Research Article Vehicle Yaw Rate Estimation Using a ...vehicle yaw rate is estimated kinematically...

Hindawi Publishing CorporationInternational Journal of Vehicular TechnologyVolume 2013, Article ID 582691, 13 pageshttp://dx.doi.org/10.1155/2013/582691

Research ArticleVehicle Yaw Rate Estimation Using a Virtual Sensor

Mümin Tolga Emirler,1 Kerim Kahraman,2 Mutlu Fentürk,2 Bilin Aksun Güvenç,2

Levent Güvenç,2 and BarJG EfendioLlu3

1 Mechanical Engineering Department, Istanbul Technical University, 34437 Istanbul, Turkey2Mekar Labs, Faculty of Engineering and Architecture, Mechanical Engineering Department, Istanbul Okan University,Tuzla Campus, Tuzla, 34959 Istanbul, Turkey

3 Tofas R&D Center, 16010 Bursa, Turkey

Correspondence should be addressed to Levent Guvenc; [email protected]

Received 9 October 2012; Revised 12 March 2013; Accepted 12 March 2013

Academic Editor: Hilario Gomez-Moreno

Copyright © 2013 Mumin Tolga Emirler et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

Road vehicle yaw stability control systems like electronic stability program (ESP) are important active safety systems used formaintaining lateral stability of the vehicle. Vehicle yaw rate is the key parameter that needs to be known by a yaw stability controlsystem. In this paper, yaw rate is estimated using a virtual sensor which contains kinematic relations and a velocity-scheduledKalman filter. Kinematic estimation is carried out using wheel speeds, dynamic tire radius, and front wheel steering angle. Inaddition, a velocity-scheduled Kalman filter utilizing the linearized single-track model of the road vehicle is used in the dynamicestimation part of the virtual sensor. The designed virtual sensor is successfully tested offline using a validated, high degrees offreedom, and high fidelity vehicle model and using hardware-in-the-loop simulations. Moreover, actual road testing is carried outand the estimated yaw rate from the virtual sensor is compared with the actual yaw rate obtained from the commercial yaw ratesensor to demonstrate the effectiveness of the virtual yaw rate sensor in practical use.

1. Introduction

Lateral stability of a road vehicle is very important for thesafety of the driver and passengers during extreme lateralmaneuvers or during lateral maneuvers under adverse envi-ronmental conditions like driving on snow or ice, sudden tirepressure loss, or sudden side wind. Vehicle stability controlsystems called ESP, vehicle dynamics control (VDC), yawstability control (YSC), and so forth are used to improve thelateral stability of vehicles under such adverse conditions.Yaw stability control systems will becomemandatory for newvehicles in Europe after 2011 (see [1]).

Yaw rate is the most vital vehicle variable that needs to beknown by a road vehicle stability system. The current state-of-the-art is that yaw rate is measured by yaw rate sensorsin the form of microelectromechanical Sensor (MEMS)units. These sensors are commercially available, and theyare used in vehicle stability systems, but like every other

component inside a road vehicle, their price is a concern formanufacturers who try to lower costs [2, 3].

Some hard and expensive to measure vehicle variableslike yaw rate can be estimated using other on-vehicle sensorssuch as lateral accelerometers and wheel speed sensors.Therehave been several attempts to estimate yaw rate using lateralaccelerometers [2–6]. In [2], the vehicle yaw rate estimationwas performed using two lateral accelerometers that areplaced at the right and left sides of the vehicle. Yaw rate isestimated using the signals obtained from these accelerom-eters. Following that, a Kalman filter-based estimation wasutilized based on the initial yaw rate estimation and lateralacceleration measurements in order to reduce the effects ofnoise on the estimation. In [3], two lateral accelerometerswere installed on the longitudinal centerline of the vehicleas front and rear accelerometers to overcome the effects oftilting on the yaw rate estimation, and a state observer whichuses lateral acceleration and steering angle measurements

2 International Journal of Vehicular Technology

was designed. In [4], yaw rate estimation depends on wheelspeed and lateral acceleration measurements, separately.These initial yaw rate calculations were combined accordingto their confidence levels, and the preliminary estimation ofyaw rate was used in the nonlinear observer which generatesthe final yaw rate estimation. In [5], a Kalman filter-based softsensormethodwas introducedwhich uses lateral accelerationand steering angle measurements. In [5], the Kalman filterwas designed based on a two degrees of freedom vehiclemodel and no vehicle kinematics-based estimation was used.In [6], a direct yaw rate estimation method was proposedbased on a set-membership framework without the need ofvehicle model using experimentally obtained lateral accelera-tion, longitudinal velocity, and steering angle measurements.In this paper, in contrast to the commonly used lateralaccelerometers in the previous work, the antilock brakingsystem (ABS) wheel speed sensors, which are available inalmost every vehicle, are used along with the steering wheelposition sensor to estimate the yaw rate. This alternativeapproach is cheaper than using lateral accelerometers.

Theoretically, the yaw rate can be estimated using wheelspeeds, front wheel steering angle, and some vehicle param-eters using kinematic relations between these variables. Thisapproach is called kinematic estimation. Unfortunately, ABSwheel speed signals may sometimes be too noisy to obtainsatisfactory yaw rate estimates [7, 8]. For this reason, dynamicestimation is used in addition to kinematic estimation forfiltering this sensor noise. In the dynamic estimation part,different types of observers can be used. Observers includingKalman filters for filtering sensor noise have been used inestimation of vehicle parameters [2–6, 8–15] before, and thisapproach is also used in this paper.

The contributions of this work are the introduction of anovel wheel speed-based kinematic estimation algorithm, itscombined use with a Kalman filter-based dynamic estimationapproach to take care of wheel speed sensor noise, the useof a hardware-in-the-loop setup to develop the estimationalgorithms in a lab environment, and road test results todemonstrate the effectiveness of the proposed method in thereal world. This paper concentrates on yaw rate estimationusing a virtual sensor based on kinematic and dynamicestimation. In the kinematic estimation part of the virtualsensor design, kinematic relations between yaw rate andwheels speeds are considered.The double-track (four wheels)geometry of the vehicle chassis is used in the kinematiccomputations for yaw rate. Then, kinematic yaw rate esti-mation is improved by an algorithm which considers wheellongitudinal slips during braking and sudden accelerating(skidding). In the dynamic estimation part, used here forattenuating possible wheel speed sensor noise, a speed-scheduled Kalman filter is introduced and used. The gainmatrix of the Kalman filter is scheduled with longitudinalvehicle velocity. The designed virtual sensor for yaw rate istested first in offline computer simulations, then in hardware-in-the-loop simulations, finally in actual road tests. In actualroad tests, the virtual sensor runs in parallel with thecommercial yaw rate sensor such that their outputs could becompared directly. The virtual yaw rate sensor is connectedto the ESP electronic control unit instead of the commercial

Kinematicestimation

𝜔𝜔 𝑟kinematic

𝑅

𝛿𝑓

𝜔𝜔or

Vehicle parameters

Dynamicestimation

(Kalman filter)

𝛿𝑓Virtual sensor

𝑟virtual

𝑚 𝑉ref 𝜇𝑙𝑓 𝑙𝑟

𝑙𝑙 𝐼𝑧𝑉ref

FL

FR

RR

RL

𝑤𝑅𝑤𝐹

Figure 1: Virtual sensor main structure.

sensor in the tests. It should be noted that instead of replacingthe actual sensor, the virtual yaw rate sensor algorithm canalso be used for diagnostic purposes to detect faulty operationof the commercial sensor.

The organization of the rest of the paper is as follows.In Section 2 and its subsections, the kinematic and dynamicvirtual sensor design is explained. Simulation results obtainedusing the virtual sensor are given in Section 3.The hardware-in-the-loop (HiL) simulator used is introduced in Section 4where real-time simulation results obtained using that HiLsimulator are also presented. The actual road test results aregiven in Section 5, and the paper ends with conclusions.

2. Virtual Sensor Design

Virtual sensor design is realized by combining the kinematicestimation method with the dynamic estimation method.Figure 1 shows themain structure of the virtual sensor. Firstly,vehicle yaw rate is estimated kinematically using wheelangular speeds, front wheel steering angle, and some vehicleparameters shown in Figure 2. After that, this kinematicallyestimated yaw rate is used in the dynamic estimation partbased on a Kalman filter for attenuating possible wheel speedsensor noise. Note that a double-track (four wheels) dynamicvehicle model is not used or needed in the work presentedin this paper as the virtual sensor that uses the geometryin Figure 2 is kinematic in nature and does not require adynamic model.

2.1. Kinematic Estimation. Basically, yaw rate is estimated forthe vehicle geometry seen in Figure 2 from rearwheel angularspeeds by using (1) and from the front wheel angular speedsby using (2) [10–12]. Consider the following:

𝑟kinematic =

𝜔RR𝑅 − 𝜔RL𝑅

𝑙𝑤𝑅

, (1)

𝑟kinematic =

𝜔FR𝑅 − 𝜔FL𝑅

𝑙𝑤𝐹

cos 𝛿𝑓

, (2)

where 𝜔FL, 𝜔FR, 𝜔RL, and 𝜔RR are the angular speeds of thefront left, the front right, the rear left and the rear right

International Journal of Vehicular Technology 3

𝜔 𝜔𝛿𝑓

𝜔 𝜔

𝛿𝑓

𝑙𝑓

𝑙𝑟

𝑙

𝑙

𝑉ref

𝑅 𝑅

𝑅 𝑅

𝑟

RL RR

FL FR

𝑤𝐹

𝑤𝑅

Figure 2: Vehicle geometry for kinematic estimation.

wheels, respectively. Here, 𝑟kinematic denotes the kinematicallyestimated yaw rate.

Previous studies show that the longitudinal slip of thewheels affects the yaw rate estimation [7]. When consideringa front wheel drive vehicle, at sudden acceleration andbraking conditions of front wheels and at braking conditionsof rear wheels, longitudinal slip (𝑠) occurs at the relevantwheels and this affects the yaw rate estimation adversely.Kinematic estimation in (1) and (2) should therefore bemodified to take this slip into account.

Slip ratio is defined as

𝑠𝑖=

𝑅𝜔𝑖− 𝑉𝑖

𝑉𝑖

, 𝑉𝑖> 𝑅𝜔𝑖, −1 < 𝑠 < 0,

𝑖 = FL, FR,RL,RR(3)

during braking and as

𝑠𝑖=


𝑅𝜔𝑖

, 𝑉𝑖< 𝑅𝜔𝑖, 0 < 𝑠 < 1 (4)

during driving [16].𝑉ref is the reference vehicle speed which is obtained from

the vehicle controller area network (CAN) bus so that thelongitudinal speeds of the wheels can be calculated as

𝑉FL = 𝑉ref − (

𝑙𝑤𝐹

2

) cos 𝛿𝑓⋅ 𝑟, (5)

𝑉FR = 𝑉ref + (

𝑙𝑤𝐹

2

) cos 𝛿𝑓⋅ 𝑟, (6)

𝑉RL = 𝑉ref − (

𝑙𝑤𝑅

2

) 𝑟, (7)

𝑉RR = 𝑉ref + (

𝑙𝑤𝑅

2

) 𝑟. (8)

The vehicle speed 𝑉ref can be read from the CAN bus inABS equipped vehicles without any difficulties. The vehiclespeed reading from thewheel speed sensors is slightly smallerthan the true speed of the vehicle as determined by a GPSsensor. This slight difference did not create any problems inthe yaw rate estimation.This paper does not deal with vehiclestate estimation. It is assumed that the reference vehiclespeed (the speed at vehicle center of gravity) can be obtaineddirectly.

Vehicle yaw rate can be calculated kinematically based onrear wheels in the case of braking using the slip definitiongiven by (3) and the longitudinal speeds of the rear wheelsgiven by (7) and (8) as follows:

𝑟kinematic (𝑡) =𝑟kinematic (𝑡 − Δ𝑡) − [𝑉ref (𝑠RR − 𝑠RL) /𝑙𝑤𝑅]

1 + ((𝑠RR + 𝑠RL) /2).

(9)

Yaw rate can also be calculated kinematically based onfront wheels in the case of braking using the slip definitiongiven by (3) and the longitudinal speeds of the front wheelsgiven by (5) and (6) as follows:

𝑟kinematic (𝑡)=𝑟kinematic (𝑡−Δ𝑡)−[𝑉ref (𝑠FR−𝑠FL) /𝑙𝑤𝐹 cos 𝛿𝑓]

1 + ((𝑠FR + 𝑠FL) /2),

(10)

and lastly it can be calculated kinematically based on frontwheels in the case of vehicle acceleration using the slipdefinition given by (4) and the longitudinal speeds of the frontwheels (5) and (6) as follows:

𝑟kinematic (𝑡)

=

𝑟kinematic (𝑡 − Δ𝑡) (1−𝑠FR) (1 − 𝑠FL) + [𝑉ref (𝑠FL − 𝑠𝐹𝑅) /𝑙𝑤𝐹 cos 𝛿𝑓]1 − ((𝑠

𝐹𝑅+ 𝑠FL) /2)

,

(11)

where 𝑡 is the current value of time, Δ𝑡 is the calculationtime interval, and the subscript of 𝑠 shows the 𝑖th wheel ofthe vehicle. The derivation details of (9)–(11) are given inthe appendix. Slip ratio of each wheel is computed utilizingslip ratio definitions ((3) and (4)) and longitudinal speeds ofwheels ((5)–(8)). These slip ratio formulae are given in thefollowing.

When braking occurs at the rear wheels,

𝑠RR =

𝜔RR𝑅 − [𝑉ref + (𝑙𝑤𝑅

/2) 𝑟 (𝑡 − Δ𝑡)]

𝑉ref + (𝑙𝑤𝑅

/2) 𝑟 (𝑡 − Δ𝑡)

, (12)

𝑠RL =

𝜔RL𝑅 − [𝑉ref − (𝑙𝑤𝑅

/2) 𝑟 (𝑡 − Δ𝑡)]

𝑉ref − (𝑙𝑤𝑅

/2) 𝑟 (𝑡 − Δ𝑡)

. (13)


Start

Return

No Yes

𝑟 = 𝑟(𝑡 − Δ𝑡) − [𝑉 (𝑆 − 𝑆 ]1 + ( 𝑆 + 𝑆2 )

𝑆 = 𝜔 𝑅 − [𝑉 + (𝑙 /2)𝑟(𝑡 − Δ𝑡)]𝑉 + (𝑙 /2)𝑟(𝑡 − Δ𝑡)

𝑆 = 𝜔 𝑅 − [𝑉 − (𝑙 /2)𝑟(𝑡 − Δ𝑡)]𝑉 − (𝑙 /2)𝑟(𝑡 − Δ𝑡)

𝑟 = 𝜔 − 𝜔 𝑅𝑙𝑅 ref

ref

ref

ref )

ref

/𝑙

RLRR

RL

RR

RL

RR

RLRR

RLRR

𝑤𝑅

𝑤𝑅

𝑤𝑅

𝑤𝑅

𝑤𝑅

𝑤𝑅

Braking ?

Figure 3: The flowchart of the rear wheel kinematic estimation algorithm.

When braking occurs at the front wheels

𝑠FR =

𝜔FR𝑅 − [𝑉ref + (𝑙𝑤𝐹

/2) cos 𝛿𝑓𝑟 (𝑡 − Δ𝑡)]

𝑉ref + (𝑙𝑤𝐹

/2) cos 𝛿𝑓𝑟 (𝑡 − Δ𝑡)

, (14)

𝑠FL =

𝜔FL𝑅 − [𝑉ref − (𝑙𝑤𝐹


𝑉ref − (𝑙𝑤𝐹

/2) cos 𝛿𝑓𝑟 (𝑡 − Δ𝑡)

. (15)

When acceleration occurs at the front wheels,

𝑠FR =

𝜔FR𝑅 − [𝑉ref + (𝑙𝑤𝐹


𝜔FR𝑅, (16)

𝑠FL =

𝜔FL𝑅 − [𝑉ref − (𝑙𝑤𝐹


𝜔FL𝑅. (17)

The basic kinematical equations ((1) and (2)) are utilizedtogether with improved kinematical estimation equations((9)–(11)) in forming a general kinematic estimation algo-rithm in the Matlab environment. This general kinematic

algorithm is embedded into the kinematic estimation part ofthe virtual yaw rate sensor.

Figure 3 shows the flowchart of the rear wheel kinematicestimation algorithm, and Figure 4 shows the flowchart ofthe front wheel kinematic estimation algorithm. In theseflowcharts, 𝑟 represents the kinematically estimated yaw rate.

It should be noted that the front wheel and rear wheelangular speed-based calculations lead to similar results withsmall differences. Since we are using a front wheel drivevehicle, rear wheel angular speed-based estimation is usuallybetter than front wheel angular speed based estimation.Our overall kinematic estimation algorithm combines infor-mation from both rear and front wheels to estimate yawrate in order to make use of both of these available data.This combination was realized with the addition of the twoestimations (from rear and front) with the proportion of 2/3times the estimated yaw rate from the rear wheels plus 1/3

times the estimated yaw rate from the front wheels.This ratiowas chosen heuristically based on an extensive trial and errorprocedure applied to simulation and experimental results.

2.2. Dynamic Estimation. The Kalman filter is an optimalobserver that estimates the system states which are hard to


Start

Return

No Yes

Sudden acceleration

?

No Yes

𝑟 = 𝑟(𝑡 − Δ𝑡)(1 − 𝑆 )(1 − 𝑆 ) + [𝑉 (𝑆 − 𝑆 )/𝑙 cos 𝛿𝑓]1 − ( 𝑆 + 𝑆2 )

𝑟 = 𝑟(𝑡 − Δ𝑡) − [𝑉 (𝑆 − 𝑆 )/ 𝑙 cos 𝛿𝑓 ]1 + ( 𝑆 + 𝑆2 )

ref ( )

ref

𝑟 = 𝜔 − 𝜔 𝑅𝑙𝑅𝑆 = 𝜔 𝑅 − [𝑉ref − (𝑙 /2) cos 𝛿𝑓𝑟(𝑡 − Δ𝑡)]

𝑉ref − (𝑙 /2) cos 𝛿𝑓𝑟(𝑡 − Δ𝑡)

𝑆 = 𝜔 𝑅 − [𝑉ref + (𝑙 /2) cos 𝛿𝑓𝑟(𝑡 − Δ𝑡)]𝑉ref + (𝑙 /2) cos 𝛿𝑓𝑟(𝑡 − Δ𝑡)

𝑆 = 𝜔 𝑅 − [𝑉ref + (𝑙 /2) 𝛿𝑓𝑟(𝑡 − Δ𝑡)]𝜔 𝑅

𝑆 = 𝜔 𝑅 − [𝑉ref − (𝑙 /2) 𝛿𝑓𝑟(𝑡 − Δ𝑡)]𝜔 𝑅

FR FL FR

FL

FRFR

FL

FR FL FRFL

FRFL

FR

FL

FR

FL

FR FL

FR FL

𝑤𝐹cos

cos

𝑤𝐹

𝑤𝐹FL

𝑤𝐹

𝑤𝐹

𝑤𝐹𝑤𝐹

𝑤𝐹𝑤𝐹

Braking ?

Figure 4: The flowchart of the front wheel kinematic estimation algorithm.

measure while filtering themeasurement noise [17]. Note thatthe Kalman filter-based dynamic virtual sensor is used tofilter wheel speed sensor noise here. The Kalman filter usedhere is a standard implementation and requires knowledgeof the system state space model, system output, system input,measurement noise covariance, and process noise covariance.The measurement noise covariance 𝑄

𝑐and the process noise

covariance 𝑅𝑐are assumed to be zero mean Gaussian white

noise here.The system model used in the Kalman filter is the single-

track vehicle model which is the simplest vehicle modelthat accurately captures lateral dynamics up to 0.3-0.4 g oflateral acceleration. In the single-track vehicle model, twotires on the same axle are lumped together, and this resultsin one front and one rear tire set. Figure 5 illustrates the

𝑦𝑥

𝐹𝑟

𝑙𝑟 𝑙𝑓

𝑉ref𝐹𝑓

𝛽𝐶𝐺

𝛿𝑓𝑟

Figure 5: Illustration of single-track vehicle model geometry andvariables.

basic parameters of the single-track model. In designing thedynamic part of the virtual sensor based on the Kalman filter,the linear single-track vehicle model is used.


The linearized model of the single-track vehicle is givenby

�� = 𝐴 (V) 𝑥 + 𝐵 (V) 𝛿𝑓, 𝑦 = 𝐶𝑥, (18)

where

𝐴 (V) =

[

[

[

[

[

[

[

− (𝐶𝑟𝑜

+ 𝐶𝑓𝑜) 𝜇

𝑚V−1 +

(𝐶𝑟𝑜𝑙𝑟+ 𝐶𝑓𝑜𝑙𝑓) 𝜇

𝑚V2

(𝐶𝑟𝑜𝑙𝑟− 𝐶𝑓𝑜𝑙𝑓) 𝜇

𝐼𝑧

− (𝐶𝑟𝑜𝑙2

𝑟+ 𝐶𝑓𝑜𝑙2

𝑓) 𝜇

𝐼𝑧V

]

]

]

]

]

]

]

,

𝐵 (V) =

[

[

[

[

[

[

𝐶𝑓𝑜𝜇

𝑚V

𝐶𝑓𝑜𝑙𝑓𝜇

𝐼𝑧

]

]

]

]

]

]

, 𝐶 = [0 1] .

(19)

𝑥 = [𝛽 𝑟]𝑇, 𝑟 is the yaw rate, 𝛽 is the side slip angle, V is

the vehicle speed, and 𝜇 is the tire-road friction coefficient[18]. All variables in the above and following equationsare explained in Table 1, and the numerical values used insimulations are given in parentheses.

System state space equations and the Kalman filter equa-tions including prediction and correction equations are

�� = 𝐴 (V) 𝑥 + 𝐵 (V) 𝑢 + 𝑤, 𝑦 = 𝐶𝑥 + 𝑛,

𝑤 ∼ (0, 𝑄𝑐) , 𝑛 ∼ (0, 𝑅

𝑐) ,

𝐿 = 𝑃𝐶𝑇

𝑅−1

𝑐,

�� = 𝐴𝑥 + 𝐵𝑢 + 𝐿 (𝑦 − 𝐶𝑥) ,

�� = −𝑃𝐶𝑇

𝑅−1

𝑐𝐶𝑃 + 𝐴𝑃 + 𝑃𝐴

𝑇

+ 𝑄𝑐,

(20)

where the system matrices 𝐴, 𝐵, and 𝐶 are the linear single-track vehicle model given in (18), 𝑤 is the process noise,𝑛 is the measurement noise, 𝐿 is the Kalman filter gainmatrix, 𝑥 is the estimated state vector, and 𝑃 is the solutionof the Riccati equation. 𝐴(V) and 𝐵(V) are system and inputcoupling matrices, varying with the vehicle speed. Therefore,the Kalman gain matrix varies with vehicle speed, makingthe estimation applicable in a real vehicle implementationwhere the measurable vehicle speed is not constant. Beforedesigning a speed-scheduled Kalman Filter, the observabilityof the system is checked and is determined to be stateobservable for all possible vehicle speed values.

The determination of the 𝑄𝑐and 𝑅

𝑐covariances are the

most important and intuitive part of the Kalman filter design.We already know that there is a trade-off between goodestimation and good noise attenuation in accordancewith theselection of covariance matrices. From this perspective, themeasurement (or sensor) noise covariance matrix is obtainedafter determining the sensor noise variance using the avail-able experimental data. After obtaining the measurementnoise covariance, the process noise covariance is tuned to geta satisfactory state prediction.

Table 1: Linear single track vehicle model parameters.

Symbol Quantity Unit𝑟 Yaw rate rad/sec𝛽 Side slip angle Rad𝑉ref Vehicle center of gravity speed m/sec𝛿𝑓 Front wheel steering angle Rad

𝜇 Tire-road friction coefficient —𝐶𝑓𝑜 Front wheels cornering stiffness (72,500) N/rad

𝐶𝑟𝑜 Rear wheels cornering stiffness (92,500) N/rad

𝑚 Vehicle mass (1,321) kg𝐼𝑧 Vehicle moment of inertia wrt 𝑧 axis (2,120) kgm2

𝑙𝑓

Distance from front axle to vehicle center ofgravity (1.07) m

𝑙𝑟

Distance from rear axle to vehicle center ofgravity (1.53) m

𝑙𝑤𝐹 Front axle width (1.485) m𝑙𝑤𝑅 Rear axle width (1.475) m𝑅 Dynamic tire radius (0.298) m

Figure 6: CarMaker user interface.

3. Simulation Results

The virtual yaw rate sensor is tested using CarMaker softwarebefore performing actual road tests. The CarMaker vehiclemodel is a highly realistic one that incorporates enginedynamics, tire dynamics, steering dynamics, suspensiondynamics, vehicle sprung body dynamics, longitudinal andlateral dynamics, a driver model, and road and environmentmodels [19]. The CarMaker user interface is shown inFigure 6.

The proposed virtual yaw rate sensor algorithm is testedusing standard maneuvers such as lane change maneuver,eight test maneuver, and the slalommaneuver. In the simula-tions, the medium sedan vehicle parameters given in Table 1are used.

Figure 7 shows the results of the lane change test maneu-ver. Figure 8 shows the results of the eight test maneuver, and


0 5 10 15 20 25 30−0.6−0.5−0.4−0.3−0.2−0.10

0.10.20.30.4

Time (s)

Yaw

rate

(rad

/s)

Simulated yaw rateEstimated yaw rate

(a)

0 5 10 15 20 25 300

0.20.40.60.8

11.21.41.6×10−3

Time (s)

Yaw

rate

estim

atio

n er

ror

(b)

Figure 7: Double lane change results.

Figure 9 shows the results of the slalom test maneuver. Thesesimulation results demonstrate the successful performance ofthe proposed virtual yaw rate sensor algorithm in offline sim-ulations with different handling maneuvers as the estimated(virtual sensor output) and actual (simulated output) yawrates are very close to each other. The estimation error, thatis, the absolute value of the difference between the estimatedand simulated or between the estimated and experimentalyaw rate, is part of every simulation or experimental resultpresented in this paper. The low estimation errors in theseplots demonstrate the effectiveness of the virtual yaw ratesensor proposed in this paper.

In the slalom maneuver in Figure 9, the noise rejectioncapability of the Kalman filter is tested by injecting Gaussianwhite noise to the wheel speed data before the kinematicestimation. Figure 9 also displays the output of the kinematicvirtual yaw rate sensor 𝑟kinematic which illustrates the impor-tance of additional dynamic filtering in the presence of alarge amount of wheel speed sensor noise. In Figure 10, theeffect of model uncertainty on virtual sensor performanceis tested by using a 0.7Hz frequency, 90 degree amplitudesinusoidal steeringwheel angle input.The yaw rate estimationerror is also displayed in the same plot. The robustness of thevirtual yaw rate sensor to model uncertainty is tested withtwo different vehicle masses and tire road friction coefficientuncertainty combinations, the top plot corresponding to the

0 20 40 60 80 100−0.4−0.3−0.2−0.1

00.10.20.30.4

Time (s)

Yaw

rate

(rad

/s)

Simulated yaw rateEstimated yaw rate

(a)

0 10 20 30 40 50 60 70 80 90 100012345678×10−3

Time (s)

Yaw

rate

estim

atio

n er

ror (

rad/

s)

(b)

Figure 8: Eight test maneuver results.

case of no uncertainty. The results show that the virtualyaw rate sensor is quite robust for the model uncertaintyconsidered.

In the simulation yaw rate comparison figures, the greensignal shows the simulated yaw rate (model yaw rate output)from CarMaker.The red (dashed) signal shows the estimatedyaw rate using the virtual yaw rate sensor.

4. Hardware-in-the-Loop Vehicle Simulator

The use of a hardware-in-the-loop (HiL) simulator is a safeand more capable alternative to real road testing and canbe used to detect and correct fatal, expensive errors andvital mistakes before the real road test phase. The developedvehicle models and the virtual sensor are simulated by usingthe dSPACE DS 1005 and DS 2210 systems. DS 1005 isthe main processor, and DS 2210 is an I/O board withCAN communication feature. The vehicle models and thevirtual sensor model are developed in the Simulink environ-ment. Figure 11 shows the virtual sensor block diagram andCarMaker software Simulink blocks. Then, the models areinstalled on theDS 1005 board by using theMath-WorksReal-Time Workshop and the dSPACE Real-Time Interface (RTI).CarMaker HiL software is used to run the CarMaker vehiclemodel in real time.


0 5 10 15 20 25 30 35 40 45−0.4−0.3−0.2−0.1

00.10.20.30.4

Time (s)

Yaw

rate

(rad

/s)

ActualKinematic estimateKinematic + dynamic estimate

(a)

0 5 10 15 20 25 30 35 40 450

0.010.020.030.040.050.060.070.08

Time (s)

Yaw

rate

estim

atio

n er

ror (

rad/

s)

(b)

Figure 9: Slalom maneuver results.

Figure 12 shows the HiL simulator used. This vehiclesimulator has a steering wheel, brake, and traction pedalsystem. The important vehicle parameters were observed onthe large animation screens in real-time. While the vehiclemodel was simulated on the dSPACE DS 1005 board, thevirtual sensor algorithm was executed in real-time on adSPACE MicroAutoBox general purpose electronic controlunit.The communication between the soft vehicle in the sim-ulator and the virtual sensor in the dSPACE MicroAutoBoxwas provided via the CAN serial interface. Thus, a realisticsimulation with actual hardware was performed by using thevehicle simulator before a real vehicle road test.

In Figure 13, the working principle of the HiL vehiclesimulator is illustrated. The vehicle model, road model,environment model, and virtual sensor were first coded inSimulink and converted into real-time C code using theMatlab Real-Time Workshop. The Real-Time Interface (RTI)of dSPACE was used to link and download the generatedcode into the dSPACEDS 1005 board and theMicroAutoBox.The virtual sensor computations were carried out in theMicroAutoBox which communicates with the DS 1005 boardusing CAN communication through the DS 2210 board. DS1005 ran the vehicle simulation and provided wheel speedsand other relevant information to the MicroAutoBox overthe CAN bus through the DS 2210 board. Driver inputs wereadded to the simulation via the dSPACE 2210 I/O board

and connector box. The driver can see the changes from theanimation screens in real time.

The HiL simulator was used with an actual driver who isone of the authors. An eight maneuver was carried out bythe human driver in the simulations. Before the kinematicestimation part of the virtual sensor, white noise was addedto the wheel speed data as sensor noise. The results shown inFigure 14 indicate that the virtual sensor presented here alsoworks successfully on the HiL simulator of the vehicle.

5. Actual Road Test Results

The designed virtual sensor was connected to the experi-mental vehicle via the dSPACE MicroAutoBox using CANcommunication. The actual yaw rate sensor and the virtualsensor worked together, and real-time data was collected forboth sensors to compare the results. The kinematic virtualsensor presented here used a switch based on the presenceof braking. This braking condition was determined by eitherusing the braking pedal information (available by the brakeswitch information on the CAN bus) or by using longitudinalacceleration information (available on the CAN bus forvehicles with ESP). We applied the first approach of using thebraking pedal information to realize the kinematic estimationalgorithm.

Three exemplary road test results are shown in Figures15, 16, and 17. The maneuver in Figure 15 is a short slalommaneuver. The driver tried a J-turn-like maneuver in thesecond test shown in Figure 16. The driver tried a slalom-likemaneuver in Figure 17 where the rear left tire pressure wasreduced from 2.1 bar to 1.2 bar (almost half of its nominalvalue). In this way, an unusual driving situation was testedwith a deflated tire. The tests were carried out on dry asphaltroad (𝜇 = 1). Extensive road testing results not presentedhere were similar in that the estimated (output of virtualyaw rate sensor algorithm) and actual (measured using thecommercial yaw rate sensor) were very close to each other.Lateral acceleration values were much larger than the validityrange of 0.3-0.4 g of the simple linear single-track modelcharacterizing noncritical driving.

6. Conclusions

In this paper, vehicle yaw rate was estimated by using a virtualsensor that is a combination of kinematic estimation anddynamic estimation methods. In the kinematic estimationpart, the kinematic relations between the yaw rate and wheelspeeds were utilized. Some improvements were realized forkinematic estimation by considering the adverse effects oflongitudinal slip of the wheels. Consequently, a generalkinematic estimation algorithm was formed. In the dynamicestimation part of the virtual sensor, a speed-scheduled-Kalman filter was used. In this way, large changes in vehiclespeed can be handled. Finally, the designed virtual sensor wastested with offline simulations, HiL simulations, and actualroad tests, and the results were found to be quite satisfactory.Current virtual sensors for yaw rate estimation are used inthe electronic stability control (ESC) system for diagnostic


0 5 10 15−0.5

00.5

−0.50

0.5

−0.50

0.5

Nominal model 𝑚 = 1321, 𝜇=1


0 5 10 15

0 5 10 15

Uncertain model𝑚 = 1421, 𝜇 = 0.8

Yaw

rate

(rad

/s)

Yaw

rate

(rad

/s)

Yaw

rate

(rad

/s)

Time (s)

Time (s)

Time (s)

Uncertain model 𝑚 = 1521, 𝜇 = 0.3

(a)

0 5 10 150

0.1

0.2

0 5 10 150

0.1

0.2

0 5 10 150

0.1

0.2

Nominal model 𝑚 = 1321, 𝜇 = 1

Uncertain model 𝑚 = 1421, 𝜇= 0.8

Yaw

rate

(rad

/s)

Yaw

rate

(rad

/s)

Yaw

rate

(rad

/s) Uncertain model 𝑚 = 1521, 𝜇 = 0.3

Time (s)

Time (s)

Time (s)

(b)

Figure 10: Sinusoidal steering input maneuver results with uncertain parameters (yaw rate estimation errors shown in the right three plots).

CarMaker Vehicle Model in dSPACE DS 1005

Virtual sensor in dSPACE MicroAutoBox

sa

vxFL

vxFR

vxRL

vxRR

Brake

v

delta f

w fl

w rl

w rr

Brake

vVirtual sensor

Est r

w fr

Est r

CM DrivMan Vehicle CM LASTFIRST

Sync Out

Sync In

Ambient.Misc

DrivMan.Steering

DrivMan.Brake

DrivMan.PT

Brake.IF.In

Sync In

Ambient.Misc

Sync Out Sync In

DrivMan.Steering

DrivMan.Brake

DrivMan.PT

Brake.IF.In

Sync Out

PowerTrain.Misc

Sync In

Sync Out

PowerTrain.Misc

Figure 11: CarMaker vehicle model and virtual sensor Simulink blocks.


dSPACE connector box CLP 2210

Simulink vehicle model screen

CarMaker animation screens

dSPACE DS 1005

dSPACEMicroAutoBox

Figure 12: The real-time HiL simulator.

Vehicle modelRoad model

Environment model

Virtual sensor∙ Kinematic estimation∙ Dynamic estimation(Kalman filter)

PC environment

dSPACE DS 1005PPC board

dSPACEMicroAutoBox

1401/1501

dSPACE DS 2210I/O board andconnector box

Driver inputs∙ Steering wheel∙ Gas pedal∙ Brake pedal

Animation screens

CANcommunication

Force feedbackby steering wheel

Matlab real-time workshop

CarMaker’s visual interface

Figure 13: The HiL simulator working principle diagram.

purposes, that is, to determine if there are any problems withthe yaw rate sensor. It will be possible to use only the virtualyaw rate sensor in the future.

Appendix

In this section, derivation of the kinematic estimation algo-rithm is explained. Firstly, the rear wheel-based estimationalgorithm for braking condition is derived. After that, thefront wheel-based estimation algorithm for braking andsudden acceleration is presented.

Thus, the vehicle yaw rate is estimated as 𝑟est using angularspeeds of the rear wheels using

𝑟est =𝜔RR𝑅 − 𝜔RL𝑅

𝑙𝑤𝑅

. (A.1)

The vehicle speed at the wheel centers is estimated using

𝑉RR = 𝑉ref + (

𝑙𝑤𝑅

2

) 𝑟act, (A.2)

𝑉RL = 𝑉ref − (

𝑙𝑤𝑅

2

) 𝑟act, (A.3)

where 𝑉ref represents the vehicle speed read from the CANbus and 𝑟act is the actual yaw rate value. During braking, slipratio of the wheels is defined using

𝑠𝑖=


𝑉𝑖

, 𝑉 > 𝑅𝜔𝑖, −1 < 𝑠 < 0. (A.4)


60 70 80 90 100 110 120 130 140 150 160

−0.6−0.4−0.2

0

0.2

0.4

0.6

Time (s)

Yaw

rate

(rad

/s)


(a)

60 70 80 90 100 110 120 130 140 150 1600

0.02

0.04

0.06

0.08

0.1

Time (s)

Yaw

rate

estim

atio

n er

ror (

rad/

s)

(b)

Figure 14: HiL test result.

Using above slip ratio definition and (A.1), 𝑟est can be writtenas

𝑟est =𝑉RR (1 + 𝑠RR) − 𝑉RL (1 + 𝑠RL)

𝑙𝑤𝑅

=

𝑉RR − 𝑉RL𝑙𝑤𝑅

+

𝑉RR𝑠RR − 𝑉RL𝑠RL𝑙𝑤𝑅

.

(A.5)

In (A.5), the first fractional equation is a kinematic formulafor the actual yaw rate 𝑟act. Replacing that part with 𝑟act andrearranging results in

𝑟act = 𝑟est − (

𝑉RR𝑠RR − 𝑉RL𝑠RL𝑙𝑤𝑅

) . (A.6)

𝑉RR and 𝑉RL are substituted for from (A.2) and (A.3).Rearranging results in

𝑟act =𝑟est − [𝑉ref (𝑠RR − 𝑠RL) /𝑙𝑤𝑅]

1 + ((𝑠RR + 𝑠RL) /2)(A.7)

which can be reexpressed as the recursive equation

𝑟 (𝑡) =

𝑟 (𝑡 − Δ𝑡) − [𝑉ref (𝑠RR − 𝑠RL) /𝑙𝑤𝑅]

1 + ((𝑠RR + 𝑠RL) /2), (A.8)

where the yaw rate estimate at time 𝑡 − Δ𝑡 is used to obtainthe estimate at time 𝑡. 𝑠RR and 𝑠RL in (A.8) can be calculatedutilizing (13) and (14) in the paper.

0 2 4 6 8 10 12 14 16 18 20

−0.4−0.2

0

0.2

0.4

0.6

Time (s)

Yaw

rate

(rad

/s)

ActualEstimated

(a)

0 2 4 6 8 10 12 14 16 18 200

0.02

0.04

0.06

0.08

0.1

Time (s)

Yaw

rate

estim

atio

n er

ror

(b)

Figure 15: Road test result 1.

The kinematic estimation algorithm development usingthe front wheels under braking condition will be presentednext. The vehicle yaw rate is estimated using angular speedsof the front wheels using

𝑟est =𝜔FR𝑅 − 𝜔FL𝑅

𝑙𝑤𝐹

cos 𝛿𝑓

. (A.9)

The vehicle speeds at the wheel centers are approximatedusing

𝑉FR = 𝑉ref + (

𝑙𝑤𝐹

2

) cos 𝛿𝑓⋅ 𝑟act, (A.10)

𝑉FL = 𝑉ref − (

𝑙𝑤𝐹

2

) cos 𝛿𝑓⋅ 𝑟act. (A.11)

Using slip ratio definition (A.9), 𝑟est can be written as

𝑟est =𝑉FR (1 + 𝑠FR) − 𝑉FL (1 + 𝑠FL)

𝑙𝑤𝐹

cos 𝛿𝑓

=

𝑉FR − 𝑉FL𝑙𝑤𝐹

cos 𝛿𝑓

+

𝑉FR𝑠FR − 𝑉FL𝑠FL𝑙𝑤𝐹

cos 𝛿𝑓

.

(A.12)

In (A.12), the first fractional equation is the yaw rate 𝑟act.Replacing that expression by 𝑟act and rearranging results in

𝑟act = 𝑟est − (

𝑉FR𝑠FR − 𝑉FL𝑠FL𝑙𝑤𝐹

cos 𝛿𝑓

) . (A.13)


0 5 10 15 20 25 30 35 40Time (s)

Yaw

rate

(rad

/s)

ActualEstimation

−0.4−0.3−0.2−0.10

0.10.20.30.40.5

(a)

0 5 10 15 20 25 30 35 400

0.010.020.030.040.050.060.070.08

Time (s)

Yaw

rate

estim

atio

n er

ror (

rad/

s)

(b)


𝑉FR and𝑉FL in (A.10) and (A.11) can be substituted into (A.13).Rearranging results in

𝑟act =𝑟est − [𝑉ref (𝑠FR − 𝑠FL) /𝑙𝑤𝐹 cos 𝛿𝑓]

1 + ((𝑠FR + 𝑠FL) /2)(A.14)

which can be reexpressed in the recursive form

𝑟 (𝑡) =

𝑟 (𝑡 − Δ𝑡) − [𝑉ref (𝑠FR − 𝑠FL) /𝑙𝑤𝐹 cos 𝛿𝑓]1 + ((𝑠FR + 𝑠FL) /2)

(A.15)

for use in the estimation algorithm. 𝑠FR and 𝑠FL in (A.15) canbe calculated utilizing (15) and (16) in the paper.

Lastly, the kinematic estimation algorithm developmentusing the front wheels under sudden acceleration conditionwill be derived in the following.

Under sudden acceleration condition, slip ratio of thewheels is defined as

𝑠𝑖=


𝑅𝜔𝑖

, 𝑉 < 𝑅𝜔𝑖, 0 < 𝑠 < 1. (A.16)

Using the above slip ratio definition and (A.9), 𝑟est can bewritten as

𝑟est =(𝑉FR/ (1 − 𝑠FR)) − (𝑉FL/ (1 − 𝑠FL))

𝑙𝑤𝐹

cos 𝛿𝑓

. (A.17)

5 10 15 20 25 30−0.5−0.4−0.3−0.2−0.10

0.10.20.30.40.5

Time (s)

Yaw

rate

(rad

/s)

ActualEstimation

(a)

5 10 15 20 25 300

0.020.040.060.08

0.10.120.140.16

Time (s)

Yaw

rate

estim

atio

n er

ror (

rad/

s)

(b)


Through manipulations similar to the ones above,

𝑟est =𝑟act

(1 − 𝑠FR) (1 − 𝑠FL)−

(𝑉FR𝑠FL − 𝑉FL𝑠FR)

𝑙𝑤𝐹

cos 𝛿𝑓(1 − 𝑠FR) (1 − 𝑠FL)

,

(A.18)

𝑟act =𝑟est (1 − 𝑠FR) (1 − 𝑠FL) + [𝑉ref (𝑠FL − 𝑠FR) /𝑙𝑤𝐹 cos 𝛿𝑓]

1 − ((𝑠FR + 𝑠FL) /2),

(A.19)

and the recursive equation

𝑟 (𝑡) =

𝑟 (𝑡 − Δ𝑡) (1 − 𝑠FR) (1 − 𝑠FL) + [𝑉ref (𝑠FL − 𝑠FR) /𝑙𝑤𝐹 cos 𝛿𝑓]1 − ((𝑠FR + 𝑠FL) /2)

(A.20)

for use in the kinematic estimation algorithm. 𝑠FR and 𝑠FL in(A.20) can be obtained by utilizing (16) and (17) [11].

Acknowledgments

The first author would like to thank the support of TUBITAK(The Scientific and Technological Research Council ofTurkey) and National Scholarship Programme for Ph.D.Students. This work was supported by TOFAS and PlatformR&D Corporation (Project 2008/189-P).


References

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[13] L. Imsland, T. A. Johansen, T. I. Fossen, H. F. Grip, J. C.Kalkkuhl, and A. Suissa, “Vehicle velocity estimation usingnonlinear observers,”Automatica, vol. 42, no. 12, pp. 2091–2103,2006.

[14] U. Kiencke and A. Daiß, “Observation of lateral vehicle dynam-ics,” Control Engineering Practice, vol. 5, no. 8, pp. 1145–1150,1997.

[15] B. Samadi, R. Kazemi, K. Y. Nikravesh, and M. Kabganian,“Real-time estimation of vehicle state and tire-road frictionforces,” in Proceedings of the IEEE American Control Conference(ACC ’01), pp. 3318–3323, Arlington, Va, USA, June 2001.

[16] B. A. Guvenc, L. Guvenc, E. S. Ozturk, and T. Yigit, “Model reg-ulator based individual wheel braking control,” in Proceedings ofthe IEEE Conference on Control Applications, Istanbul, Turkey,2003.

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[19] CarMaker Reference Manual and User’s Guide.

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