A Vehicle Rollover Evaluation System Based on Enabling State and Parameter Estimation

Abstract

There is an increasing awareness of the need to reduce traffic accidents and fatality rates due to vehicle rollover incidents. Accurate detection of impending rollover is necessary to effectively implement vehicle rollover prevention. To this end, a real-time rollover index and a rollover tendency evaluation system are needed. These should give high accuracy and be of a low application cost. This paper proposes a rollover evaluation system taking lateral load transfer ratio (LTR) as the rollover index, with inertial measurement unit (IMU) as the system input. A nonlinear suspension model and a rolling plane vehicle model are established for state and parameter estimation. An adaptive extended Kalman filter (AEKF) is utilized to estimate the roll angle and rate, which adjusts noise covariance matrices to accommodate the nonlinear model characteristic and the unknown noise characteristic. In the meantime, the recursive least squares method with forgetting factor (FFRLS) is utilized to identify the height of the center of gravity (CG). The Butterworth filter is used to filter out the high frequency noise of acceleration signal and the index of LTR is accordingly calculated based on the estimation results. The proposed scheme is verified and compared through hardware-in-loop (HIL) tests. The results show that the developed scheme performs well in a variety of operating conditions.

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Abstract—There is an increasing awareness of the need to
reduce traffic accidents and fatality rates due to vehicle rollover
incidents. Accurate detection of impending rollover is necessary to
effectively implement vehicle rollover prevention. To this end, a
real-time rollover index and a rollover tendency evaluation system
are needed. These should give high accuracy and be of a low
application cost. This paper proposes a rollover evaluation system
taking lateral load transfer ratio (LTR) as the rollover index, with
inertial measurement unit (IMU) as the system input. A nonlinear
suspension model and a rolling plane vehicle model are established
for state and parameter estimation. An adaptive extended Kalman
filter (AEKF) is utilized to estimate the roll angle and rate, which
adjusts noise covariance matrices to accommodate the nonlinear
model characteristic and the unknown noise characteristic. In the
meantime, the forgetting factor recursive least squares (FFRLS)
method is utilized to identify the height of the center of gravity
(CG). The Butterworth filter is used to filter out the high
frequency noise of acceleration signal and the index of LTR is
accordingly calculated based on the estimation results. The
proposed scheme is verified and compared through hardware-in-
loop (HIL) tests. The results show that the developed scheme
performs well in a variety of operating conditions.
Index Terms—rollover evaluation system, vehicle state
estimation, CG height identification
I. INTRODUCTION
UTOMOTIVE electrification and safety are two main
subjects of the modern automobile industry [1]-[4].
Rollover constitutes a major cause of road accidents that result
in severe and fatal injuries of passengers. Statistics showed that
31.5% of highway fatalities in the US related with rollover
albeit that only a minute fraction of traffic crashes involved with
rollover [5]. To reduce the potential risks of rollover and protect
passengers from injury, substantial efforts have been directed
to developing reliable and efficient roll stability control systems.
For example, active and air suspensions have been utilized to
enhance the vehicle roll stability [6], [7]. Besides, active control
systems such as active front steering and optimal control
allocation braking have also been widely investigated for
rollover mitigation [8], [9]. However, it is imperative to timely
and accurately evaluate the potential and circumstances of
rollover occurrence before implementing these rollover
mitigation systems. Thus, a rollover index is necessary to
determine the likelihood of vehicle rollover for automatic and
assistant driving systems [10], [11].
Several stability indexes have been used in the literature to
predict vehicle rollover. These can be grouped into three
categories: characteristic state method, energy analysis method
and force analysis method. The characteristic state method
takes lateral acceleration, roll angle or some other typical
vehicle states as the stability index [12], which is often
compared to a set threshold for judging roll motion stability.
However, this method cannot reflect the dynamic evolution of
roll motion because of inertial system characteristic caused by
suspension. The energy analysis method usually calculates the
energy change during roll motion from a stable position to its
tip-over point to assess the rollover stability. In this regard,
Nalecz put forward a Rollover Prevention Energy Reserve
(RPER) method for precise rollover stability assessment [13].
The force analysis method adopts mechanics index to assess the
rollover tendency such as zero-moment point (ZMP) and lateral
load transfer ratio (LTR) [14], [15], which will also benefit
lateral stability control systems [16]. To obtain a better rollover
prediction performance, some studies have combined the use of
time-to-rollover (TTR) and LTR or ZMP [17], [18].
To accurately evaluate the rollover tendency, some crucial
vehicle parameters and states are needed [19]. These mainly
include roll angle, lateral acceleration and height of the center
of gravity (CG). Lateral acceleration is usually required for a
lateral stability control system and can be readily obtained via
commercial sensors. However, roll angle cannot be readily
measured in a vehicle and needs to be estimated. Existing
methods can be divided into two groups: sensor information
fusion-based and model-based approaches. With the
development of sensor technology, suspension deflection
sensors [20], inertial measurement unit (IMU) and two-antenna
Novatel Beeline GPS [21], [22] have been researched to
calculate the roll angle. However, the high cost of related
sensors hinders their commercial application. Except for the
fusion of multiple sensors, model-based algorithms have been
developed to estimate the roll angle [23]. Roll plane model
considering computational efficiency [24] and multi-degree of
freedom model considering precision [25], [26] have been
established. Unknown Input Observer (UIO) [27] and Kalman
Filter (KF) [28] have been utilized to estimate the roll angle.
With the progress of artificial intelligence, Guzman et al.
explored the use of artificial neural networks (ANNs) in
A Vehicle Rollover Evaluation System Based on
Enabling State and Parameter Estimation
Cong Wang, Zhenpo Wang, Lei Zhang, Member IEEE, Dongpu Cao, Member IEEE, and David G. Dorrell, Fellow
IEEE
A
Manuscript received XXXX; accepted XXXX. Date of publication
XXXX; date of current version XXXX. This work was supported in part by
the Ministry of Science and Technology of the People’s Republic of China
under Grant 2017YFB0103600. Paper no. XXXX. (Corresponding author:
Lei Zhang, email: lei_zhang@bit.edu.cn)
Cong Wang, Zhenpo Wang and Lei Zhang are with the National
Engineering Laboratory for Electric Vehicles, Beijing Institute of
Technology, Beijing 100081, China.
Dongpo Cao is with the University of Waterloo, Canada.
David G. Dorrell is with the University of Witwatersrand, South Africa.
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combination with the KF [29]-[31]. Vehicle-to-vehicle (V2V)
communication can also be utilized to pre-estimate the roll
angle [32]. Considering the algorithm robustness to parameter
variation, especially CG height, some integrated and modular
estimation structures have been researched. For example, Dual-
Kalman Filter (DKF) was utilized for joint estimation of the roll
angle and the CG height [26], [33]. The modular structure
includes different observers such as the Adaptive Kalman Filter
(AKF) and the Extended Kalman Filter (EKF) in [34] and the
Recursive Least Squares (RLS) and the UIO in [35] to improve
robustness.
Previous studies have described various methods for rollover
evaluation and state estimation. Challenges remain in model
reliability and algorithms’ robustness to unknown disturbance.
In this study, the nonlinear characteristics of suspension system
and the road bank angle are considered in model formulation,
which is often neglected in other studies. Moreover, the
adaptive extended Kalman filter (AEKF) is developed for state
estimation to deal with the unknown characteristics of noise,
and the CG height is corrected based on the forgetting factor
recursive least squares (FFRLS) method. Furthermore, a
systematic approach to evaluating rollover propensity based on
the LTR is developed since existing studies merely revealed
parts of the link. The schematic of the proposed scheme is
shown in Fig.1.
The remainder of this paper is structured as follows: Section
II introduces the nonlinear suspension system and the vehicle
roll motion model. Section III elaborates the proposed AEKF
scheme combined with the FFRLS estimation and the LTR
calculation. Section IV offers hardware-in-loop (HIL)
experimental verifications, followed by the key conclusions
summarized in Section V.
Fig. 1. The schematic of the proposed scheme for LTR calculation.
II. VEHICLE MODELLING WITH NONLINEAR SUSPENSION
In this section, a simplified vehicle roll motion model with a
nonlinear suspension system is established. A coordinate
system is defined where the x-axis corresponds to the
longitudinal axis of the vehicle and is positive in the forward
direction, the y-axis corresponds to the lateral axis and is
positive to the left, and the z-axis is perpendicular to the x-y
plane and is positive in the upward direction. Roll, pitch and
yaw are defined around the x-, y- and z-axis, respectively. Some
assumptions are made for model simplification:
• The longitudinal speed is regarded as constant during a
short time;
• The effect of side wind is neglected;
• The coupling effect between the roll and other motions is
not considered;
• The roll angle of the unsprung mass is neglected.
According to the D'Alembert principle, every accelerated
movement can be equivalent to a D'Alembert inertia force or
moment. A dynamics problem can be transformed into a
pseudo-static one. The components of the inertia force system
due to lateral and roll accelerations of a sprung mass are given
by
''
y s y x xx
F m a M I

==，
(1)
where ms is the sprung mass of the vehicle, ay is the lateral
acceleration due to vehicle lateral motion, Ixx is the moment of
inertia about the x-axis around the CG of the sprung mass, and
ϕ is the roll acceleration of the sprung mass. The overall force
system consists of inertia forces, gravity and suspension forces.
The force analysis and distribution are shown in Fig. 1.
The roll angle of the vehicle comprises of the contributions
from the sprung ϕs and the unsprung mass ϕus, which can be
given by
s
=us
  
+
(2)
In the vehicle modelling, the roll angle of the unsprung mass is
neglected since the vertical stiffness of tires is much larger than
that of the suspension. Thus, the roll angle of the vehicle ϕ is
assumed to equal to that of the sprung mass ϕs. The vertical
deformation characteristic of a tire is given in Fig. 2. It can be
seen that the effective radius of tires changes slightly with the
vertical force, which well matches the assumption.
Fig. 2. The tire vertical stiffness based on experiments.
The force system of the sprung mass is transformed into the
moment balance about the roll center O' to derive the roll
dynamics model. The coupling effect between the roll and other
motions is considered as [36], which results in
''
cos sin( ) ( ) ( )
x y s r xz C K
M F h m gh I M M
     
= + + + − −
(3)
where Ixz, h, ϕ, ϕr, ϕ, ψ, g, MK and MC represent the product of
inertia about the x- and z-axis, roll radius, roll angle, road bank
angle, roll rate, yaw acceleration, gravitational acceleration, and
equivalent resisting moments from the spring and the damping,
respectively. The road bank angle is regarded as a known input
which is considered as a constant during a short instance in this
study.
The item of Ixzψ represents the influence of the yaw motion
on the roll dynamics due to the existence of the product of
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inertia Ixz. To quantitatively assess the influence, the value of
each item collected from the Carsim is shown in Fig. 3 and their
absolute proportions during the double lane change (DLC)
process are listed in Table Ⅰ. The proportion is calculated by
6
1
()
()
()
p
Item i
Proportion i
Item p
=
=

(4)
where Item(i) refers to the i-th item in Eq. (3). The initial value
of Ixz is set to be 166 kg*m2 according to [36] with the other
parameters set the same as in Table Ⅱ. It can be found that the
coupling item Ixz ψ is always small during the entire DLC
maneuver. Compared with the other items, the coupling item
can be reasonably neglected since its absolute proportion is only
0.57% in average with a maximum value of 4.91%. This
justifies the assumption that the coupling effect between the roll
and other motions is not considered.
Fig. 3. Values of different items during the DLC maneuver.
TABLE Ⅰ
ABSOLUTE PROPORTION
Item
IXZΨ
Mx
'
msghsin(φ+φr)
MC
Fy
'hcosϕ
MK
Max value (%)
4.91
14.99
50.37
41.07
49.59
50.42
Average (%)
0.57
2.65
29.89
4.18
21.07
41.63
MK and MC are hard to directly obtain, so an approximate
calculation method is developed here. The resisting moment MK
mainly results from the suspension spring MKs and the lateral
stabilizer bar MKb. MKb can be regarded as a linear function of
the roll angle, which is given by
Kb b
MK

=
(5)
where Kb is the angular stiffness of the lateral stabilizer bar.
When there is a roll angle existing for the sprung mass, the
suspension force of the rear axle can be calculated by
' 3 ' 3
22
GG
srr r r srl r r
FF
F k x k x F k x k x= +  +  = −  − ，
(6)
where Fsrr, Fsrl, FG, and Δx represent the right suspension spring
force, the left suspension spring force, the rear axle load and the
deflection relative to the steady state. Instead of taking the
spring stiffness as a constant, the nonlinear characteristic of the
suspension is considered in this model. In practice, the
suspension stiffness changes with the amount of compression
in order to achieve better stability. Several technologies such as
hydro-pneumatic suspension, variable stiffness spring and
pneumatic suspension can be utilized [37]. Usually the stiffness
increases with the amount of compression and a cubic
polynomial is utilized to represent the spring [38]. 
 and 
are the coefficients of the cubic polynomial of the rear
suspension. It is worth mentioning that the suspension vibration
due to road conditions is neglected since it has small amplitude
and high frequency. With the front suspension defined in the
same way and similar parameters of the front axle defined as 

and , the roll moment is calculated by
( )
( )
( )
( )
'3
'3
2
2
Kr srr srl r r
Kf srf srf f f
l
M F F k x k x l
l
M F F k x k x l
= − =  + 
= − =  + 
(7)
where l is the distance between the suspension mounting
positions. The roll moment due to rear suspension can be
deduced in the same way. The suspension deflection due to the
roll motion is given by
sin
22
ll
x


 = 
(8)
The total roll moment from the spring of suspension can be
calculated by
K Kr Kf b
M M M M= + +
(9)
Substituting Eqs. (7) and (8) into Eq. (9), it is derived as
42
' ' 3
( ) ( ) ( )
82
k f r f r b
ll
M k k k k K
  

= + + + +


(10)
The damping will come to play a role when the vehicle is not
in a steady state, and thus another equivalent resisting moment
appears. The nonlinear characteristic of the damping force is
also considered in the model rather than to simply adopt a
constant damping coefficient.
Usually, to acquire the best driving experience, the damping
coefficient in compression travel is smaller than that in the
recovery travel. When an impact is applied to the wheel, less
impact force will be transmitted to the driver and the impact
energy will be dissipated in the recovery travel as soon as
possible. The damping coefficient is often designed to decrease
with the velocity so that high frequency vibrations can be
filtered while less impact force will be transmitted.
Taking the rear axle for example, a separate cubic
polynomial function is utilized to represent the suspension
damping. The force due to damping is
( )
( )
32
32
0
comp
v
ressi
reco e y
on
0r
tq
rc rc rc
dr tq
rr rr rr
v
c v c v c v
Fv
c v c v c v

 +  + 


=
 +  + 


(11)
where Δv is the relative velocity of damping; crc
t, crc
q and crc are
the coefficients of the rear suspension damping during
compression while crr
t, crr
q and crr are during recovery. Similar
parameters of the front axle are defined as cfc
t, cfc
q, cfc for
compression and cfr
t, cfr
q, cfr for recovery.
When a positive roll rate exists, the right side is in
compression travel while the left side in recovery travel. With
the assumption of small angle, the relationship between the roll
rate and the relative speed of damping is
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cos cos
2 2 2 2
rl
l l l l
vv
   

 =   = −  −，
(12)
where Δvr and Δvl are the velocities of the right and the left
damping.
The roll moment due to rear suspension damping can be
derived from Eq. (12) as
( ) ( )
( )
4 3 2
32
16 8 4
t t q q
Cr rc rr rc rr rc rr
l l l
M c c c c c c
  
= + + + + +
(13)
The front axle moment can be calculated in the same way.
The total roll moment is the sum of the front and the rear
suspension damping, which is given by
( )
4 3 2
32
16 8 4
tq
C Cr Cf l l l
M M M c c c
   
= + = + +
(14)
where
t t t t t
rc rr fc fr
q q q q q
rc rr fc fr
rc rr fc fr
c c c c c
c c c c c
c c c c c
= + + +
= + + +
= + + +
(15)
III. ROLLOVER INDEX EVALUATION SYSTEM
A. AEKF State Estimation
The KF has been widely used for vehicle states estimation
because it provides an efficient recursive means for estimating
the states of a process in such a way as to minimize the mean of
the squared errors. The fundamental operation of the KF is a
successive process of predictions based on system inputs and
corrections based on measurable system outputs. However, the
classic Kalman filter can only deal with the state estimation
problem of a linear system. A typical nonlinear state-space form
is
( )
( )
1
1 1 1
,
,
k k k
k k k
+
+ + +
=+
=+
x f x u w
y g x u v
(16)
where w and v are the process noise that affects the system states,
and the measurement noise that reflects the measurement
accuracy; w is assumed to be the Gaussian white noise with zero
mean and covariance Q, and v is also assumed to be the
Gaussian white noise with zero mean and covariance R; xk and
yk are the state and the measurement vector at time step k, and
the functions of f and g represent the nonlinear relationships.
To apply the Kalman filter to nonlinear systems, the EKF,
Unscented Kalman filter (UKF), Cubature Kalman filter (CKF)
and some other variates have also been developed. The EKF
deals with the nonlinear problem by the linearization of the
system around the previous posterior estimate result [39]. The
Jacobian matrix will replace the state and the observation
matrix for prediction and correction. But there is still a
drawback that it relies heavily on a good estimation of Q and R.
Typical Kalman filters usually assume that the covariances of
both the process and measurement noises are known. However,
the noise information in an actual environment can be time-
varying and complicated, thus restricting the KF and its
feasibility in practice. To overcome this problem, an AEKF
approach, deduced from a maximum-likelihood (ML)
estimation solution, is applied to the state estimation in this
study.
The ML estimation is a statistics solution based on the
maximum likelihood principle which provides a method of
evaluating the model parameters based on experimental data.
Once the probability distribution is certain, the best parameters
that make the occurrence probability of the sample highest can
always be found through independent and identical
measurements. Thus, the ML can find the weights that will
result in the smallest error norm. This means that the adaptive
weight estimation is complementary to the state estimation.
Since it is assumed that the noise has a Gaussian distribution
and the measurement at time step k is independent from other
time steps, the observation noise covariance matrix R can be
calculated through a partial derivative operation from as
ˆ
ˆ-T
k vk k k k
R = C - H P H
(17)
Fig. 4. The moving observation window.
The process noise covariance matrix Q can be obtained using
the same strategy on the basis of obtaining R and an
approximate representation so that
'
1
ˆ ˆ T
k k vk k k k k k
++
−
+−Q = K C K P G P G
(18)
The whole derivation is given in [40] and will not be described
in detail here.
R
k and Q
k are the estimated measurement noise covariance
matrix and process noise covariance matrix at time step k which
will be used for the Kalman gain and state covariance update in
the next step. Hk, Pk
-, 
 and Kk are the observation matrix,
priori state covariance matrix, posteriori state covariance matrix
and Kalman gain matrix at time step k respectively. A moving
observation window is utilized to gather independent
measurement data as shown in Fig. 4, and C
vk is the innovation
matrix which can be calculated through averaging the
prediction error inside the window by
1
1
ˆkT
vk j j
j k N
N= − +
=
C e e
(19)
where N is the size of the moving estimation window. Generally,
the ML estimate is biased for small sample sizes. This suggests
an additional constraint on the choice of the estimation size. The
larger the estimation size, the less unlikely the biasness of the
estimation. However, an oversized estimation window will
reduce the algorithm in tracking performance of high frequency
changing state. Therefore, a trade-off between the biasness and
the tractability of the estimate, according to the application,
should be taken into account. ek is the innovation sequence that
is calculated at each step using
( )
ˆ,
k k k k
−
=−e y g x u
(20)
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The AEKF which consists of the classical EKF followed by a
ML covariance estimator is constructed to estimate the roll
angle and roll rate. The overall implementation flowchart of the
AEKF algorithm is shown in Fig. 5, where Gk and Hk are the
Jacobian matrices of the discrete system and observation
equations at time step k, respectively.
In order to apply the AEKF in practice, the continuity
equation based on Eqs. (1) and (3) should be transformed into a
discrete equation. The roll acceleration ϕ is equivalent to the
difference of the adjacent roll rates so that
1kk
kT


+−
=
(21)
where T is the sample time. The discrete equation can be shown
to be
( )
( )
( )
1cos sin(
k s yk k s k r k C k K k
xx xx xx
T T T
m a h m gh M M
I I I
      
+= + + + − −
(22)
Fig. 5. The flowchart of the proposed AEKF method.
The six-axle IMU sensor with three axles of acceleration and
three axles of roll velocities provides information for some
states in the discrete equation. The IMU system is widely used
in the navigation systems of aircrafts and ships. With the
technological advancements, the micro-electromechanical
system (MEMS)-based IMU sensors have been developed and
have an extremely small volume and a relatively low cost. The
MEMS-based IMU sensor is becoming more popular in smart
cellphones and other small devices, which is also adopted in this
study.
Fig. 6. The relationship between different accelerations and measurements.
The lateral acceleration bias induced by the sensor
installation is neglected. However, the lateral acceleration
measurement can be disturbed by the attitude angle as the
sensor is fixed to the vehicle body. As shown in Fig. 6, due to
the movements with the vehicle body and the road bank angle,
the measured lateral and vertical accelerations aymk and a

mk at
step time k can be described as a combination of the horizontal
lateral acceleration ayk and the vertical gravity acceleration g,
which are given by
sin( ) cos
ymk k r yk k
a g a
  
= + +
(23)
kcos( ) sin
zm k r yk k
a g a
  
= + −
(24)
Substituting Eq. (23) into Eq. (22), it deduces as
1( ( ) ( ))
k k s ymk C k K k
xx
Tm a h M M
I
   
+= + − −
(25)
The discrete iterative relation between the roll rate and the
roll angle can be given by
1k k kT
  
+=+
(26)
Eqs. (25) and (26) constitute the discrete state space
expressions which are used for the state estimation. The roll rate
and the roll angle are chosen as state variables while the lateral
acceleration is regarded as an input. The measurement of roll
rate is chosen as the observation equation in
mk k

=
(27)
The overall estimation system is
( ) ( )
1
1
T
k k k k mk
C k K k
kxx xx k
k
y
MM
TT
II
T
  



   
==
   


−−

=




，x
G
(28)
3 ' ' 2
4 3 2
22
3 ( ) ( )
3
1 ( ) ( )
=16 4 4 8 2
1
tq f r f r b
xx xx
l k k l k k
T l c l c l c T K
II
T
  

++
− + + − + +




0 [1 0]
T
k s k
xx
Tmh
I

==


BH，
B. FFRLS CG Height Identification
As mentioned before, the vehicle states during roll motion
are estimated under the assumption of known system
parameters. However, the CG height is usually a key parameter
that varies with mass distribution and cannot be acquired easily,
but it plays an important role in the roll dynamics. Thus, the
FFRLS method is adopted for CG height identification in this
study. The FFRLS method is deduced from the adaptive
filtering theory and widely used for parameter identification.
The periodic correction of parameters using the FFRLS can
solve the model uncertainty and thus improve the estimation
robustness.
The traditional RLS has the disadvantage of relatively poor
performance when applied to a time-varying parameter
estimation. When there is a change of parameter, it cannot track
the change in a timely manner. The FFRLS method introduces
a forgetting factor into the measurement data to reduce the
amount of old data. Thus, data super-saturation is alleviated and
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new data can come into play. A small forgetting factor will
make the system converge fast but more sensitive to noise;
however, an overlarge factor will deteriorate the system
tracking performance. On top of this, a compromise should be
made in the choice of the forgetting factor, which is usually
chosen from 0.9 to 1.
The system formulation could be considered as
, , ,P k P k k P k
=+yφ θ e
(29)
where yP,k, φP,k, θk and eP,k are the system output vector, input
vector, parameter vector and deviation at time step k
respectively; eP,k is usually assumed to be the white noise with
zero mean.
At the beginning of each cycle, the system output and input
vectors will be observed, and the deviation is calculated using
, , ,P k P k P k k 1−
=−eyφ θ
(30)
Then, the correction gain is calculated from
1
, , 1 , , , 1 ,
TT
P k P k P k P k P k P k

−
−−

=+

KPφ φ Pφ
(31)
where KP,k and PP,k are the algorithm gain and noise covariance
matrix at time step k; μ is the forgetting factor.
At the end of a cycle, the parameter is estimated and its noise
covariance will be updated as follows:
1 , ,k k P k P k−
=+θ θ Ke
(32)
1
, , , , 1P k P k P k P k

−
−
=−


P I K φP
(33)
It is worth noting that the FFRLS formulations are given in a
generic format here.
In order to apply the FFRLS for CG height estimation, the
discrete state update equation in Eq. (25) combined with Eq.
(21) will be utilized again. The equation after modification can
be represented as
( ) ( )
xx k C k K k s ymk
I M M m a h
  
+ + =
(34)
Thus, the roll radius h is regarded as the parameter to be
estimated. The system input and output are given by
( ) ( )
( )
,P k xx k C k K k
y I M M
  
= + +
(35)
,P k s ymk
ma

=
(36)
kh

=
(37)
With the vertical displacement of roll center neglected, the
CG height can be seen as the sum of the roll radius h and the
height of the roll center hR, which is given by
CG R
h h h=+
(38)
It can be easily found that to estimate the roll radius and the
CG height, the state of ϕk and aymk should be acquired first. The
lateral acceleration and the roll rate can be obtained from the
IMU. The roll acceleration can be obtained by numerical
differentiation of the roll rate. However, to take the derivative
directly will not be appropriate since the sensor information
carries noise and the differentiation operation will magnify the
noise because of the short sample period usually in milliseconds.
In order to avoid this problem, a multi-step differentiation is
adopted to take the place of Eq. (21), which is given as
k M k
kMT


+−
=
(39)
where M is the interval of time step used to take the derivative.
However, the interval should not be too large or else it may
introduce a signal delay and thus compromise the performance
of the parameter identification.
For the source of ϕk, a rough roll angle measurement from the
kinematic relationship between the lateral and the vertical
acceleration measurement as shown in Fig. 6 can be used since
the parameter identification will not be required to work all the
time and the FFRLS has a noise filtering ability to some extent.
Combining the lateral and vertical accelerations in Eqs. (23)
and (24). The relationship between the two acceleration
measurements can be obtained as
sin( ) cos( ) cos( )
ymk k zmk k r
a a g
  
+=
(40)
The roll angle can be solved using a small angle assumption,
which is expressed as
2
sin( ) , cos( ) 1 0.5
k k k k
   
  −
(41)
The second order term is preserved to improve the accuracy.
It needs to be emphasized that the road roughness can
introduce extra noise, thus disturbing the identification system.
Some preconditions are made for the system operation to ensure
a relative high signal-to-noise ratio. When the lateral
acceleration is higher than 0.5 m/s2, the roll angle is calculated
and exported. Only when the roll angle output is larger than
0.015 rad for five consecutive time steps, the parameter is
updated from the last value in the memory. Otherwise the value
in the memory will be kept and utilized for state estimation.
C. Butterworth Filter
The direct utilization of acceleration measurement may
introduce noise, which makes it hard to get a stable output. In
order to smooth the signal, a second-order Butterworth filter is
used. It has the smoothest performance in the pass-band and the
gain decays gradually in the stop-band. The system transfer
function in the continuous-time domain after normalization is
( )
21
1.414 1
Hs ss
=++
(42)
(a) Time-domain comparison
(b) Frequency-domain comparison
Fig. 7. The evolution of lateral acceleration during the DLC maneuver.
The transfer function in the discrete-time domain is
1
1
1
11
1z
sCz
−
−
−
=
+
(43)
where s and z are the complex variables of Laplace-
transformation and Z-transformation respectively. C1 can be
calculated from
1tan c
s
f
Cf


=

(44)
where fs and fc are the sample and passband cut-off frequencies
respectively. A small fc may bring a delay into the filtered signal
while a large fc may complicate the filtering effect. The cut-off
frequency of 4 Hz is adopted to realize a tradeoff. fs is set to be
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100 Hz which is the same with that of the HIL tests.
In order to verify the filtering effect, a comparison between
the original and the filtered lateral acceleration signal in the
time- and frequency-domain during the DLC maneuver is
shown in Fig.7. The noise added is a white noise with the
variance of 0.02. It can be seen in Fig. 7(a) that the lateral
acceleration signal is effectively smoothed without obvious
delay. Upon a close observation on Fig. 7(b), it is evident from
the power spectrum that the high-frequency noise is attenuated.
D. LTR Calculation
Using the state estimation and parameter identification
results, the LTR can then be calculated. The definition of LTR
is
zo zi
zo zi
FF
LTR FF
−
=+
(45)
where Fzo and Fzi are the outside and inside vertical forces of
the vehicle tires respectively.
To accurately obtain the vertical forces, a force analysis is
conducted for the sprung and unsprung masses, which is given
by
sin( )
yO s yk s r
F m a m g


=+
(46)
where FyO represents the horizontal force acting on the sprung
mass at the roll center. Eq. (46) can be obtained using the
horizontal force balance of the sprung mass by assuming that
the roll center is regarded as a fictitious junction point.
The force and moment of the sprung mass will be conducted
to the unsprung mass from the suspension and the fictitious
junction point. With the load transfer of the unsprung mass
neglected, the moment equation in the x-direction can be
represented as
( ) ( )
( )
2
zo zi yO R K k C k
t
F F F h M M

− = + +
(47)
where t represents the interval of ground attachment points
between two sides of the vehicle. The horizontal lateral
acceleration can be obtained from
sin( )
cos
ymk k r
yk k
ag
a


−+
=
(48)
where aymk
 is the filtered lateral acceleration by the Butterworth.
When driving on flat roads, the overall vertical force can be
obtained by
cos( )
zo zi r
F F mg

+=
(49)
where
su
m m m=+
(50)
Substituting Eqs. (47), (48) and (49) into Eq. (45), it derives
as
( )
( )
sin( )cos( )
2cos( )cos( ) cos( )
K k C k
ymk k r
sR r k r
MM
ag
LTR m h mgt mgt


  

+
−

=+


(51)
IV. EXPERIMENT RESULTS AND DISCUSSIONS
The estimation methods described in the sections above were
evaluated using the HIL tests, which can be utilized to reflect
and verify the actual performance influenced by the computing
power, signal transmission delay and protocol precision. The
HIL system mainly consists of the ETAS Labcar, an OpenECU
and a CANape. The Labcar can carry the predefined vehicle
model established in Carsim, and multiple CAN buses are used
for analysis and communication with the controller. As a kind
of rapid prototyping tool, the OpenECU can be used to load the
strategies constructed in Simulink easily. Through the CANape,
the developer can conveniently monitor the signals. The HIL
system and its overall network framework are shown as Fig.8.
Fig. 8. The HIL system and its network framework.
TABLE Ⅱ
VEHICLE PARAMETERS
Symbol
Description
Value
ms
Sprung mass
1430 kg
mu
Unsprung mass
120 kg
Ixx
Vehicle roll moment of inertia about CG
700 kg*m2
Ixz
product of inertia about x- and z- axises
166 kg*m2
l
Track width
1.48 m
t
Distance between left and right
suspensions
1.28 m
hCG
Height of CG
0.7 m
hR
Height of roll center
≈0.2m


Spring parameters of rear suspension
0.002 N/mm3

30 N/mm


Spring parameters of front suspension
0

30 N/mm
Kb
angular stiffness of lateral stabilizer bar
108 Nm/deg


Damping
parameters of
suspension
Compression
-6.5×10-7 N(s/mm)3


0.2×10-3 N(s/mm)2

1.8 Ns/mm


Recovery
-5×10-7 N(s/mm)3


-3×10-3 N(s/mm)2

2.4 Ns/mm
During HIL tests, a sampling time of 0.01 s is adopted and
the protocol of database for CAN communication (DBC) is also
made for the signal parse of the OpenECU and the LabCAR.
The simulated sensors and the noise imposed on the output
signal are constructed in Carsim and loaded into the LabCAR.
The algorithms constructed in Simulink are flashed into the
OpenECU through the CANape. The OpenECU receives
signals from the CAN network and the operation results are
broadcast to the same CAN bus, and the CANape monitors the
outputs by the Vector CAN Card.
A small SUV vehicle is established and used in the Labcar
for HIL tests and its main parameters are given in Table Ⅱ. It is
assumed that the front and the rear axle damping have the same
parameters and the rear axle is equipped with a lateral stabilizer
bar. The reference signals are gathered from the Labcar such as
the roll angle. But the LTR is a human-defined index that does
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not exist in the output list. Ref. [41] calculates the LTR based
on the ground vertical forces and the calculation method is
adopted as the reference, which is given by
fr rr fl rl
reference fr rr fl rl
F F F F
LTR F F F F
+ − −
=+ + +
(52)
where Ffr, Ffl, Frr and Frl represent the vertical forces at the front
right, front left, rear right, and rear left tire which can be
exported from the Carsim.
A. Stable Cornering Maneuver
Stable cornering is a normal maneuver in daily driving at
traffic crossings and on the highway. An accurate evaluation of
rollover tendency can assist the driver to avoid pending rollover
accidents through slowing down and/or controlling the steering
wheel. The performance of the proposed AEKF is examined
and compared with the traditional EKF. A time-varying noise
is imposed to show the adaption characteristic of the AEKF.
The stable cornering path is illustrated in Fig.9 (a) and the
sensor signals with imposed noise is shown in Fig.9 (b). A
closed-loop path follower with a preview time of 0.5 s is used
to track the path. The vehicle velocity is set to be 80 km/h and
the road friction coefficient is set to be 1 with a road bank angle
of 0.04 rad. The initial noise variances for the lateral
acceleration and the roll rate are set to be 0.02 (m/s2)2 and
0.0002 (rad/s)2 respectively. These variances change to 0.2
(m/s2)2 and 0.002 (rad/s)2 at 5 s, which means ten times the
initial values. A well-tuned EKF is utilized with Q= [1.5E-6, 0;
0, 2E-8] and R=[2E-5], which is also adopted as the initials of
the proposed AEKF for fair comparison.
(a) The stable cornering path.
(b) The signals with noise.
Fig. 9. Maneuver configuration of the stable cornering.
The HIL test results are depicted in Fig 10. The evolutions of
the covariances of the AEKF are shown Fig. 10 (a) and (b). It
can be found that the measurement noise covariance matrix R
is updated to respond to the noise variation. Considering that R
is simple and contains the sensor error only, the roll rate signal
noise variance is added as the reference and R can follow the
reference well. The main diagonal elements of the process noise
covariance Q can also be timely adjusted along with the
changed noise and maneuver. Compared with the traditional
EKF, more appropriate R and Q are obtained by the adaptive
method and a better estimation performance is achieved.
(a) The evolution of the covariance R.
(b) The evolution of the covariance Q.
(c) The roll angle evolution.
(d) The CG height evolution.
(e) The evolution of LTR.
Fig. 10. Estimation results under the stable cornering maneuver in HIL tests.
In Fig.10 (c)-(e), it can be seen that the proposed algorithm
can realize high-accuracy states estimation throughout the
maneuver. As shown in Fig. 10 (c), the EKF can merely follow
the reference before 5 s at which the noise characteristic sees a
dramatic change, but exhibits significant deterioration
afterwards and loses the tracking at about 8 s. These lead to a
similar deviation tendency for the LTR as shown in Fig. 10 (e).
In contrast, the proposed AEKF can realize accurate roll angle
and LTR estimations despite of some oscillations. Besides, the
CG height is refreshed from the initial value of 0.6 m to 0.72 m
as shown in Fig.10 (d), which is quite close to its true value of
0.7 m.
B. Double Lane Change Maneuver
In order to further verify the effectiveness of the proposed
method, the DLC maneuver is also used with its path shown in
Fig. 11 (a). It can simulate the emergency scenario in which a
swift lane change must be executed in order to avoid obstacles.
This would induce an instantaneous, large lateral acceleration
which may result in vehicle rollover. The initial vehicle velocity
is set to be 85 km/h with a road bank angle of 0.04 rad. The
rollover index (RI) presented in [42] and [43] is used in this
study for comparison, which determines the rollover propensity
based on the lateral acceleration and formulates the RI after
normalization as
sin 2
cos
yr
r
ag h
RI gt


+
=
(53)
(a) The double lane changing path.
(b) The roll angle evolution.
(c) The rollover extent evolution.
(d) The CG height evolution.
Fig. 11. Estimation results under the DLC maneuver in HIL tests.
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The HIL test results under the DLC maneuver are delineated
in Fig. 11 (b)-(d). As shown in Fig. 11 (b), it can be seen that
the proposed AEKF can closely track the reference roll angle in
Fig. 11 (b). The estimation sees some enlarged deviations from
the reference at the peaks, which may originate from the
negligence of the unsprung mass. But these deviations are still
within an acceptable range and have little influence on the
rollover determination as shown in Fig. 11 (c). Besides, the CG
height can also be precisely identified albeit there is some
fluctuation.
The performance of the proposed AEKF-based LTR
algorithm is compared with the RI method based on
acceleration. Additionally, the LTR based on actual tire forces
from the Carsim is added as the reference as shown in Fig. 11
(c). It can be seen that both the AEFK-based LTR and the RI
method can track the reference in the quasi-static phase between
2.5 s and 8 s. However, the RI method fails to indicate the
maximum rollover extent during the dynamic phase while the
proposed AEKF-based LTR value can still track the reference
with high accuracy. For example, both the reference and the
AEKF-based LTR approach the value of 1 at around 6 s, which
indicates a vehicle rollover. The Carsim Visualizer monitor
shows that the rear left wheel has gotten off the ground and the
rollover is happening, which confirms the judgement from the
AEKF-LTR. In comparison, the RI method only presents a
reading of 0.82, which registers a huge error and will fool the
roll stability control system. The failure of the RI method may
be ascribed to the negligence of the system inertia and the
dynamics of suspension.
As indicated in the extensive experiments conducted, one
wheel may get off the road surface when the LTR is larger than
0.9 despite the vehicle doesn’t roll over completely. In fact, the
vehicle has entered the unstable state as the vehicle has lost the
road adhesion, and any possible disturbance or improper
maneuver may aggravate the rollover propensity. Thus, it is
desirable for the rollover controller to maintain the LTR below
0.9. To this end, a lower value such as LTR=0.7 should be set
as the threshold to kick off the rollover stability system. This
analysis can only serve as a reference and the thresholds need
to be calibrated through field tests.
The HIL test results stay favorable under both stable and
dynamic conditions. It should be noted that part of the reason
for signal bias and jitter may derive from the accuracy of CAN
communication protocol. Adopting more binary digits to
express a signal can improve the situation but would increase
the CAN bus load factor at the same time. Also, not surprisingly,
there exists slight delay between the estimated and the reference
signal on account of time-consuming communication and
calculation.
V. CONCLUSIONS
An accurate rollover tendency evaluation system is necessary
for the roll stability control system. The existing studies often
use multiple sensor fusion; but the associated high cost restricts
it from mass application. This paper focuses on providing an
LTR evaluation system which adopts an IMU as the signal input.
The AEKF is utilized to estimate the states of the roll angle and
the roll rate, which deals with the unknown noise covariance
problem. The FFRLS is adopted to identify the CG height to
correct the model establishment. The Butterworth filter is
designed to filter out noise for a smooth lateral acceleration
signal. Last, the LTR is calculated using the estimation results.
The complete scheme is constructed in the Matlab/Simulink
environment. The HIL tests using the ETAS system have been
accomplished. The test results verified the feasibility and
effectiveness of the proposed rollover risk evaluation scheme.
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Cong Wang received the B.S. degree in Automotive
Engineering from the Beijing Institute of Technology,
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 mainly include vehicle dynamics and safety
control for 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 the 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 Beijing Institute of Technology,
Beijing, China, and the Ph.D. degree in Electrical Engineering
from University of Technology, Sydney, Australia, in 2016.
He is now an Associate Professor with the School of
Mechanical Engineering, Beijing Institute of Technology.
His research interest includes management techniques for
energy storage systems, and vehicle dynamics and advanced
control for electric vehicles.
Dongpu Cao received the Ph.D. degree from Concordia
University, Canada, in 2008. He is the Canada Research Chair
in Driver Cognition and Automated Driving, and currently an
Associate Professor and Director of Waterloo Cognitive
Autonomous Driving (CogDrive) Lab at University of
Waterloo, Canada. His current research focuses on driver
cognition, automated driving and cognitive autonomous
driving. He has contributed more than 200 papers and 3 books. He received the
SAE Arch T. Colwell Merit Award in 2012, and three Best Paper Awards from
the ASME and IEEE conferences. Dr. Cao serves as an Associate Editor for
IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, IEEE
TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS,
IEEE/ASME TRANSACTIONS ON MECHATRONICS, IEEE
TRANSACTIONS ON INDUSTRIAL ELECTRONICS, IEEE/CAA
JOURNAL OF AUTOMATICA SINICA and ASME JOURNAL OF
DYNAMIC SYSTEMS, MEASUREMENT AND CONTROL. He was a Guest
Editor for VEHICLE SYSTEM DYNAMICS and IEEE TRANSACTIONS ON
SMC: SYSTEMS. He serves on the SAE Vehicle Dynamics Standards
Committee and acts as the Co-Chair of IEEE ITSS Technical Committee on
Cooperative Driving.
David G. Dorrell (M95, SM08, F19) was born in St Helens, UK. He has a
BEng (Hons) from The University of Leeds (1988), MSc from The University
of Bradford (1989) and PhD from The University of Cambridge (1993). He is
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2020.3012003, IEEE
Transactions on Industrial Informatics
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currently a Distinguished Professor with The University of the
Witwatersrand. He was Professor of Electrical Machines with
The University of KwaZulu-Natal in Durban, South Africa
(2015-2020) and Director of the EPPEI Specialization Centre
in HVDC and FACTS at UKZN (2016-2020). He has held
positions with The Robert Gordon University, UK, The
University of Reading, UK, The University of Glasgow, UK,
and the University of Technology Sydney, Australia. His
research interests cover electrical machines, renewable energy and power
systems. He has worked in industry and carried out several industrial
consultancies. He is a Chartered Engineer in the UK and a Fellow of the IET.
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