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Transactions on Industrial Informatics
IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 1
Event-Triggered Vehicle Sideslip Angle Estimation
Based on Low-Cost Sensors
Xiaolin Ding, Zhenpo Wang, Member, IEEE and Lei Zhang, Member, IEEE
Abstract—Accurate vehicle sideslip angle estimation is crucial
for vehicle stability control. In this paper, an enabling event-
triggered sideslip angle estimator is proposed by using the
kinematic information from a low-cost Global Positioning System
(GPS) and an on-board Inertial Measurement Unit (IMU). First,
a preliminary vehicle sideslip angle is derived using the heading
angle of GPS and the yaw rate of IMU, and an event-triggered
mechanism is proposed to eliminate the accumulative estimation
error. The algorithm convergence is guaranteed through theo-
retical deduction. Second, a longitudinal and a lateral vehicle
velocity are obtained using the preliminary vehicle sideslip angle
and the measured GPS velocity and their kinematic relationship,
based on which a multi-sensor fusion and a multi-step Kalman
filter scheme are respectively presented to realize longitudinal
and lateral vehicle velocity estimation. By doing this, the update
frequency and estimation accuracy of the vehicle sideslip angle
estimate can be further improved to meet the requirement of
online implementation. Finally, the effectiveness and reliability of
the proposed scheme are verified under comprehensive driving
conditions through both hardware-in-loop (HIL) and field tests.
The results show that the proposed event-triggered sideslip angle
estimator has a mean estimation error of 0.029 deg and of
0.14 deg in the HIL and field tests, exhibiting better estimation
accuracy, reliability and real-time performance compared with
other typical estimators.
Index Terms—vehicle sideslip angle, event-triggered estima-
tion, vehicle kinematics.
I. INT ROD UC TI ON
VEHICLE stability control systems (VSCs) such as Elec-
tronic Stability Program, Torque Vectoring and Active
Front Steering System play a pivotal role in ensuring safe op-
erations of vehicles [1]–[3]. The efficient functionality realiza-
tion of these VSCs hinges on accurate and robust acquisition
of vehicle sideslip angle in real-time. However, vehicle sideslip
angle measurement devices like optical sensors or inertial
navigation systems are commercially prohibitive for being
used in mass-production vehicles. Instead, substantial research
efforts have been funneled to developing enabling estimation
algorithms based on conventional low-cost on-board sensors
in past decades, and these result in a rich library of related
literature. The existing estimation methods can be roughly
Manuscript received April 28, 2021; revised August 31, 2021. This work
was partly supported by the Beijing Municipal Science and Technology Com-
mission via the Beijing Nova Program [Grant number: Z201100006820007]
and by the Ministry of Science and Technology of the People’s Republic of
China [Grant number: 2017YFB0103600].
Xiaolin Ding, Zhenpo Wang, and Lei Zhang are with the Collabora-
tive Innovation Center for Electric Vehicles, Beijing, and the National
Engineering Laboratory for Electric Vehicles, Beijing Institute of Tech-
nology, Beijing 100081, China. Corresponding author: Lei Zhang; e-mail:
lei zhang@bit.edu.cn.
classified into two groups, i.e., model- and neural network-
based methods [4].
The model-based methods can be further categorized
into the kinematics- and dynamics-based approaches. The
kinematics-based methods utilize the Global Positioning Sys-
tem (GPS), Inertia Measurement Unit (IMU) and other
kinematics-related sensors for vehicle sideslip angle estima-
tion. These methods are robust to the variations of vehicle
parameters, road adhesion and driver’s operations, and the
underlying kinematic vehicle models are also straightforward
and easy to understand. An intuitive approach is to integrate
IMU acceleration measurements to obtain longitudinal and
lateral vehicle velocities based on the 2-Degree-of-Freedom
(2-DoF) vehicle model [5]. However, the measured accel-
erations are often sensitive to road roughness and vehicle
motions, and the accumulative estimation error is inevitable
due to the consistent existence of measurement bias and noise
at each time step [6]. To tackle this issue, Selmanaj et al.
[7] developed a heuristic schedule for adjusting the observer
gain to regulate the accumulative estimation error. Also, GPS
measurements have been widely incorporated into vehicle
sideslip angle estimation formulations [8]. A major concern
for GPS-based methods is the low update frequency of GPS
measurements [9]. Moreover, the measurement abnormality
and signal synchronization pose also great challenges for
realizing robust sideslip angle estimation [10].
In contrast, the dynamics-based methods usually integrate
vehicle dynamics and tire models with specialized state ob-
servers for vehicle sideslip angle estimation. To improve
computational efficiency, tire model linearization is often
necessitated [5]. However, these linearized tire models are
incompetent for describing tire dynamics in the nonlinear
region [11]. Studies have also been conducted to realize real-
time acquisitions of tire model parameters and road friction
coefficient. Usually, two cascaded estimators are synthesized
for successively estimating tire cornering stiffness and road
friction coefficient to improve modeling efficacy under diverse
driving conditions [12], [13]. Although tire forces can be
measured using bearing sensors [14], their sensitiveness to
road adhesion variation and high cost curtail the feasibility
in real-world applications. Dynamics-model-based observers
such as the Kalman filter [15] and its variants [16], [17]
and other nonlinear filtering observers [18], [19] have also
been extensively studied to realize vehicle sideslip angle
estimation thanks to their capability of dealing with nonlinear
dynamics. But the efficacy of these observers is strongly
related to modelling accuracy, and both modelling uncertainty
and time-varying parameters can significantly compromise the
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Transactions on Industrial Informatics
IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2
estimation performance, and prevent its engineering applica-
tions. Combining kinematics- and dynamics-based methods
represents a promising solution by optimally using kinematics
and dynamics information [20].
With the development of artificial intelligence and the in-
creasing computational capability of embedded controllers, the
neural network-based methods are gaining attention in vehicle
sideslip angle estimation. Without requiring a prior model,
the neural network-based methods can explicitly describe
the relationship between sensor measurements and vehicle
sideslip angle [21], [22]. This requires comprehensive and
high-fidelity training datasets, which are challenging to obtain
under diverse and ever-changing driving conditions. Moreover,
the trained neural network usually exhibits poor robustness to
the variations of road adhesion, tire cornering stiffness and
other vehicle parameters. To improve the robustness to road
adhesion variation, Bonfitto et al. [23] developed three neural
network models to estimate vehicle sideslip angle on dry, wet,
and icy roads, respectively. Some studies are also trying to
combine the neural network- and model-based methods to
enhance estimation performance. Therein, the neural network
model is mainly responsible for algorithm calibration [24] or
works as a pseudo-estimator [25]–[27].
Previous studies have presented various methods for vehicle
sideslip angle estimation. The neural network-based method
needs to improve the robustness to varying driving conditions
and different sensor configurations. The model-based approach
offers a feasible way to realize vehicle sideslip angle estima-
tion. However, sensor measurements are necessary and used as
the inputs of specialized estimators or observers. Wide-range
driving conditions would inevitably introduce sensor bias and
noise to the measurements. Although these can be corrected
through enabling filtering techniques to some extent, signifi-
cant estimation errors can be accumulated over time due to the
integration operator. To address this issue [28]–[32], this paper
proposes an enabling event-triggered estimator to improve
vehicle sideslip angle accuracy under comprehensive driving
conditions. First, a preliminary vehicle sideslip angle is derived
using the heading angle from a low-cost GPS and the yaw rate
from an on-board IMU, and an event-triggered mechanism
is proposed to eliminate the accumulative estimation error
caused by sensor bias and noise. The algorithm convergence
is guaranteed through theoretical deduction. To improve the
update frequency and estimation accuracy, the longitudinal and
lateral vehicle velocities are obtained using the preliminary
sideslip angle and the measured GPS velocity, based on
which a multi-sensor fusion and a multi-step Kalman filter
scheme are respectively presented to refine the longitudinal
and lateral vehicle velocity estimates. Finally, the effectiveness
and reliability of the proposed scheme are verified under
comprehensive driving conditions through hardware-in-loop
(HIL) and field tests. The major contributions of this study
to the related literature lie in the following aspects.
•An enabling event-triggered vehicle sideslip angle esti-
mator is proposed based on low-cost sensors to eliminate
the accumulative estimation error.
•The convergence of the proposed event-triggered vehicle
sideslip angle estimator is guaranteed through theoretical
deduction.
•The proposed event-triggered vehicle sideslip angle esti-
mator is robust to the variations of vehicle parameters,
road adhesion and driving conditions.
The remainder of this paper is arranged as follows: Section
II introduces the used kinematic vehicle model. Section III
elaborates on the proposed event-triggered vehicle sideslip
angle estimator. Section IV provides the experimental veri-
fication based on HIL and field tests, followed by the key
conclusions summarized in Section V.
II. SY ST EM MO DE LL IN G
A. The Vehicle- and the Geodetic-Coordinate System
As shown in Fig. 1, in order to describe the relationship
between the heading angle, yaw angle and sideslip angle of
the vehicle, the geodetic and the vehicle coordinate system are
appropriately defined. In the Geodetic-Coordinate system, the
x-, y-, and z-axis are positive in the East (E), North (N), and
Upward (U) directions, respectively; in the Vehicle-Coordinate
system, the x-, y-, and z-axis are positive in the forward, left
and upward directions of the vehicle. The angle between the
vehicle’s moving direction and the North is defined as the
heading angle γ, which is positive in the clockwise direction;
The angle between the vehicle’s x-axis and the North is the
yaw angle ψ, which is positive in the clockwise direction.
Thus, the vehicle sideslip angle βcan be given by
β=ψ−γ(1)
The relationship between the vehicle yaw angle ψand yaw
rate ωzcan be deduced by
ψ=Zt
0
ωzdt (2)
B. The 3-DOF Kinematic Vehicle Model
Longitudinal and lateral vehicle velocities are two major
parameters for vehicle sideslip angle derivation. The vehicle
sideslip angle can be given by
β= arctan vy
vx
(3)
where vxand vyare the longitudinal and lateral vehicle
velocities, respectively. Herein, a simplified 3-DoF kinematic
vehicle model is adopted to describe the relationship between
the longitudinal, lateral and yaw motions of the vehicle as
shown in Fig. 2. The equations of motion are given by
˙vx=ax+vyωz
˙vy=ay−vxωz
(4)
where axand ayare the longitudinal and lateral accelerations;
˙vxand ˙vyrepresent the longitudinal and lateral vehicle veloc-
ity derivatives.
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Transactions on Industrial Informatics
IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 3
E
N
J
E
z
Z
O
\
x
v
y
v
v
x
y
Fig. 1. The relationship between the heading angle, yaw angle and sideslip
angle of the vehicle in the Geodetic-Coordinate system.
y
v
x
v
z
IMU
z
IMU
x
a
IMU
y
a
CoG
IMU
x
y
x
Fig. 2. The 3-DoF kinematic vehicle model.
C. The Vehicle Roll Kinematic Model
For obtaining accurate lateral acceleration, a simplified
vehicle roll model is established to compensate for the impact
of roll motion on the lateral acceleration measurement of IMU.
As shown in Fig. 3, the IMU cannot be precisely installed at
the Gravity of Center (CoG) of the vehicle, and the position of
CoG also varies with cabin occupants distribution. Besides, the
IMU lateral acceleration measurement aIM U
yis also sensitive
to the sensor installation error and the gravity acceleration.
According to Ref. [13], a refined expression for the IMU
lateral acceleration measurement can be given by
aIM U
y= (ay+ ˙ωz·xIM U −ωz2·yIM U −¨ϕ·hIM U
−˙ϕ2·yIM U )·cosϕ+g·sinϕ+eIM U +τ(5)
where ϕ,˙ϕand ¨ϕare the vehicle roll angle, roll rate and
roll acceleration; g·sinϕrepresents the lateral acceleration bias
caused by the vehicle roll angle; eIM U and τare the IMU
installment error and the measurement noise in the lateral
acceleration measurement; xIM U ,yIM U and hI MU are the
longitudinal, lateral and vertical distances between the IMU
and the CoG. Herein, the IMU is placed in the center line of
the vehicle along the x-axis, i.e., yIM U =0. For a passenger car,
the vehicle roll angle usually varies from -10 degrees to 10
degrees in daily driving conditions [3], it conforms to the small
angle approximation with sinϕ≈ϕand cosϕ≈1. Thereby
Equation (5) can be simplified as
aIM U
y=ay+ ˙ωz·xIM U −¨ϕ·hIM U +g·sinϕ+eIM U +τ
(6)
As the IMU installment error eIM U can be eliminated by
automatic zero-setting during the vehicle initiation phase, the
actual lateral acceleration can be derived by estimating the
vehicle roll angle. To improve the robustness of roll angle
estimation to vehicle parameters variation, the discrete iterative
relation between roll rate and roll motion can be given by
(ϕ=Rt
0˙ϕdt
˙ϕ=Rt
0¨ϕdt
(7)
y
z
CoG
O
φ
x
IMU
y
a
y
a
g
IMU
y
a
y
a
g
IMU
y
IMU
h
Fig. 3. The vehicle roll model.
III. THE EV EN T-TR IG GE RE D SID ES LI P ANG LE ES TI MATO R
A. The Schematic of the Proposed Event-Triggered Vehicle
Sideslip Angle Estimator
The schematic of the proposed sideslip angle estimator is
illustrated in Fig. 4. Therein, the ETSE-1 aims to realize a
preliminary vehicle sideslip angle estimation using the low-
frequency GPS heading angle and the IMU yaw rate. The
event-triggered mechanism uses the vehicle yaw rate as an
event. The event is triggered when the vehicle yaw rate is
less than a preset threshold. When the vehicle runs in straight
line, the event-triggered measurements can be transmitted to
the estimator, which contributes to the vehicle yaw angle
approaching to the vehicle heading angle, and the vehicle
sideslip angle converges to 0. By doing this, the accumulative
integration error caused by sensor bias and noise under the
straight-line driving condition can be eliminated. When the
event is untriggered, the system measurements can be trans-
mitted to the estimator. In this case, the IMU yaw rate can be
used to estimate the vehicle yaw angle based on the kinematic
relationship (See Equation (1)). In addition, ETSE-1 also out-
puts the preliminary longitudinal and lateral vehicle velocities
based on the GPS velocity and the estimated vehicle sideslip
angle. Similar to the working principle of ETSE-1, ETSE-
2 employs the IMU roll rate and roll acceleration to obtain
vehicle roll state for eliminating the impact of gravity on the
IMU lateral acceleration measurement for further improving
the lateral vehicle velocity estimation accuracy.
As the update frequency of the used low-cost GPS module
is 20 Hz (see the yellow background module), which is
much lower than that of the vehicle control unit (VCU). It is
necessary to increase the update frequency of ETSE-1 to meet
the requirements of VSCs (a control cycle of 10 ms, i.e. 100
Hz). Thus, a multi-sensor fusion based longitudinal vehicle
velocity estimator and a lateral vehicle velocity estimator are
developed to derive high-update-frequency longitudinal and
lateral vehicle velocities. The longitudinal vehicle velocity
estimator is synthesized by combining the GPS longitudinal
speed (output from ETSE-1), motor rotational speed and IMU
longitudinal acceleration to ensure the estimation robustness
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Transactions on Industrial Informatics
IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 4
to a diverse range of driving conditions. The lateral vehicle
velocity estimator utilizes the GPS lateral speed (output from
ETSE-1) and the corrected vehicle lateral acceleration to
obtain the high-accuracy lateral vehicle velocity.
B. The Event-Triggered State Estimation Algorithm
In this paper, the Kalman filter is employed to form the
event-triggered state estimation algorithm by combining with
the event-triggered mechanism. Consider a discrete time-
varying linear system described as
xk=Axk−1+Buk−1+ωk−1
zk=Hxk+vk
(8)
where xk∈Rn,uk∈Rpand zk∈Rmare the system state, input
and measurement at time step k, respectively; the process noise
ωk∈Rrand the measurement noise vk∈Rmare assumed to
be the white noises with the respective covariance matrices
Q∈Rp∗pand R∈Rm∗m.A,Band Hare time-varying
matrices.
The optimal Kalman filter can be given by
ˆ
xk+1 =ˆ
xk+1|k+Kk+1 zk+1 −ˆ
zk+1|k(9)
where Kk+1 represents the Kalman gain, which can be derived
by
Kk+1 =Pk+1|kHT
HPk+1|HT+R(10)
Pk+1|k=APkAT+Q(11)
Pk+1 = (I−Kk+1H)Pk+1|k(12)
where Pk+1 and Pk+1|kare the filtering and prior prediction
error variance matrices, respectively. I= [1,1,· · · 1]T.
Herein, an event-triggered mechanism is developed to de-
cide whether the sensor measurements can be transmitted to
the estimator. The ‘Send on Delta’ strategy is used to define
the event-triggered condition [28], which is given by
ζk+1 =1,if (zk+1 −zτk)T(zk+1 −zτk)≤δ
0,otherwise (13)
where zk+1 and zτkare the system and the event-triggered
measurement; the subscript τkrepresents the time step at
which the event-triggered measurement is transmitted; δ>0
is the predetermined trigger threshold; ζk= 1 refers to a
triggered event when the sensor measurements can be trans-
mitted to the estimator, while ζk= 0 means that the event is
untriggered and the sensor measurements cannot be delivered
to the estimator.
Thus, the event-triggered Kalman filtering estimator is de-
fined as
ˆ
xk+1 =ˆ
xk+1|k+ (1 −γk+1)Kk+1 zk+1 −ˆ
zk+1|k
+γk+1Mk+1 zτk−ˆ
zk+1|k(14)
where Mk+1 denotes the event-triggered gain, which can be
expressed as
Mk+1=η1Pk+1|kTHT
η1HPk+1|kHT+η2Rk+1+η3δI (15)
where η1,η2and η3>1 are all positive scalars.
Convergence Analysis: To ensure the convergence of the
proposed state estimator, it is necessary to ensure the conver-
gence of the estimator both in event triggered and untriggered
states. When ζk= 0, the proposed scheme is a classic Kalman
filter estimator, and its convergence has been well proven in
the literature. For ζk= 1, the convergence of the proposed
estimator is derived as follow:
Define the prior prediction error as
˜
xk+1|k=xk+1 −ˆ
xk+1|k(16)
The estimation error can be given by
˜
xk+1 =xk+1 −ˆ
xk+1 (17)
Considering ζk= 1, Equation (14) can be rewritten as
ˆ
xk+1=ˆ
xk+1|k+Mk+1
(zτk−zk+1)+Mk+1
zk+1−ˆ
zk+1|k
(18)
Substituting Equation (18) into Equation (17), and combining
Equation (16), the estimation error can be deduced as
˜
xk+1=˜
xk+1|k+Mk+1(zτk−zk+1)+Mk+1
zk+1 −ˆ
zk+1|k
(19)
where the zk+1 and ˆ
zk+1 can be expressed by
zk+1 =Hxk+1 +v
ˆ
zk+1|k=Hˆ
xk+1|k
(20)
Substituting Equation (20) into Equation (19) to get
˜
xk+1 =˜
xk+1|k+Mk+1(zτk−zk+1)+Mk+1
H˜
xk+1|k+v
(21)
Set Ωk+1 =I−Mk+1H
ρk+1 =zτk−zk+1
(22)
Equation (21) can be rewritten as
˜
xk+1 =Ωk+1 ˜
xk+1|k−Mk+1ρk+1 −Mk+1 vk+1 (23)
Based on the definition of the estimation covariance, Pk+1
can be derived as
Pk+1 =En˜xk+1(˜xk+1 )To
=Ωk+1 ˜xk+1|k(˜xk+1|k)T(Ωk+1 )T−Mk+1 ρk+1 (˜xk+1|k)T(Ωk+1 )T
|{z }
Θk+1
T
−Mk+1 vk+1(˜xk+1|k)T(Ωk+1)T
| {z }
Γk+1
T
−Ωk+1 ˜xk+1|k(ρk+1)T(Mk+1)T
| {z }
Θk+1
+Mk+1 ρk+1(ρk+1 )T(Mk+1)T+Mk+1vk+1(ρk+1)T(Mk+1)T
| {z }
Ok+1
T
−Ωk+1 ˜xk+1|k(vk+1)T(Mk+1 )T
| {z }
Γk+1
+Mk+1 ρk+1(vk+1 )T(Mk+1)T
| {z }
Ok+1
+Mk+1vk+1 (vk+1)T(Mk+1 )T
=Ωk+1Pk+1|k(Ωk+1 )T−Θk+1 −Θk+1T−Γk+1 −Γk+1 T
+Ok+1 +Ok+1 T+Mk+1 δ(Mk+1)T+Mk+1 Rk+1(Mk+1 )T
(24)
where
Θk+1 =Ωk+1 ˜xk+1|k(ρk+1)T(Mk+1 )T
Γk+1 =Ωk+1 ˜xk+1|k(vk+1)T(Mk+1 )T
Ok+1 =Mk+1ρk+1 (vk+1)T(Mk+1 )
(25)
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Transactions on Industrial Informatics
IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 5
ETSE-1 for Sideslip Angle Estimation
Event-Tri ggered M echanism
GPS
Heading AngleHeading Angle
Measurement
Event-Tri ggered V ehicle Sideslip Angle Est imator
(Eq. 36)
?Y
N
k
Yaw Angle
k
Yaw Angle
Longitudinal a nd Lateral Velocity Calc ulation
Preliminary Sideslip Angle Longitudinal- and lateral
Velocity Calculation
(Eq. 41)
ETSE-2 for Roll Angle Estimation
IMU
z
GPS
IMU
z
GPS
IMU
z
GPS
Update Fre quency 20 Hz Update Fre quency 10 0 Hz
Event-Tri ggered M echanism
Measurement
(Eq. 45)
Event-Tri ggered Vehi cle Roll Angle Estimator
(Eq. 43)
?Y
N
Roll AngleRoll Angle
IMU
IMU
IMU
IMU
IMU
IMU
Roll Acceler ation
Lateral Acceleration Correction
IMU
y y z IMU IMU
a =a x h +g
+ −
Lateral Acceleration Correction
IMU
y y z IMU IMU
a =a x h +g
+ −
Multi-Sensor Fusion based Longitudinal
Vehicle Velocity Estimator
Longitudi nal Veloc ity Lateral Ve locity
Update Freque ncy 10 0 Hz
Lateral Vehicle Velocity Estimator Update Frequency 100 Hz
y
a
Lateral Ac celer ation
GPS
y,k
v
GPS
x,k
v
Input
y
a
Measurement Measurement Update
Lateral Velocity update ?
Time Update
GPS
y,k
v
Input
y
a
Measurement Measurement Update
Lateral Velocity update ?
Time Update
GPS
y,k
v
y
v
Estimated Latera l Velo city
y
v
Estimated Latera l Velo city
Estimated Longi tudinal Veloc ity
x
v
Estimated Longi tudinal Veloc ity
x
v
Roll Rate
IMU
Roll Accelera tion
IMU
IMU Roll Rate
IMU
Roll Accelera tion
IMU
IMU
IMUIMU
Yaw Rate
IMU
z
Yaw Rate
IMU
z
IMU
Yaw Rate
IMU
z
arctan y
kx
v
v
=
( ) ( )
11kk
T
k k k
−−
= − −z z z z
(Eq. 13)
k
(Eq.40)
GPS
k k k
=−
,
,
cos
sin
GPS
xk kGPS
k
GPS k
yk
vv
v
=
k
(Eq. 13)
( ) ( )
11kk
T
k k k
−−
= − −z z z z
Event-Tri ggered
Measureme nt
k
GPS
IMU
z
=
z
(Eq. 38)
(Eq. 39) Event-Triggered
Measure ment
(Eq. 44)
0
k
IMU
IMU
=
z
1ˆk
kk
+=+z C x D z
1ˆk
kk
+=+z C x D z
Fig. 4. The schematic of the event-triggered vehicle sideslip angle estimator.
According to the Lemma presented in Ref. [33], for any given
x,y∈Rn, and scalar δ>0, we can get
xyT+yxT≤σxxT+σ−1yyT(26)
As the system measurement noise vkis irrelevant with Ω,
Mk+1 and ˜xk+1, so the Γk+1 =0. Then, we get
−Θk+1−ΘT
k+1 ≤σ1Ωk+1 Pk+1|k(Ωk+1
)T+σ−1
1Mk+1 δ(Mk+1
)T
(27)
And
Ok+1 +OT
k+1 ≤σ2Mk+1 Rk+1 (Mk+1)T+σ−1
2Mk+1 δ(Mk+1)T
(28)
According to Equation (13) and Equation (22), when ζk= 1,
we get
ρk+1 ·(ρk+1)T≤δ(29)
The estimation error covariance can be written as
Pk+1
≤(1+σ1
)Ωk+1 Pk+1|k(Ωk+1)T+(1+σ2)Mk+1 Rk+1 (Mk+1)
T
+1 + σ−1
1+σ−1
2Mk+1δ(Mk+1 )T
=η1Ωk+1Pk+1|k(Ωk+1 )T+η2Mk+1Rk+1 (Mk+1 )T
+η3Mk+1δ(Mk+1 )T
(30)
where η1= 1 + σ1
η2= 1 + σ2
η3= 1 + σ−1
1+σ−1
2
(31)
where σ1and σ2are positive scalars. Define the upper bound
of the estimation error covariance as Pk+1, and a unified upper
bound can then be derived as
Rk+1 =(1−ζk+1 )·(I−Kk+1H)Pk+1|k+ζk+1 ·Pk+1|k
(32)
Equation (32) indicates the existence of an upper bound of
the estimation error variance, which ensures the convergence
of the proposed estimator. In order to obtain the optimal event-
triggered gain Mk+1 when ζk= 1, set
∂tr Pk+1
∂Mk+1
=2η1Mk+1 HPk+1|kHT−Pk+1|kTHT
+2η2Mk+1Rk+1 + 2η3Mk+1 δ
= 0
(33)
and the event-triggered gain can be deduced as
Mk+1=η1Pk+1|kTHT
η1HPk+1|kHT+η2Rk+1+η3δI (34)
The proof is completed.
Zeno behavior: The Zeno behavior is an important issue
for an event-triggered system. In order to avoid the Zeno
behavior, it is necessary to ensure the existence of a lower
bound for inter execution times for the controller [35]. But
the vehicle control system is a typical, discrete periodic
system with a control cycle of 10 ms due to the operating
characteristics of the CAN bus network. The VCU achieves
state estimation through fixed-cycle sampling, so there is no
such Zeno behavior for this type of system.
C. Vehicle Sideslip Angle and Roll Angle Estimation
1) Vehicle Sideslip Angle Estimation: An event-triggered
state estimation scheme is established by utilizing the GPS
heading angle and the IMU yaw rate. According to Equation
(13), when the vehicle runs straight, the vehicle yaw rate below
a preset threshold and the event is triggered. At the moment
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the vehicle heading angle is equal to the vehicle yaw angle and
the vehicle sideslip angle is 0. When the vehicle is cornering,
the vehicle yaw rate will exceed the predetermined threshold
and the IMU yaw rate is used to estimate the vehicle yaw
angle based on discrete-time integration.
The system state is given by
xγ
k+1 =ψ
ωz(35)
The event-triggered vehicle yaw angle estimator can be
given by
ˆ
xγ
k+1 =ˆ
xγ
k+1|k+1−ζγ
k+1Kγ
k+1 zγ
k+1 −ˆ
zγ
k+1|k
+ζγ
k+1Mγ
k+1 zγ
τk−ˆ
zγ
k+1|k(36)
where zγ
k+1 and zγ
τkare the system and the event-triggered
measurement; zγ
k+1|kdenotes the observation, which is given
by
ˆ
zγ
k+1|k=HγAγˆ
xγ
k(37)
where Hγ=[1, 0; 0, 1] is the observation matrix; Aγ=[1,
TGP S ; 0, 1] is the state-transition matrix, and TGP S is the
sampling time of GPS.
The event-triggered measurement is synthesized by employ-
ing the GPS heading angle γGP S and the IMU yaw rate ωGP S
z,
which can be formulated as
zγ
τk=γGP S
ωIM U
z(38)
It is worth noted that the system measurement zγ
k+1 consists
of the estimate at the previous time step kand the measured
yaw rate, which can be given by
zγ
k+1 =Cγˆ
xγ
k+Dγzγ
τk(39)
where Cγ=[1, TGP S ; 0, 0]; Dγ=[0, 0; 0, 1].
Based on Equation (1), the estimated vehicle sideslip angle
at time step kcan be calculated by
βk=ψk−γGP S
k(40)
The longitudinal and lateral vehicle velocities at time step
kcan be calculated by
"vGP S
x,k
vGP S
y,k #="cos βk
sin βk#vGP S
k(41)
where vGP S
kis the vehicle velocity measured by the GPS at
time step k.
2) Roll Angle Estimation: In order to eliminate the impact
of vehicle roll motion on the IMU lateral acceleration mea-
surement, it is necessary to estimate the vehicle roll angle.
Similarly, a roll angle estimator is developed based on the
event-triggered state estimation algorithm.
Taking the roll angle ϕand roll rate ˙ϕas the system states,
Equation (7) can be discretized as
xϕ
k+1 =Aϕxϕ
k
zϕ
k+1 =Hϕxϕ
k+1
(42)
where xϕ
k=[ϕ, ˙ϕ, ¨ϕ]T;Aϕ=[1, TIM U , 0; 0, 1, TIM U ; 0, 0,
1] is the state-transition matrix, TIM U is the sampling time
of the IMU; Hϕ=[0, 0, 0; 0, 1, 0; 0, 0, 1] is the observation
matrix.
The event-triggered vehicle roll angle estimator can be
expressed by
ˆ
xϕ
k+1 =ˆ
xϕ
k+1|k+1−ζϕ
k+1Kϕ
k+1 zϕ
k+1 −ˆ
zϕ
k+1|k
+ζϕ
k+1Mϕ
k+1 zϕ
τk−ˆ
zϕ
k+1|k(43)
where the event-triggered measurement zϕ
τkconsists of the roll
angle and roll rate, which can be expressed by
zϕ
τk=
ϕ0
˙ϕIM U
¨ϕIM U
(44)
where ϕ0represents the roll angle when the event is untrig-
gered; ˙ϕIM U and ¨ϕIM U are the roll rate and roll acceleration
measured by the IMU, respectively.
The system measurement zϕ
k+1 also consists of the estimate
at the previous time step and the measured yaw rate, which
can be given by
zϕ
k+1 =Cϕˆ
xϕ
k+Dϕzϕ
τk(45)
where Cϕ=[1, TIM U , 0; 0, 0, 0; 0, 0, 0]; Dϕ=[0, 0, 0; 0, 1,
0; 0, 0, 1].
D. Longitudinal and Lateral Velocity Estimation
The update frequency of the preliminary vehicle sideslip
angle is insufficient for online implementation. Therefore, a
combined longitudinal and lateral vehicle velocity estimator
is developed using the low-update-frequency vehicle sideslip
angle estimates and the high-update-frequency IMU signals.
1) Multi-Sensor Fusion for Longitudinal Vehicle Velocity
Estimation: A multi-sensor fusion estimator was proposed
in our previous work to obtain accurate longitudinal vehicle
velocity based on the GPS velocity measurement, the motor
rotational speed and the IMU longitudinal acceleration [34].
The readers may refer to Ref. [34] for more technical details.
2) Lateral Vehicle Velocity Estimation: A multi-step
Kalman filter is proposed to estimate the high-update-
frequency lateral vehicle velocity by using the GPS lateral
vehicle velocity vGP S
y,k and the corrected lateral acceleration
ay. The linear interpolation is used to combine vGP S
y,k and ay
for state prediction of the multi-step Kalman filter.
Equation (4) can be discretized as
xv
k=Avxv
k−1+Bvuv
k−1+ωv
k−1
zv
k=Hvxv
k+vv
k
(46)
where xv
k=[vx, vy]T,zv
kand uv
k−1are the system state,
measurement and input, respectively; Av=[1, ωIM U
zTIM U ;
−ωIM U
zTIM U , 1]; Bv=[TIM U , 0; 0, TIM U ]; Hv=[1, 0;
0, 1].
The procedure of the multi-step Kalman filter scheme is
given as follow:
Step 1: Set xv
0and Pv
0.
Step 2: Calculate ˆxv
k+1|kand Pv
k+1|kusing Equation (8)
and Equation (11).
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Step 3: Determine whether the GPS signal is updated.
Step 4: If the GPS signal is updated, calculate the Kalman
gain Kv
k+1, the optimal estimate ˆxv
k+1 and the prediction error
Pv
k+1 using Equation (9), (10) and (12), respectively.
Step 5: If the GPS signal is not updated, go back to Step 2.
IV. EXP ER IM EN TAL VERIFICATIO NS
To examine the effectiveness, reliability and real-time per-
formance of the proposed event-triggered vehicle sideslip
angle estimator, comprehensive HIL and field tests are con-
ducted.
DC Power Source
Vector CANape
Vehicle Control Unit
Host PC1
-Labcar-CarSim
Host PC2
-Labcar-CarSim
ETAS RTPC
CAN Bus Interface
Fig. 5. The HIL platform.
A. Hardware-In-Loop Verifications
As shown in Fig. 5, an HIL platform is purposely estab-
lished. It consists of two host computers, a real-time personal
computer (RTPC), a CANape, a VCU and a DC power source.
The host computer PC-1 aims to generate the executable file
by integrating the vehicle model and the Labcar project. The
executable file can be complied and downloaded into the
RTPC, which is used to simulate vehicle dynamics response
as well as to provide vehicle sensor signals. The host PC-2 is
responsible for compiling the proposed vehicle sideslip angle
estimator from the Simulink model into the executable code
in the VCU. The CANape is used for application download
and parameters calibration. The proposed event-triggered ve-
hicle sideslip angle estimator is examined under the slalom
and double lane change (DLC) maneuvers. The slalom and
DLC maneuvers are set in accordance to GB/T 6323-2014
and ISO 3888-2:2002, respectively. The test vehicle runs on
a flat road with the speeds of 60 km/h, 65 km/h and 70
km/h. More specifications of the used low-cost sensors and
mainstream navigation devices are given in Table I. The HIL
estimation results are shown in Fig. 6 and Fig. 7. The detailed
specifications of the used test vehicle are listed in TABLE II.
Seen from Fig. 6 (a), the estimated vehicle roll angle can
track the true value in all the tests, and the maximum error
of 0.253 deg occurs at the speed of 65 km/h in the slalom
maneuver. As shown in Fig. 6 (b), there is an obvious devia-
tion between the IMU lateral acceleration and the true lateral
acceleration. In contrast, the corrected lateral acceleration can
accurately follow the true value. Upon a close observation on
Fig. 6 (c) and (d), it can be seen that both the lateral vehicle
velocity and the vehicle sideslip angle can closely track their
respective true values throughout the tests with a mean error
of 0.01 m/s and of 0.029 deg, respectively. In a nutshell,
the proposed vehicle sideslip angle estimator exhibits high
(a)
(b)
(c)
(d)
Test Speed 60km/h Test Speed 65km/h Test Speed 70km/h
40 50 60 70 80 90 100 110 120
-6
-3
0
3
6
9
12
Lateral Acceleration (m/s
2
)
Time (s)
Corrected Lateral Acceleration
IMU Lateral Acceleration
True Lateral Acceleration
40 50 60 70 80 90 100 110 120
-2
0
2
4
Roll Angle (deg)
Time (s)
Estimated Roll Angle
True Roll Angle
40 50 60 70 80 90 100 110 120
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Sideslip Angle (deg)
Time (s)
Estimated Sideslip Angle
True Sideslip Angle
Slalom
DLC
40 50 60 70 80 90 100 110 120
-0.4
-0.2
0.0
0.2
0.4
0.6
Lateral Vehicle Velocity (m/s)
Time (s)
Estimated Lateral Vehicle Velocity
True Lateral Vehicle Velocity
Fig. 6. The HIL verification results of the proposed vehicle sideslip angle
estimator.(a) is the estimated roll angle, (b) is the corrected vehicle lateral
acceleration, (c) is the estimated lateral vehicle velocity, and (d) is the
estimated vehicle sideslip angle.
accuracy and robustness under various driving conditions in
the HIL tests.
The kinematic- and dynamic-based methods are also pre-
sented and compared with the proposed vehicle sideslip angle
estimator. It is worth noted that the kinematic-based method
utilizes the GPS-IMU fusion to obtain vehicle sideslip angle
while the dynamic-based approach employs a UKF-based
observer combined with a 2-DOF vehicle model to realize
sideslip angle estimation. For fair comparison, the parameters
of these two estimators are set to be identical with that in the
proposed event-triggered estimator.
Seen from Fig. 7 (a), when the vehicle runs with a speed
of 60 km/h, the proposed vehicle sideslip angle estimator
can accurately track the true value, and the dynamic-based
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TABLE I
SPE CIFI CATI ONS O F TH E USE D LOW-C OST S EN SOR S AN D MAI NS TRE AM I NERT IA L NAVIGAT ION D EVI CE S
Type Update Frequency Output Range Accuracy (RMS) Price
IMU: Yaw rate 100 H z [-180, 180] deg/sNoise: 0.1 deg/s;
Offset: ±0.6 deg/s\
GPS: Heading angle, Speed 20 Hz Angle: [0, -360] deg;
Speed: [0, 1851.8] km/h
Angle: 0.5 deg;
Speed: 0.16 km/h17.00 USD
ASENSING INS570D:
Heading angle, Speed 100 Hz Angle: [-180, 180] deg ;
Speed: [0, 1851.8] km/h
Angle: 0.2 deg;
Speed: 0.11 km/h3,000.00 USD
Oxford RT3100:
Heading angle, Speed 100 Hz Angle: [0, 360] deg ;
Speed: [0, 1851.8] km/h
Angle: 0.1 deg;
Speed: 0.10 km/h38,500.00 USD
TABLE II
PARA MET ER S OF TH E VE HIC LE M ODE L
Name Value (Unit)
Vehicle mass (with two passengers) 1617 kg
Length from the CG to the front wheel axis 1.389 m
Wheel base 2.50 m
Front tire cornering stiffness -60000 N/rad
Rear tire cornering stiffness -60000 N/rad
estimator has a certain lag despite it exhibits the same trend
with the true value. This is because the two-degree-of-freedom
vehicle model cannot represent the tire elastic hysteresis
characteristics. The kinematic-based estimator has a larger
amplitude than the true value because of the cumulative error
originating from sensor bias and noise, and gradually deviates
from the true value with time.
Seen from Fig. 7 (b), when the vehicle speed increases to
65 km/h, both the proposed and the dynamic-based method can
closely follow the true value, but the dynamic-based method
still has an obvious lag. The estimation error of the kinematic-
based method is reduced compared with that under the speed
of 60 km/h. These can be ascribed to the improved signal-to-
noise ratios for the vehicle yaw rate and lateral acceleration
measurements. Similarly, the estimation error of the kinematic-
based method is further reduced at the speed of 70 km/h as
shown in Fig. 7 (c), while the proposed estimator can still
trace its true value with high accuracy. It should be noted that
the proposed event-triggered vehicle sideslip angle estimator
is only relevant to sensor measurements and is independent
of vehicle speed. An estimation accuracy comparison of these
three methods is shown in Table III. It is evident that the
proposed vehicle sideslip angle estimator exhibits the best
estimation performance.
B. Field Tests
The field tests have also been conducted to further examine
the performance of the proposed vehicle sideslip angle esti-
mator under practical road conditions. As shown in Fig. 8, the
test vehicle is equipped with a VCU, a GPS module, an IMU,
an Oxford RT3100 and a CANoe, all of which communicate
through the CAN network. It is worth noted that the low-cost
35 40 45 50 55 60
-1.0
-0.5
0.0
0.5
1.0
1.5
Sideslip Angle (deg)
Time (s)
Sideslip Angle-True Sideslip Angle-Proposed
Sideslip Angle-Dynamic Sideslip Angle-Kinematic
Slalom DLC
@ 60km/h
(a)
70 75 80 85 90 95
-1.0
-0.5
0.0
0.5
1.0
1.5
Sideslip Angle (deg)
Time (s)
Sideslip Angle-True Sideslip Angle-Proposed
Sideslip Angle-Dynamic Sideslip Angle-Kinematic
@ 65km/h
Slalom DLC
(b)
100 105 110 115 120 125
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Sideslip Angle (deg)
Time (s)
Sideslip Angle-True Sideslip Angle-Proposed
Sideslip Angle-Dynamic Sideslip Angle-Kinematic
@ 70km/h
Slalom DLC
(c)
Fig. 7. The HIL verification results of the proposed-, dynamic- and
kinematics-based estimator. (a), (b) and (c) are the estimated vehicle sideslip
angle at 60, 65 and 70 km/h, respectively.
GPS module is connected with a Micro Control Unit (MCU)
to convert the serial port data into the CAN messages. The
Oxford-RT3100 is a high-precision inertial navigation device
to acquire true vehicle sideslip angle in the field tests. The
CANoe is responsible for data logging and analysis.
The test venue is located at our campus with relatively short
test road (around 110 min total), it is difficult to fully carry out
the vehicle tests dictated by GB/T 6323-2014 and ISO 3888-
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TABLE III
THE HIL T EST S ACC URA CY OF T HE P ROPO SE D-, D YNAM IC -AND
KI NEM ATIC -BAS ED ES TI MATOR
Maneuvers Slalom and DLC tests accuracy (RMS)
Speed
Methods Proposed Dynamic Kinematic
60 km/h 0.0281 0.1323 0.2573
65 km/h 0.0705 0.1652 0.1756
70 km/h 0.0833 0.1728 0.1122
2:2002. Thus, a short-distance slalom and a J-turn test were
carried out under the vehicle speeds of 25 km/h and 35 km/h.
The pile distance for the short-distance slalom test is set as 15
m. Despite the used vehicle speeds are lower than that of the
standard tests, the vehicle lateral acceleration exhibits a similar
pattern with wide fluctuations. This means that the used test
conditions are sufficient for examining the performance of the
proposed vehicle sideslip angle estimator. The test results are
shown in Fig. 9.
E
N
z
O
x
v
y
v
v
Event Triggered State Estimation for Vehicle Side-Slip Angle
Vehicle Side-Slip Ang le Estimation Based on E vent-triggered Kalman Filter and Multi-Senso r Fusion
y
x
x
y
CAN-L
CAN-H
VCU IMU RT3100 CANoe
GPS
MCU
CAN
Network
CAN-L
CAN-H
VCU IMU RT3100 CANoe
GPS
MCU
CAN
Network
IMUIMU
GPSGPS
Test trajectory
CANoeCANoe
RT3100RT3100
VCUVCU
IMU
GPS
Test trajectory
CANoe
RT3100
VCU
CAN-L
CAN-H
VCU IMU RT3100 CANoe
GPS
MCU
CAN
Network
IMU
GPS
Test trajectory
CANoe
RT3100
VCU
DC Power SourceDC Power Source Vector CANapeVector CANape
Vehicle Control UnitV ehicle Control Unit
Host PC1-Labcar-CarSimHost PC1-Labcar-CarSim
Host PC2-Labcar-CarSimHost PC2-Labcar-CarSim ETAS RTPCETAS RTPC
CAN Bus InterfaceCAN Bus Interface
DC Power Source Vector CANape
Vehicle Control Unit
Host PC1-Labcar-CarSim
Host PC2-Labcar-CarSim ETAS RTPC
CAN Bus Interface
Length 110mLength 110mLength 110m
Fig. 8. The field test details.
As shown in Fig. 9 (a), the estimated vehicle roll angle
can still track the RT3100 measurement throughout the test
with a maximum error of 0.5 deg and a mean error of 0.04
deg. Fig. 9 (b) shows that there is merely a minute derivation
between the corrected lateral acceleration and the RT3100
measurement. Fig. 9 (c) and (d) depict that the proposed vehi-
cle sideslip angle estimator can achieve accurate lateral vehicle
velocity and vehicle sideslip angle estimation. Compared with
the HIL results, a slightly increased error can be spotted in the
field test results, and the mean error of the estimated lateral
velocity and of vehicle sideslip angle are 0.023 m/s and 0.14
deg, respectively. These can be ascribed to the complicated
field test conditions such as road roughness and measurement
errors of the GPS.
The field test results of the proposed, dynamic-based and
kinematic-based estimators are shown in Fig. 10. It is worth
mentioning that all the parameters of the three estimators are
set the same to those used in the HIL tests. It can be seen
that the proposed estimator can closely track the RT3100
measurement throughout the test, while both the kinematic-
and dynamic-based methods exhibit large errors. Although the
estimated sideslip angle with the dynamic-based method has
the same trend with the RT3100 measurement, it shows a
large deviation caused by the lateral tire model error. The
estimated sideslip angle with the kinematics-based method
exhibits a significant offset from the RT3100 measurement due
to error accumulation. This is because the vehicle vibration
and road unevenness in field tests can aggravate the sensor
bias and noise, thus significantly curtailing the performance
of the comparison method in the field tests. In conclusion, the
proposed event-triggered estimator can achieve a considerable
estimation accuracy with a relatively low cost, which offers a
feasible solution for low-cost vehicle sideslip angle estimation.
V. CONC LU SI ON
In this paper, an enabling event-triggered sideslip angle
estimator is proposed using a low-cost GPS and an on-board
IMU. To eliminate the accumulative estimation error of the
kinematics-based methods, a preliminary sideslip angle is first
derived based on the GPS heading angle and the IMU yaw rate
and an event-triggered mechanism. The algorithm convergence
is guaranteed through theoretical deduction. To improve the
update frequency and estimation accuracy, the longitudinal
and lateral vehicle velocities are derived using the preliminary
sideslip angle and the GPS velocity measurement, based on
which a multi-sensor fusion and a multi-step Kalman filter
scheme are respectively presented to refine the longitudinal
and lateral vehicle velocity estimates. Finally, the effectiveness
and reliability of the proposed scheme are verified under
comprehensive driving conditions through hardware-in-loop
(HIL) and field tests. The results show that the proposed event-
triggered sideslip angle estimator has a mean estimation error
of 0.029 deg and of 0.14 deg under the HIL and field tests,
exhibiting high estimation accuracy, reliability and real-time
performance.
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Transactions on Industrial Informatics
IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 10
(b)
(c)
(a)
(d)
Test Speed 25km/hTest Speed 25km/hTest Speed 25km/h Test Speed 35km/hTest Speed 35km/hTest Speed 35km/h
10 15 20 25 30 35 40 45 50 55 60 65
-8
-4
0
4
8
12
Lateral Acceleration (m/s2)
Time (s)
Corrected Lateral Acceleration
IMU Lateral Acceleration
RT3100 Measurement
Test Speed 25km/h Test Speed 35km/h
10 15 20 25 30 35 40 45 50 55 60 65
-8
-4
0
4
8
12
Lateral Acceleration (m/s2)
Time (s)
Corrected Lateral Acceleration
IMU Lateral Acceleration
RT3100 Measurement
10 15 20 25 30 35 40 45 50 55 60 65
-6
-3
0
3
6
Roll Angle (deg)
Time (s)
Estimated Roll Angle
RT3100 Measurement
10 15 20 25 30 35 40 45 50 55 60 65
-6
-3
0
3
6
Roll Angle (deg)
Time (s)
Estimated Roll Angle
RT3100 Measurement
10 15 20 25 30 35 40 45 50 55 60 65
-18
-12
-6
0
6
12
Sideslip Angle (deg)
Time (s)
Estimated Sideslip Angle
RT3100 Measurement
10 15 20 25 30 35 40 45 50 55 60 65
-18
-12
-6
0
6
12
Sideslip Angle (deg)
Time (s)
Estimated Sideslip Angle
RT3100 Measurement
SlalomSlalom J turnJ turn
10 15 20 25 30 35 40 45 50 55 60 65
-0.9
-0.6
-0.3
0.0
0.3
0.6
0.9
Lateral Vehicle Velocity (m/s)
Time (s)
Estimated Lateral Vehicle Velocity
RT3100 Measurement
Fig. 9. The field tests results of the proposed vehicle sideslip angle estimator.
(a) the estimated roll angle, (b) the corrected vehicle lateral acceleration, (c)
the estimated lateral vehicle velocity, and (d) the estimated vehicle sideslip
angle.
10 20 30 40 50 60 70
-30
-20
-10
0
10
20
30
40
Sideslip Angle (deg)
Time (s)
Sideslip Angle-RT3100 Sideslip Angle-Proposed
Sideslip Angle-Dynamic Sideslip Angle-Kinematic
SlalomSlalom J turnJ turn SlalomSlalom
10 20 30 40 50 60 70
-30
-20
-10
0
10
20
30
40
Sideslip Angle (deg)
Time (s)
Sideslip Angle-RT3100 Sideslip Angle-Proposed
Sideslip Angle-Dynamic Sideslip Angle-Kinematic
Slalom J turn Slalom
Fig. 10. The field test results of the proposed, dynamic-based and kinematics-
based estimators.
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Xiaolin Ding received the B.S. degree in automotive
engineering from Hebei University of Technology,
Tianjin, China, in 2016, and he is currently pursuing
the Ph.D. degree in Mechanical Engineering with
the National Engineering Laboratory for Electric
Vehicles, Beijing Institute of Technology, Beijing,
China.
His research interests include vehicle system
dynamics and control of Four-Wheel-Independent-
Actuated Electric Vehicles.
Zhenpo Wang (M’11) received the Ph.D. degree
in Automotive Engineering from Beijing Institute
of Technology, Beijing, China, in 2005.
He is currently a Professor with Beijing
Institute of Technology, and the Director of
National Engineering Laboratory for Electric
Vehicles. His current research interests include pure
electric vehicle integration, packaging and energy
management of battery systems and charging station
design.
Prof. Zhenpo Wang has been the recipient of
numerous awards including the second National Prize for Progress in Science
and Technology and the first Prize for Progress in Science and Technology
from the Ministry of Education, China and the second Prize for Progress in
Science and Technology from Beijing Municipal, China. He has published 4
monographs and translated books as well as more than 80 technical papers.
He also holds more than 60 patents.
Lei Zhang (S’12-M’16) received the Ph.D. degree in
Mechanical Engineering from the Beijing Institute of
Technology, Beijing, China, in 2016, and the Ph.D.
degree in Electrical Engineering from the University
of Technology, Sydney, Australia, in 2016. He is
now an Associate Professor with the School of Me-
chanical Engineering, Beijing Institute of Technol-
ogy. His research interests lie in the area of control
theory and engineering applied to electrified vehicles
with emphases on battery management techniques,
vehicle dynamics control and autonomous driving
technology.
Dr. Zhang is a member of Institute of Electrical and Electronics Engineers
(IEEE) and of China Society of Automotive Engineers (CSAE). He serves
on the Technical Committee on Vehicle Control and Intelligence and the
Technical Committee on Parallel Intelligence in Chinese Association of
Automation (CAA). He has served as Guest Editors for several journals,
including International Journal of Vehicle Design, Chinese Journal of Me-
chanical Engineering, and China Journal of Highway and Transport. He
serves as an Associate Editor for PROCEEDINGS OF THE INSTITUTION
OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL
ENGINEERING SCIENCE, SAE INTERNATIONAL JOURNAL OF CON-
NECTED AND AUTONOMOUS VEHICLES, and SAE JOURNAL OF
ELETRIFIED VEHICLES. He is also on the Editorial Boards of ELEC-
TRONICS, SUSTAINABILITY and CHINA JOURNAL OF HIGHWAY AND
TRANSPORT.
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