. During his nine-year tenure at GMR, he
worked on the design and development of various electronic control systems
for power train and chassis. Since 1993, he has led research activities as a
Professor with the Department of Automotive Engineering, Hanyang Univer-
sity: one of the largest engineering schools in Korea. His work has focused
on automotive electronics and control such as modeling and control of internal
combustion engines, design of automotive distributed real-time control systems,
intelligent autonomous vehicles, and automotive education programs. During
his professional career, he has published 55 international journal papers and
68 international conference papers and has held 19 patents. In addition, he
successfully accomplished more than 50 research projects with the Korean
government and automotive companies such as Hyundai, Kia, Mando, Hyundai
MOBIS, Freescale, and many others. He has continuously consulted for the
Korean government and the automotive industry.
Dr. Sunwoo currently serves as the Chairman of the steering committee for
the Green Car Strategy Forum of the Ministry of the Knowledge Economy and
is also an Academician of the National Academy of Engineering of Korea. His
laboratory, i.e., ACE Lab, has been selected as a National Research Laboratory
by the Korean government because of its outstanding research accomplish-
ments. His autonomous vehicle named “A1” won the first National Autonomous
Vehicle Competition organized by Hyundai Motor Company hosted in Korea
in November 2010. In recognition of his distinguished achievements, he has
received notable awards, such as the Grand Award of Academic-Industrial
Cooperation from the Korean Academic-Industrial Foundation, the Best
Scientist/Engineer Award of the Month from the Korean Ministry of Science
and Technology, and the Award for Technology Innovation from the Prime
Minister of Korea.
