Original Article

Proc IMechE Part D:J Automobile Engineering227(4) 577–590� IMechE 2013Reprints and permissions:sagepub.co.uk/journalsPermissions.navDOI: 10.1177/0954407012459138pid.sagepub.com

Vehicle roll and pitch angle estimationusing a cost-effective six-dimensionalinertial measurement unit

Jiwon Oh and Seibum B Choi

AbstractThe purpose of this paper is to estimate accurately the vehicle attitudes, i.e. the vehicle roll and pitch angles. It isassumed that a set of data obtained from a low-price six-dimensional inertial measurement unit is available. This includesthe linear acceleration of the vehicle and the angular rates of all axes. In addition, the observer exploits the data fromthe wheel speed sensors, and the steering-wheel angle, which are already available for recent production cars. Using theabove, based on the combination of the velocity kinematics and pseudointegration of the angle kinematics, a novelscheme for reference angle selection dependent on the cornering-stiffness adaptation is adopted to observe the angles.The stability of each component of the proposed observer is investigated, and a set of assessments to confirm the per-formance of the entire system is arranged via experiments using a real production sport utility vehicle.

KeywordsAdaptive algorithm, inertial measurement unit, observers, pitch angle, roll angle, state estimation, vehicle dynamics

Date received: 8 June 2012; accepted: 26 July 2012

Introduction

As a result of the heavy dependence on the use of vehi-cles by humans, the cost of the associated drivinghazards always accompanies the convenience. In orderto reduce the risk factors as much as possible, numer-ous engineers have been inspired to work on advancingthe electronic safety control technology of vehicles;these various types of computerized electronic safetycontrol technology facilitate securing the comfort andsafety of passengers. For instance, knowing the vehiclepitch, and thus the road gradient, contributes to gener-ating the desired clutch pressure values in controllingan automated manual transmission1 and a dual-clutchtransmission,2,3 or in processing the laser sensor signalsfor longitudinal vehicle control schemes4 such as colli-sion damage mitigation, idle stop-and-go system, obsta-cle avoidance or adaptive cruise control. Also, theavailability of information on the roll angle contributesto the safety and convenience of passengers throughimplementation of roll control,5–7 vehicle yaw stabilitycontrol8–12 and roll-over mitigation.13–15 Also, morefundamentally, identification of the vehicle attitudesfacilitates estimation of other vehicle states by increas-ing the vehicle model accuracy for the studies in whichthe roll and pitch effects are neglected.16–18

The problem related to this field, however, is theneed for a high-precision sensor to measure the requiredvehicle states. This is a critical hindrance for vehicleswith a wide range of costs to have such technologiesmounted and, without a solution, vehicle safety mayonly remain reachable for the affluent minority. Inorder to raise the passenger comfort and safety level,accurate information on the vehicle states must beavailable even with an affordable sensor. Also, thisassumption must be satisfied under all conditions,regardless of the severity of vehicle motion, since thedriving environment varies widely between differentdrivers and various driving conditions. Such require-ments have been the major limitation in the previousefforts to develop wholly satisfactory vehicle attitudeobservers.

Korea Advanced Institute of Science and Technology, Daejeon, Republic

of Korea

Corresponding author:

Seibum B Choi, Automotive Control Laboratory, Department of

Mechanical Engineering, Korea Advanced Institute of Science and

Technology, 335 Gwahangno, Yuseong-gu, Daejeon 305-701, Republic of

Korea.

Email: sbchoi@kaist.ac.kr

Schiffman14 attempted to identify the roll dynamicsvia sensor integration, but this involves drift error andis effective for only a short duration. Some studiesattempted to use inertial sensors to form the observerwhich estimates information on the vehicle attitude, butthey required a Global Positioning System (GPS).19–21

Here, the option of GPS use is unfavourable, sinceusing the GPS signals for purposes other than a naviga-tion service requires additional hardware and proces-sors. Furthermore, heavy dependence on the GPSsignal frequently causes the system robustness to dete-riorate when the vehicle enters areas with weak signals(i.e. driving near a tall building or through a tunnel).Tseng and co-workers22,23 designed observers that useboth a vehicle model and sensor kinematics to obtainroll and pitch angle information, but they involved anunqualified assumption regarding the vehicle yaw rateand ignored the lateral and vertical velocity compo-nents. Park et al.24 and Kim et al.25 proposed rolldynamics estimators using modified bicycle models, butthey assumed fixed cornering stiffnesses and omittedexperiments performed on slippery surfaces (i.e. sur-faces with a high-slip condition). Hence, the scope ofthis research is to maximize the estimation performanceof vehicle attitude with only a low-cost six-dimensional(6D) inertial measurement unit (IMU), regardless ofhow severely a vehicle is manoeuvred, and without theaid of a GPS.

This research introduces a novel scheme to estimatethe vehicle roll and pitch angles through combining thevelocity observer and the sensor kinematics. While thebicycle-model-based observer estimation and pseudoin-tegration of the angle kinematics are combined inaccordance with the estimated front and rear corneringstiffnesses obtained by an adaptation scheme to gener-ate the reference angle used in the attitude observer, theobserver itself revises the estimation using the gyro-scope sensor measurements. This process of multipleestimations induces a high estimation accuracy for boththe low-frequency components and the high-frequencycomponents of the changing vehicle attitudes.

The basic organization of this paper is as follows.The second section describes the way in which the flowof logic can be facilitated as follows: first, the generallayout of the observer with the block diagram is dis-played; second, the principle behind the primary longi-tudinal velocity approximation based on the angularvelocities of the wheels is briefly dealt with; third, thecornering-stiffness adaptation is described; fourth, thedetails of the bicycle-model-based observer which isused to generate the lateral velocity used for pseudoin-tegration are focused on; fifth and finally, the formationof the two reference angles obtained by the velocitykinematics and pseudointegration, and the attitudeobserver design obtained by the fusion of the two refer-ences, are described. The third section displays theresults of the real-car-based experiments performedunder different scenarios that verify a robust vehicleattitude estimation performance.

Observer design

General observer flow chart

The general structure of the entire observer is given inFigure 1.

Longitudinal velocity estimation

The vehicle controller area network mounted on mod-ern mass production cars provides the speeds of eachindividual wheel. When these speed data are trans-formed so that they correspond to the speed at the cen-tre of gravity (CG) using the vehicle yaw rate and wheeltrack compensation, a rough estimation of the longitu-dinal velocity of the vehicle can be obtained. However,this value is equivalent to the real velocity of the vehi-cle, only when there is no longitudinal or lateral slipinvolved in the tyres. Taking an extreme case, a vehiclewithout an anti-lock braking system may still have asignificant amount of inertia to maintain the longitudi-nal velocity even when the brakes have locked all thewheels. In this case, the vehicle velocity approximatedfrom the wheel speed sensors is unusable.

To maximize the range of reliable wheel speed use,only the speeds of the undriven wheels (rear wheels, inthe case of front-drive vehicles) are taken into accountwhen the vehicle is accelerating to minimize the wheelspin effect. The maximum value of the four-wheel speeddata is taken when the brake is applied, since wheelscannot rotate more rapidly than the velocity of the carbut only become slower or even locked during braking.

Figure 1. General flow chart of the subcomponents of theproposed vehicle attitude observer.6D: six-dimensional; IMU: inertial measurement unit.

578 Proc IMechE Part D: J Automobile Engineering 227(4)

The result is then filtered with a rate limiter, whichtakes the physical limitation and ax as the references torestrict the change in the vehicle velocity within the rea-listically allowable boundary. This refinement givesvcar, a rough estimation of the vehicle velocity, which isused throughout the rest of this paper.

Cornering-stiffness adaptation

Figure 2 shows the bicycle model representation of thevehicle which deals with the lateral dynamics. With theassumptions that the left- and the right-hand sides ofthe vehicle experience identical dynamics with equiva-lent tyre cornering stiffnesses and that the longitudinalvelocity of the vehicle is slowly varying, the bicyclemodel considerably reduces the amount of requiredcomputational effort and has been proven to be effec-tive for identification of the vehicle states. Also, the factthat there is no requirement for a high IMU sensorinput makes the bicycle model robust against sensorerror.

On the other hand, however, a weakness involved inthe use of the bicycle model is that the unmodelled dis-turbance including the road bank angle and the discre-pancy between the nominal cornering stiffness and theactual cornering stiffness may cause a significantamount of deviation from the real lateral dynamics ofthe vehicle. To alleviate this problem, lateral dynamicscompensation with knowledge of the road disturbancethrough the estimation of the total vehicle roll andpitch angles with respect to the earth axes is required.Also, model error due to parameter uncertainty isreduced through the front- and rear-cornering-stiffnessadaptation.

On the basis of the bicycle model, the front and rearcornering stiffnesses can be updated using an adaptivescheme. Simple moment balance equations lead to theexpression for the front-tyre lateral force given by

Fyf =mlray + Iz _r

lf + lrð1aÞ

and the expression for the rear-tyre lateral force givenby

Fyr =mlfay � Iz _r

lf + lrð1bÞ

where m, Iz, ay and r are the vehicle mass, the yaw iner-tia, the lateral acceleration and the yaw rate respec-tively. Here, it must be noted that each tyre forcecorresponds to the total lateral force on each axle ofthe actual vehicle. Also, structural investigation of thebicycle model leads to the expression for the front-tyreslip angle given by

af =b+lfvx

r� df ð2aÞ

and the expression for the rear-tyre slip angle given by

ar =b� lrvx

r ð2bÞ

where vx,b and df are the longitudinal velocity, theside-slip angle and the front-tyre steering angle respec-tively. In order to connect equations (1) and (2) regard-ing the vehicle dynamics, a tyre model is essential. Forsimplicity, the linear tyre model is chosen to give a sim-ple relationship between the tyre lateral force and thetyre slip angle, according to

Fyf = �Cfaf ð3aÞFyr = �Crar ð3bÞ

The linear tyre model shows increasing inaccuracywith increasing tyre slip, because the cornering stiff-nesses are left as constants. Hence, the actual imple-mentation is compensated by the tyre cornering-stiffness adaptation, and so Cf and Cr in the linear tyremodel are not necessarily constants.26

After equation (2) is substituted into equation (3)and some algebraic manipulation is performed, we canobtain

b= �Fyf

Cf+ df �

lfvx

r ð4aÞ

b= �Fyr

Cr+

lrvx

r ð4bÞ

In order to eliminate the unknown variable b (the side-slip angle), equations (4a) and (4b) are equated to give

Fyf

Cf� Fyr

Cr= df �

lf + lrvx

r ð5Þ

Here, 1/Cf and 1/Cr are modelled as

1

Cf=

1

Cf

� �n

+ zf ð6aÞ

and

1

Cr=

1

Cr

� �n

+ zr ð6bÞ

Figure 2. Bicycle model representation of a vehicle.

Oh and Choi 579

where (1/Cf)n and (1/Cr)n are the nominal values, and zfand zr are the unknown parts.13

By substituting equation (6) into equation (5), weobtain

Fyf1

Cf

� �n

+ zf

� �� Fyr

1

Cr

� �n

+ zr

� �= df �

lf + lrvx

r

ð7Þ

Now define a variable z as

z [ df �lf + lrvx

r� Fyf1

Cf

� �n

+Fyr1

Cr

� �n

=Fyfzf � Fyrzr ð8Þ

To make certain that the system is causal, a low-passfilter is applied to equation (8) according to

_z= �g z� Fyfzf +Fyrzr� �

ð9Þ

where g is the filter gain.In a similar manner, the estimated z can be expressed

as

_z= �g z� Fyfzf +Fyrzr� �

ð10Þ

Now an update law for zf and zr is designed to esti-mate the unknown parts of the cornering stiffnessaccording to

_zf = ggfFyfe ð11aÞ_zr = �ggrFyre ð11bÞ

where gf and gr are the adaptation gains and e ¼D z� z .Stability of the system can be proved easily using an

analysis of the Lyapunov function. Define ~zf = zf � zfand ~zr = zr � zr, with the radially unbounded, decres-cent and positive definite Lyapunov candidate functionchosen as

V=1

2e2 +

~zf2

gf

+~zr

2

gr

!ð12Þ

with

dV

dt= e _e+

~zf _~zfgf

+~zr _~zrgr

= e _e� g~zf _zfgf

� g~zr _zrgr

= ge �e+Fyf~zf � Fyr~zr� �

� gFyf~zfe+ gFyr~zre

= �ge2

4 0

ð13Þ

Applying the Barbalat lemma, the system actuallyturns out to be asymptotically stable, given that the per-sistent excitation condition27 applies to Fyf and Fyr .Although the actual lateral tyre force characteristics aretime varying, it is assumed that the estimation targets

_zf and _zr are slowly varying and thus close to zero. Inmany cases, systems are modelled as time-invariant sys-tems whose parameters are to be estimated throughadaptation. This is possible by considering the effects ofthe parameter variations as unmodelled perturbations,so that the robust adaptive control techniques used fortime-invariant plants in the presence of bounded distur-bances and unmodelled dynamics work effectively forthe actual plants when their parameters are smooth andvary slowly with time.28

Here, the threshold between the parameters thatvary discontinuously and greatly with high frequencyand those that are smooth and vary slowly with timemay be obscure. Thus, the suggested adaptive schemeis shown to work via careful selection of adaptive gainsand applications on various samples of empirical data.

The adaptive scheme hitherto dealt with raises anissue that the cornering stiffness changes as a functionof the vertical load, and the amount of its fluctuationis quite substantial. Increasing the adaptation gain isnot an option, since doing so results in a noise issue.Thus, the former adaptive scheme is altered to updatethe cornering stiffness normalized by the vertical load.For this purpose, by neglecting the aerodynamic dragand using the estimated states, the front vertical loadis estimated as

Fzf =mglr cos u�mgh sin u�mh _vx +mlr _vz � Iy _qm

L

ð14aÞ

and the rear vertical load as

Fzr =mglf cos u+mgh sin u+mh _vx +mlf _vz + Iy _qm

L

ð14bÞ

where vx, vz and u are the estimated longitudinal velo-city, the vertical velocity29 and the pitch anglerespectively.

Analogous to the previously shown linear tyremodel, the model used is

Fyf = � �CfFzf af ð15aÞ

Fyr = � �CrFzrar ð15bÞ

where �Cf and �Cr are the normalized cornering stiff-nesses, i.e.

�Cf =Cf

Fzfð16aÞ

�Cr =Cr

Fzrð16bÞ

After similar processes as in the non-normalizedcase, we obtain

bf = � Fyf

Fzf�Cf

+ df �lfvx

r ð17aÞ

580 Proc IMechE Part D: J Automobile Engineering 227(4)

br = � Fyr

Fzr�Cf

+lrvx

r ð17bÞ

which are equated to become

Fyf

Fzf�Cf

� Fyr

Fzr�Cr

= df �lf + lrvx

r ð18Þ

This time, modelling �Cf and �Cr instead of Cf and Cr

as the nominal and unknown parts, we find that

1�Cf

=1�Cf

� �n

+ zf ð19aÞ

and

1�Cr

=1�Cr

� �n

+ zr ð19bÞ

where

1�Cf

� �n

=Fzf1

Cf

� �n

and

1�Cr

� �n

=Fzr1

Cr

� �n

are the nominal values and where zf and zr are theunknown parts.

Substituting the above gives

Fyf

Fzf

1�Cf

� �n

+ zf

� �� Fyr

Fzr

1�Cr

� �n

+ zr

� �= df �

lf + lrvx

r

ð20Þ

Now the variable z can be defined as

z [Fyf

Fzfzf �

Fyr

Fzrzr

= df �lf + lrvx

r� Fyf

Fzf

1�Cf

� �n

+Fyr

Fzr

1�Cr

� �n

ð21Þ

so that it can be expressed in terms of the known states.Then z is defined likewise and a low-pass filter is

applied to it according to

_z = �h z � Fyf

Fzfzf +

Fyr

Fzrzr

� �ð22Þ

where h is the filter gain.Then the resulting update laws for zf and zr are

obtained as

_zf =hf

Fyf

Fzfen ð23aÞ

_zr = �hr

Fyr

Fzren ð23bÞ

where hf and hr are the adaptation gains anden = z � z.

A system stability check of the altered cornering-stiffness adaptation scheme is omitted, since it is nearlyidentical with that of the non-normalized case.

Bicycle-model-based observer

The bicycle model representation of the vehicledynamics is expressed in a state-space format as

_x=Ax+Bu ð24Þ

where

x=b

r

� �, u= df

A=a11 a12

a21 a22

� �

=� 2 Cf +Crð Þ

mvx

�2 Cflf�Crlrð Þmv2x

� 1

�2 Cflf�Crlrð ÞIz

� 2 Cfl2f+Crl

2rð Þ

Izvx

264

375

and

B=b1b2

� �=

2Cf

mvx2CflfIz

" #

For clarity, the cornering stiffnesses Cf and Cr thatappear in the bicycle model (24) henceforth refer to thevalues obtained by cornering-stiffness adaptation. Also,the influence due to the pure vertical heave dynamics ofthe vehicle is considered negligible in this section of thepaper.

By using the lateral acceleration sensor measure-ment, an observer based on the bicycle model isdesigned. Introducing the lateral acceleration, therelationship

ay = _vy + rvx ð25Þ

holds.Now replacing the right-hand side of equation (25)

with the terms that appear in the expression for thebicycle model,30 the lateral acceleration is newly definedin terms of the state variables of the bicycle model as

ay = a11vxb+ a12 +1ð Þvxr+ b1vxdf ð26Þ

Before proceeding, it must be clarified that the lat-eral acceleration sensor measurement may not alwaysrefer to the lateral acceleration in equations (25) and(26). These two are equivalent to each other only in theabsence of road angles and suspension angles. The sus-pension angle creates a false contribution to the vehiclelateral dynamics, since the effect of gravity changes themeasurement taken by the sensor. On the other hand,the road terrain other than a nearly horizontal surface,especially in the case of the bank angle, actually causesthe vehicle lateral dynamics to change. Hence, while theeffect of the gravity reading due to the suspension angle

Oh and Choi 581

must be eliminated, the effect of the static road anglemust be maintained in the lateral acceleration sensorreading to reflect truly what is meant by equation (26).

To meet such requirements, the suspension angleand the road angle information must be available sepa-rately. For this purpose, the suspension angle is eithermeasured from the suspension travel or estimatedthrough the open-loop spring–damper system model-ling of the vehicle. This information is then subtractedfrom the estimated roll and pitch angles to obtain theroad angles. Once this process is carried out, the lateralacceleration necessary for the bicycle-model-basedobserver is computed through the relationship

ay = ay, sensor + �g sinf cos u+ g sinf0 cos u0ð Þ ð27Þ

where

f=f0+fsus

u= u0+ usus

Here, f, f0, fsus, u, u0 and usus indicate the total roll,the static road bank, the pure suspension roll, the totalpitch, the static road inclination and the pure suspen-sion pitch angle respectively.

Now, using the above-mentioned expression for thelateral acceleration, the output equation can be set upas

y=Cx+Du ð28Þ

where

y=r

ay

� �, x=

b

r

" #

C=0 1

a11vx a12 +1ð Þvx

� �

D=0

b1vx

� �

This allows the observer design

_x=Ax+Bu+K y� yð Þ ð29Þ

with

K=K1 K2

K3 K4

� �

Expanding the above leads to the state-space equation

_b

_r

" #=

a11 � K2a11vcar a12 � K1 � K2 a12 +1ð Þvcara21 � K4a11vcar a22 � K3 � K4 a12 +1ð Þvcar

� �

b

r

" #+

b1 � K2b1vcar

b2 � K4b1vcar

� �df +

K1 K2

K3 K4

� �r

ay

� �

ð30Þ

where b, r, r and ay are the side-slip angle estimation,the yaw rate estimation, the measured sensor yaw rate

and the compensated lateral acceleration measurementrespectively. Also

K=K1 K2

K3 K4

� �

=

Iz Cflf�Crlrð Þ2CfCr lf + lrð Þ2

p2o � 1 1vcar

�2pom Cfl

2f+Crl

2rð Þ

Iz Cflf�Crlrð Þ

2664

3775

ð31Þ

Restricting po to be a negative tuning constant, thesystem stability is confirmed, since the observer statematrix in equation (30) turns out to be strictly Hurwitz,as long as K2 and K4 are prevented from becoming illconditioned. This is achieved by switching their valuesto zero whenever their denominators are near zero.Finally, the bicycle-model-based observer estimation ofthe lateral velocity is obtained next using

vy, bic = vcar tan b ð32Þ

Euler angle observer

Reference angle obtained by velocity kinematics. To estimatethe roll and pitch angles, logic that combines two typesof reference is used: one calculated from the velocitykinematics equations and the other from the pseudoin-tegral kinematic estimations.

Here, the velocity kinematics are given as

_vx_vy_vz

24

35=

0 r �q�r 0 pq �p 0

24

35 vx

vyvz

24

35

+axayaz

24

35+ g

sin u

� sinf cos u

� cosf cos u

24

35 ð33Þ

Thus, exploiting the longitudinal and lateral kine-matics leads to the expressions

f0ref = ff0ref vx, vy, vz, u0ref� �

= sin �1� _vy + ay � rvx + pvz

g cos u0ref

!ð34Þ

u0ref= fu0ref vx, vy, vz� �

= sin�1_vx � ax � rvy + qvz

g

!ð35Þ

Here, the velocities are estimated using the kinematicfilter with multiple lateral velocity references from thecornering-stiffness adaptation in equation (17), themodel-based observer in equation (32) and the kine-matic observer in equation (33). For further details, seethe paper by Oh and Choi.29

Reference angle obtained by pseudointegration. The kine-matic equations that express the time derivatives of theEuler angles are given by

582 Proc IMechE Part D: J Automobile Engineering 227(4)

_f= p+ q sinf+ r cosfð Þ tan u ð36aÞ

_u= q cosf� r sinf ð36bÞ

These are the foundation on which the vehicle rolland pitch angle pseudointegration is performed. Here,the yaw angle differential equation is excluded, sinceestimation of the vehicle yaw angle with respect to theglobal coordinate system is not within the scope of thisresearch.

Before proceeding, the transient flag index TF mustbe defined. This variable is a normalized value between0 and 1 obtained by summing the scaled variances ofthe 6D IMU signals. A high TF indicates that the vehi-cle is going through a transient state in its motion,whereas a low TF corresponds to the steady state.

Using the above, the pseudointegral angle estimationcan be described in terms of the system

_f�int = p+ q sin fint + r cos fint

� tan uint ð37Þ

_u�int = q cos fint � r sin fint ð38Þ

fint =TF f�int

+ 1� TFð Þff0ref vcar, vy, bic, 0, fu0ref vcar, vy, bic, 0� ��

ð39Þuint =TF u�int + 1� TFð Þfu0ref vcar, vy, bic, 0

� �ð40Þ

Through obtaining the pseudointegral estimation ofthe angles according to the above-mentioned system, itcalculates fint and uint via pure integration only whenTF is close to 1. The integrated angles tend to returnimmediately back to the stable reference valuesff0ref vcar, vy, bic, 0

� �and fu0ref vcar, vy, bic, 0

� �to avoid the

drift issue whenever TF’0 and integration is not neces-sary. It must be noted that ff0ref and fu0ref mentionedhere in the pseudointegral estimation part are notexactly identical with those defined in equations (34)and (35). While the reference angles in equations (34)and (35) are functions of the final velocity estimations,those in equations (39) and (40) are selected to be func-tions of vcar and vy, bic . This selection is sensible, since alow TF guarantees that vcar and vy, bic are reliable data.

Reference angle formation. The conventional attitudeobserver designed by Tseng et al.23 chooses to useequations (34) and (35) alone as the reference feedbackfor the attitude observers, neglecting the lateral andvertical velocity components. This causes estimationinaccuracy under severe manoeuvring conditions. Also,it requires that the vehicle yaw rate satisfies the non-zero condition, in order to utilize the reference angleinformation f0ref and u0ref effectively, since the observerdiscards the feedback term when the yaw rate is nearlyzero. However, it is difficult to meet this condition,because the vehicle does not always go through transi-ent states. The second part of the paper by Tsenget al.23 deals with the ‘‘attitude observer without steady

state error’’ which does not rely on the reference angleto estimate the vehicle attitudes during the steady state.This, however, is possible only with angular rate sen-sors of ideal accuracy.

This predicament is resolved in the novel attitudeobserver by using information on the newly designedreference angle during both the transient state and thesteady state. The reference angles of the proposed workconsist of both components from the pseudointegralestimation of the roll and pitch angles and the referencevalues obtained by velocity kinematics in equations(34) and (35) by adjusting the reference selector (RS)between them. RS is defined as

RS=sat max1

2etCf � GfFzf+ et� �

,1

2et

�

Cr � GrFzr + etð Þ��

ð41Þ

Figure 3 illustrates how the RS is formulated as afunction of the cornering stiffnesses. When eitherCf or Cr is in the linear region, indirect use of the refer-ence lateral velocity vy, ref by taking the velocity estima-tions as the reference is reliable. However, when thetyres show non-linear characteristics, maintaining suchindirect use of the reference lateral velocity for theangle estimation causes an unnecessary involvement ofthe pseudointegral velocity estimation with all six sen-sor measurements and their possible errors, becausevelocity estimation by integration fully requires the 6DIMU. Hence, in this case, it is wiser rather to use thepseudointegral estimation of the angles only, whichtakes only three sensor measurements of the gyroscope.This shift thus naturally causes the observer to be lesssensitive to the sensor errors. This is enabled bydecreasing the RS which increases the portion of fint

and uint in the reference angles.Incorporating the RS into the observer design as

explained, the two references designed in equations(34), (35), (39) and (40) are merged according to

Figure 3. RS acquisition.RS: reference selector.

Oh and Choi 583

fref=RS ff0ref vx, vy, vz, u0ref� �

+ 1�RSð Þfint ð42Þ

uref=RS fu0ref vx, vy, vz� �

+ 1�RSð Þuint ð43Þ

Two reference angles obtained from the velocitykinematics and pseudointegration are compared inFigure 4. As expected, the estimation obtained by pseu-dointegration involves an instantaneous drift issue dur-ing the transient state and a discrete change in thesignal as the TF changes. However, its accuracy andability to track the rapidly changing estimation targetsare useful. On the other hand, although the estimationacquired using the velocity kinematics compromiseshigh bandwidth accuracy, it constantly tracks the actualestimation target without a drift issue when the corner-ing stiffnesses do not deviate from their nominal values(i.e. when the linear bicycle model suffices to describethe vehicle dynamics). As mentioned earlier, inaccuracyduring a severe vehicle manoeuvre may be caused by

the velocity estimation errors and the use of all six IMUsensors, and so it is favourable to discard its result whenthe vehicle exhibits highly non-linear tyre dynamics.

Figures 5 and 6 show the cornering-stiffness adapta-tion results and calculation of the RS respectively, andthey indeed show that the reference selection process isdesigned to use the reference selectively with higherreliability. While the vehicle experiences a severedouble-lane-change manoeuvre, the cornering-stiffnessestimations fall, which then cause the RS to drop inaccordance. As intended, this happens only during thetime period when the tyres experience non-linear char-acteristics so that, for the generation of the observerreference feedback, more emphasis can be laid on thepseudointegration than the use of velocity kinematicswhich requires an increased burden on the cornering-stiffness adaptation for accurate velocity tracking.

Considering these, the tactic of using the RS as afunction of the estimated cornering stiffnesses to obtainthe reference angles is indeed effective.

Principal kinematic angle observer. The principal kinematicangle observer forms the last part of the integrated vehi-cle angle estimation process. This scheme improves theestimation performance of the high-frequency compo-nents of the estimation targets especially in their transi-ent states. Also, it eliminates the noise in the referenceangle formed in the previous section without causing aphase lag in the signal.

With the modified reference angles designed in equa-tions (42) and (43), the attitude observer is designed as

_f= p+ q sin f+ r cos f

� tan u+ar fref � f

� ð44Þ

_u= q cos f� r sin f+ap uref � u

� �ð45Þ

where ar and ap are positive tuning constants.

Figure 5. Cornering-stiffness adaptation result (low passfiltered).

Figure 4. Roll and pitch reference angles (low pass filtered).

Figure 6. Calculation of the RS (low pass filtered).

584 Proc IMechE Part D: J Automobile Engineering 227(4)

The estimation results for a double-lane-change caseare shown in Figure 7. As expected, the principal kine-matic angle observer gives the final estimation througheffectively filtering the inaccuracy and noise mixed inthe reference angles without causing any phase lagissue. At the same time, the reference angles contributeto repressing the signal drift involved in the kinematics.Further evaluation under various cases is dealt with inthe following experiment section.

Experiment results

Test environments

Using a real production sport utility vehicle, HyundaiTucsan ix, experiments are conducted to show the esti-mation performance of the suggested vehicle attitudeobserver. The specification data of the car used forexperiment are given in Table 1.

The gyroscope and accelerometer used for this angleobserver algorithm are ADW22307 and ADXL103

respectively from Analog Devices, Inc. Also, for testverification purposes, a high-accuracy GPS–inertialnavigation system (INS) RT3100 from OxfordTechnical Solutions Ltd is used. Figure 8 shows thisinstrument mounted on the test vehicle.

The 6D IMU is mounted at the CG of the vehicle,and the RT3100 sensor according to Table 2. Here, theRT3100 sensor is internally adjusted so that it gives thesensor measurements at the CG.

In Table 3, the list of conditions in which the vehicleattitude observer is tested is given. Each case involves arigorous change in the vehicle dynamics, and/or fairlyhigh value(s) of the roll and/or pitch angles. By con-ducting the experiment in various types of situation, therobustness of the proposed attitude observer is verified.

Test results and analysis

In Figure 9, the roll and pitch angle estimation resultsfor the severe double-lane-change manoeuvres are dis-played. While trying to maintain a vehicle velocity of 70km/h, three sets of manoeuvres are made to show theestimation robustness in both the transient state andthe steady state during and between each manoeuvre.

Observation of Figure 9 reveals that the proposedattitude observer effectively estimates the roll and pitchangles, even in the condition when the vehicle is goingthrough a continued series of severe lateral accelera-tions through double lane changes.

The circle turn manoeuvre induces a constant rollangle of the vehicle with lateral weight shifting. Theobserver effectively handles the situation well, and boththe roll angle and the pitch angle are estimated withfairly high accuracy. The test results are displayed inFigure 10.

In the bumpy road experiment, the ability of theobserver to estimate the rapidly changing roll and pitchangles is tested. While the road condition exerts a sinu-soidal excitation on the tyres, the roll and pitch angles

Table 1. Specifications for the Tucsan ix 2WD gasoline Theta II 2.0 test vehicle.

Feature (units) Front Rear

Left Right Left Right

Dimension (mm) Wheelbase 2640Overhang 800 890Track 1585 1586Overall Length 4410Overall Width 1820Height (unloaded) 1655

Weight (kgf) Kerb weight 450 417 326 330867 656

1523Gross vehicle weight (2 up) 487 458 360 368

945 7281673

Wheel radius (mm) 336 338 340 340337 340

Figure 7. Roll and pitch reference angles and estimationresults (low pass filtered).

Oh and Choi 585

vigorously change. As Figure 11 shows, the observeralgorithm effectively estimates the vehicle attitudes evenduring this extended period of the transient state.

The next test scenario, the results of which are illu-strated in Figure 12, focuses on a sudden steering input.A significant amount of side-slip is induced by inten-tionally causing the vehicle to spin out, or to be over-steered, on the surface with a low friction coefficient.Up to a certain level of severity in the lateral dynamics,

the reference angle obtained from velocity kinematicseffectively estimates the angles.

However, in the presence of extremely high side-slipsuch as in case IV, the velocities, too, are obtained byintegration, which give rise to reference angle inaccu-racy, worsened by sensor errors. In this case of highside-slip and highly non-linear tyre characteristics, theattitude observer effectively discards the informationobtained from the velocity estimations and ratherexploits pseudointegration for accurate attitude estima-tion; its effectiveness can be seen in the result.

In this special case of high slip, the absence of suchtactics to avoid error and ignoring the lateral dynamics,or even merely using the bicycle-model-based lateraldynamics information obtained with fixed corneringstiffnesses, may cause a significant amount of error inthe estimation performance of the previous study,23 andeven divergence from the measured estimation target,as shown in Figure 12.

The fifth scenario (case V), the results of which areshown in Figure 13, deals with the condition in whichall the factors that may cause the attitude observationaccuracy to deteriorate are combined. Here, the vehicleexperiences a constant turn at the same time as a severestatic bank angle and a severe sine steering input. Evenin this harsh condition, the proposed observer accu-rately estimates the angles, whose magnitudes increaseto over 20�.

The comparison between the roll and pitch angle esti-mation performances of the conventional observerdesigned and described in the paper by Tseng et al.23 andthat of the newly designed attitude observer is given inFigure 14. This test for comparison is conducted on wetasphalt, on which the vehicle is driven downhill whichinvolves a bank angle and speed bumps, in order to seethe effect of changing vehicle orientation on the estima-tion performance over an extended period of time.

If the conventional observer is made to rely more onthe reference signals, it certainly drifts less but loses itsestimation accuracy during the transient state.Relatively free from this trade-off, the new angle obser-ver manages the drift issue better without losing thetransient state estimation accuracy, as shown in theplot. This is accounted for by incorporation of the velo-city estimation into the reference angle generation.Furthermore, as mentioned above, the non-zero yawrate requirement utilized by Tseng et al.23 causes a driftissue, and thus a steady state error, when the yaw rateis near zero.

Figure 8. Oxford Technical Solutions Ltd RT3100 GPS–INSmounted on the test vehicle.GPS: Gobal Positioning System; INS: inertial navigation system.

Table 3. Test scenarios.

Case Driver control Bank Incline Road condition

Case I DLC None None Dry asphaltCase II Circle turn None None Wet asphaltCase III Bumpy road Sinusoidal Sinusoidal Dry asphaltCase IV Spin out None None Snow and/or iceCase V Bank turn sine steer 0�!20�!0�!20�!0� Irregular (depends on the vehicle position) Dry asphaltCase VI Lane keeping Random Random Wet asphalt

Table 2. Mounting positions of the instruments.

Distance between instruments Distance (mm)

Length (x axis) RT3100–rear axle center 1000RT3100–6D IMU 930

Height (z axis) RT3100–antenna 600RT3100–6D IMU 430

6D: six-dimensional; IMU: inertial measurement unit.

586 Proc IMechE Part D: J Automobile Engineering 227(4)

Conclusion

Without having to use the GPS or a high-cost INS, thesuggested attitude observer has proved its worththrough effectively estimating the vehicle roll and pitchangles dynamically in both the transient state and the

steady state by using the low-cost 6D IMU and the ref-erence angle obtained from the stable velocity observer.In doing so, a novel method to generate the referenceangle, to combine their results effectively as a functionof cornering-stiffness estimation and to use it in thekinematic observer is suggested.

Figure 10. Test results for a circle turn test on wet asphalt (case II): (a) vehicle states; (b) vehicle roll angle estimation; (c) vehiclepitch angle estimation.SWA: steering-wheel angle.

Figure 9. Test results for the DLC test on dry asphalt (case I): (a) vehicle states; (b) vehicle roll angle estimation; (c) vehicle pitchangle estimation.SWA: steering-wheel angle.

Oh and Choi 587

Summarizing the paper, the original contributionsdistinguished from the previously reported papers arethe following: elimination of the need for GPS, elimina-tion of the signal drift issue that exists over an extendedperiod and resolution of the inaccuracy issue duringsevere vehicle manoeuvres and high slips.

With numerous real-car-based experiments, the pro-posed attitude estimation performance is tested and isverified to be robust. The experiments are conductedunder various conditions involving rigorous man-oeuvres, so that the suggested algorithm is ready foractual production car application.

Figure 12. Test results for a spin-out test on snow (case IV): (a) vehicle states; (b) vehicle roll angle estimation; (c) vehicle pitchangle estimation.SWA: steering-wheel angle.

Figure 11. Test results for a bumpy road test on dry asphalt (case III): (a) vehicle states; (b) vehicle roll angle estimation; (c) vehiclepitch angle estimation.SWA: steering-wheel angle.

588 Proc IMechE Part D: J Automobile Engineering 227(4)

Funding

This work was supported by the National ResearchFoundation of Korea grant funded by the Koreagovernment (Ministry of Education, Science andTechnology) (grant no. 2012-0000991).

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Appendix

Notation

ax longitudinal acceleration measured at thecentre of gravity

ay lateral acceleration measured at the centreof gravity

az vertical acceleration measured at thecentre of gravity

Cf front-tyre cornering stiffnessCr rear-tyre cornering stiffnessFyf front-tyre lateral forceFyr rear-tyre lateral forceFzf front-tyre vertical forceFzr rear-tyre vertical forceg acceleration due to gravityIz moment of inertia about the z axislf distance between the centre of gravity and

the front axlelr distance between the centre of gravity and

the rear axleL distance between the front axle and the

rear axlem mass of the vehiclep roll rate measured at the centre of gravityq pitch rate measured at the centre of

gravityr yaw rate measured at the centre of gravityvx longitudinal velocity at the centre of

gravityvy lateral velocity at the centre of gravityvz vertical velocity at the centre of gravity

af front-tyre slip anglear rear-tyre slip angleb side-slip angle at the centre of gravitydf front-tyre steering angleu pitch anglef roll angle

590 Proc IMechE Part D: J Automobile Engineering 227(4)