04244393

IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 12, NO. 3, JUNE 2007 375

Development of a Novel Sensorless LongitudinalRoad Gradient Estimation Method Based on Vehicle

CAN Bus DataStephen Mangan and Jihong Wang, Member, IEEE

Abstract—The availability of road gradient information willhave a big impact upon the quality of vehicle control. This paperpresents a novel “sensorless” longitudinal road-gradient estimationmethod, which was developed in two steps starting from a bench-mark system design. The gradient benchmark system consists ofan inclinometer sensor and an acceleration-based error correctionalgorithm, which can be used to verify the accuracy of the roadgradient obtained using a sensorless estimation method. The sen-sorless road-gradient estimation algorithm uses the vehicle datacurrently available on the vehicle controller area network (CAN)bus. The completed gradient estimation algorithm was success-fully tested online in variable road conditions and different drivingmanners. The test results showed that the resulting longitudinalroad-gradient estimation algorithm fulfilled the specified accuracyrequirement, and provided a cost effective and reliable way forlongitudinal road-gradient estimation in real time.

Index Terms—Estimation, road vehicle control, road vehicleidentification, system modeling, wall-climbing.

I. INTRODUCTION

THE longitudinal road gradient is essentially the degree ofsteepness of the road on which a vehicle is driving. Great

efforts have been made in investigating the influences of theroad gradient on the vehicle performance. For instance, withthe information of road gradient on a steep uphill, the accel-eration performance of a vehicle can be improved, and on asteep downhill, the control and safety of the vehicle can be im-proved [6], [12]. Roumegoux [20] has developed vehicle modelsthat calculate the pollutant emissions for a vehicle. These mod-els show the importance of the road gradient on the level ofpollutant output by a vehicle [19]. Road gradient has been stud-ied and employed to improve the performance of an automatictransmission control algorithm in [6] and [15]. The availabilityof road gradient information to vehicle control systems suchas automatic transmission gear shifting, fuel consumption, andadaptive cruise control (ACC) [5] will have a big impact onthe improvement of vehicle control quality and driving safety.Therefore, it is important to obtain the road gradient in a reliableand economic way.

Manuscript received October 17, 2005; revised December 27, 2006. Recom-mended by Technical Editor R. Rajamani. This work was supported in part bythe Engineering and Physical Sciences Research Council (EPSRC), U.K., andin part by Jaguar Cars Ltd.

S. Mangan was with the Department of Electrical Engineering and Electron-ics, Liverpool University, Liverpool, U.K. He is now with Energetix Group plc,Capenhurst, CHI 6EH, U.K. (e-mail: [email protected]).

J. Wang is with the Department of Electrical Engineering and Electronics,University of Liverpool, Liverpool, L69 3GJ, U.K. (e-mail: [email protected]).

Digital Object Identifier 10.1109/TMECH.2007.897286

However, the information about the road gradient is currentlyunavailable for vehicles dynamically running on the road. Themost obvious method of providing road gradient information isto place a sensor onto a vehicle to measure the road gradient. Anumber of sensor-based methods in obtaining the informationof road gradients have been reported (see, for example, [6],[12], [15], and [19]). Adding an extra sensor is not a desirableoption for vehicle manufacturers, as it will increase productioncosts through additional hardware and wiring complexity. Froma wide range of literature, there are only a few reports forsensorless road-gradient estimation methods [4], [20], [21].Fairgrieve [4] proposes a method for estimation of road gradientto improve the steady-state suspension-deflection control, andthe algorithm can only estimate the road gradient at a steady statein offline simulation. A work related to simulation study for of-fline estimation of road gradients is reported in [20]. Therefore,the project was proposed to develop a sensorless, cost effective,reliable, and accurate method to estimate the longitudinalinclination of a road in real time for ACC. The research projectwas cosponsored by Jaguar Cars Ltd. and the Engineering andPhysical Sciences Research Council (EPSRC), U.K.

The project is organized into two phases, namely, the develop-ment of a new gradient benchmark system and the developmentof a novel sensorless gradient estimation algorithm. The gradientbenchmark consists of an inclinometer and an error correctionalgorithm. The sensorless road-gradient estimation algorithmuses the vehicle data available on the CAN bus [10] to estimatethe road gradient. Initially, the gradient estimation algorithmand the gradient benchmark system were executed in parallelunder variable road conditions and different driving mannersin order to verify the sensorless road-gradient estimation algo-rithm. Once the sensorless estimation algorithm is validated,the benchmark system will be removed, and the estimation al-gorithm will work online to provide an estimated road gradientfor vehicle control systems.

II. DEVELOPMENT OF A NEW GRADIENT BENCHMARK SYSTEM

Developing a sensorless road-gradient estimation algorithm isthe ultimate aim of the research project. To assess how accuratethe estimated road gradient is, it is necessary to have a bench-mark that can serve as an accurate road gradient for comparisonwith the estimated results. Different types of sensors may beused for the gradient benchmark system, for example, gyro, op-tical sensor, accelerometer, inclinometer, etc. The sensors mostcommonly used to measure the longitudinal road gradient arethe accelerometer and inclinometer [11], [13], [14], [16], [19],

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376 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 12, NO. 3, JUNE 2007

[22], [23]. The internal construction of the accelerometer meansthat it is sensitive to gravity; and when it is pitched, the outputwill be offset by some degrees proportional to the degree ofthe pitch motion. The offset caused by pitching will be muchsmaller compared to the full scale output of the accelerome-ter. In contrast, an inclinometer allows a greater measurementresolution because it has been designed to output its full scalevoltage, as it is pitched through ± 90◦. The main advantage ofusing these two sensors is their low cost. The project adopted aninclinometer as the gradient benchmark sensor. The inclinome-ter is a micromachined acceleration-sensing element with a dcresponse to measure inclination relative to gravity [3]. Unfor-tunately, inclinometers are very susceptible to noise caused bytheir movement; this is especially true when the inclinometeris accelerated along its measurement axis. Therefore, they aregenerally more suitable for tilt measurements in static situa-tions. The inclinometer is used in a dynamic environment, soit is necessary to remove the errors before a reliable gradientmeasurement can be obtained. To study the inclinometer’s op-eration under dynamic conditions, a test rig was set up in theauthors’ laboratory to simulate the sensor dynamics [18]. Thetest rig consisted of an angular adjustable test track, a vehicle, acrossbow CXTA01 inclinometer [3], a drive system, and a dataacquisition system. The vehicle was driven along the track, andthe speed of the vehicle was varied [17] while the inclinometeris attached on the top of the vehicle.

There were two main sources of noise in the inclinometermeasurement signals: 1) high frequency noise caused by vibra-tion of the vehicle and 2) the lower frequency noise caused by theacceleration and deceleration of the vehicle. A number of low-pass filters were used to remove the high frequency noise. Todecouple the acceleration error from the gradient signal math-ematical morphological (MM) technique was investigated [8].The MM algorithms worked very well for the test rig and someoffline vehicle signals. But the online test did not give the desiredperformance under the variable driving patterns.

The main problem associated with the above algorithm is theserious contamination of acceleration signals. To eliminate theacceleration from the gradient measurement, a straightforwardidea is that if the acceleration information could be obtained,it could be used to remove the noise caused by the variationsof acceleration. Since the velocity is available from the vehicleCAN bus, the acceleration can be derived by differentiatingthe velocity signal. Therefore, a new acceleration-based error-correction algorithm was proposed. This process is describedin Fig. 1. This acceleration-based error-correction algorithm issimulated using the steady and erratic run data. Examples of theresults are shown in Fig. 2(a) and (b).

From the offline tests, the acceleration-based method is verysuccessful in removing the errors caused by acceleration signals.There are a few spikes on the corrected inclinometer signal,which are due to the speed bumps around the test track on site.

III. ONLINE TEST OF THE GRADIENT BENCHMARK SYSTEM

For online testing of the benchmark system, a rapid prototyp-ing system at Jaguar Cars [18] is used. The system is interfaced

Fig. 1. Acceleration-based error correction algorithm.

Fig. 2. Offline test results for the acceleration based on the error correctionalgorithm.

directly to the CAN bus so that it has access to any data avail-able from CAN bus on the vehicle. The testing is carried out andrepeated with the fine tuning of the error-correction algorithmparameters until the algorithm is accurate and robust.

The tests were conducted along a test rack at Jaguar Cars Ltd.in Coventry, U.K. The gradient along the track is known, whichcan be adopted to judge how accurate the benchmark is Fig. 3shows the results recorded for a steady run online.

Fig. 3(a) shows the velocity profile recorded during the onlinetest. For the majority of the test, the velocity is maintainedat a reasonably constant level. There are a few points wherethe vehicle is decelerated and accelerated suddenly. The effectthat the acceleration and deceleration has upon the inclinometer

MANGAN AND WANG: DEVELOPMENT OF A NOVEL SENSORLESS LONGITUDINAL ROAD GRADIENT ESTIMATION METHOD 377

Fig. 3. Online steady run test.

signal can be seen in Fig. 3(a). The output of the acceleration-based error correction algorithm from the online tests that isvery close to the actual road gradient is shown in Fig. 3(b).

Fig. 4 shows an example of the results of the benchmarkalgorithm tested online during an erratic run. Fig. 4(a) showsthe velocity profile recorded during the test run. This clearlyshows a large amount of acceleration and deceleration duringthe test run. This is mirrored by the filtered inclinometer data;the acceleration and decelerations have produced very large (±20◦) errors. Fig. 4(b) shows the results produced by the accel-erationbased error correction algorithm. The large amount ofacceleration errors were removed from the inclinometer signal,and the result was very close to the actual road gradient.

The style of driving in the steady runs is most representative ofthe type of driving that can be expected during ACC. Therefore,the accuracy of the gradient benchmark under these conditionswas assessed. The gradient benchmark measurement was com-pared against a known road gradient of the test track. The steadyruns were repeated over 10 times. The statistical features of thetest results are that the absolute average error is 0.15◦, and thestandard deviation is 0.31◦. The road gradient benchmark per-formed reasonably well, as the project specification required anaccuracy of ±1◦. One area of concern was that the inclinometer

Fig. 4. Online erratic run test.

would not be able to differentiate between vehicle pitch androad gradient. Each time the output of the gradient benchmarkwas calibrated against an area of the test track where the roadgradient was zero degrees. During the test runs the pitchingcaused by acceleration and deceleration did not prove to be aproblem. The pitching of the vehicle was proportional to the ac-celeration and deceleration, therefore, small adjustments to thegain (see Fig. 3) in the error correction algorithm compensatedfor any vehicle pitch. Therefore, the gradient benchmark is ac-curate enough to be used to assess the success of the sensorlessgradient estimation algorithm, and the benchmark errors will becountered in the final results as well.

IV. DEVELOPMENT OF A NOVEL SENSORLESS

ROAD-GRADIENT ESTIMATION ALGORITHM

There are only a limited number of reports on the topic ofonline longitudinal road-gradient estimation without using anysensors. Some methods reported in the past are based on an ideato calculate the torque being used to drive the vehicle up or downan incline [9]. This extra torque required can be assumed to beused to overcome any road gradient. Soo-Yong [21] put forwarda method of using fuzzy logic to determine the road gradient.The major problem with the above methods is that the brakeforce is not considered. Fairgrieve [4] introduced an extendedKalman filter to estimate the underlying vertical road velocity,which is only suitable for detecting steady-state gradients or theroad gradients with very slow variations.


Fig. 5. Proposed gradient estimation algorithm.

Fig. 6. Typical torque converter characteristics.

The idea behind the method proposed in this paper is that ifa torque for driving a vehicle to accelerate along a horizontalroad is known, using the same amount of torque to drive thesame vehicle will generate a smaller acceleration for the vehicletraveling uphill or larger acceleration for the vehicle travelingdownhill. Therefore, the road gradient should be proportional tothe acceleration difference. The road gradient can be obtainedby observing the acceleration variation. In this paper, the ac-celeration difference will be monitored using a vehicle-model-based method, which is then led to create a gradient estimationalgorithm. The sensorless gradient estimation algorithm wasdeveloped as illustrated in Fig. 5.

To ensure that the estimation algorithm can operate in realtime, it is important that the vehicle model is not too compli-cated. The vehicle model also needs to be fairly generic so thatit can be used for different types of vehicles.

A. Development of Vehicle Models

In this section, two vehicle models will be derived for usein the gradient estimation algorithm. From the project specifi-cation, the gradient estimation algorithm is required to operatewith the ACC system so that the vehicle will travel at above30 mi/h speed without introducing any excessive braking oracceleration. Due to these operating constraints, a number ofassumptions can be made for vehicle modeling. The first as-sumption is that a simple model of the coupling between theengine and gearbox can be used. The second assumption is thatthere will not be any excessive acceleration or deceleration sothat the longitudinal slip and wheel spin can be ignored. How-

Fig. 7. Brake line pressure versus deceleration.

ever, it should be noted that if this gradient estimation algorithmis to be extended to work below 30 mi/h, then, the vehicle modelwill have to be adapted to take into consideration the more com-plicated vehicle dynamics at a low speed, for example, slippagein the engine–sgearbox coupling, tire deflection, etc.

The engine in conjunction with the rest of the driveline pro-vides a force to propel the vehicle, which is represented byFdriveline. The drive force is required to overcome any opposingforces that act against the movement of the vehicle, which isrepresented by FR. The motion of the vehicle should satisfythe Newton’s second law, that is, ma = Fdriveline − FR. Thedriveline and resistance forces can be modeled in a number ofways. In this paper, two models are studied. The first model isdescribed in (1)

ma =

Driveline force︷︸︸︷((Teµ)itid

r

)−

Brake force︷︸︸︷(bpkb)

−

Running resistance force︷︸︸︷((fmg(cos θ)) + (0.5σcwAv2) + (mg sin θ)) (1)

where m is the vehicle weight (kilogram) and a is the vehicleacceleration or deceleration (meter/square second). In (1), thereare three parts, namely, driveline force, brake force, and runningresistance force. These three forces are nonlinear and vary withthe condition variations. For the term of the driveline force, Te isthe engine torque (N·m), it is the current transmission gear ratio,id is the final drive (differential) gear ratio, r is the vehicle tireradius (meter), and µ is the torque converter multiplication ratiothat can be found from the torque converter characteristic chartnormally available from the torque converter manufacturers. Atypical torque converter conversion chart is illustrated in Fig. 7[2]. In the brake force, bp is the brake line pressure (bar), and kb

is the brake coefficient that can be calculated from the brakingforce test. For example, during a series of braking tests for theJaguar XKR car, the characteristics of the braking line pressure


Fig. 8. Running resistances.

TABLE ICALCULATING THE DRAG AND ROLLING COEFFICIENTS

versus decelerations is shown in Fig. 8. If the bias in the figureis ignored, then, kb = 0.13 × 1950 = 253.5.

The running resistance forces have three parts: 1) FRo isthe rolling resistance (Newton); 2) FL is the aerodynamic drag(Newton); and 3) FSt is the climbing resistance and downgradeforce (Newton).

Bosch Automotive Handbook [1] explains how to carryout these tests, and describes that FRo can be calculated byFRo = fG = fmg, in which the coefficient of rolling resis-tance f can be estimated. Aerodynamic drag is calculated usingFL = 0.5σ cwAv2, where σ is the air density that is 1.202 kg/m3

at 200 m altitude, cw is the vehicle drag coefficient that is uniqueto individual vehicles. A is the front area of the vehicle that is2.2 m2 for the Jaguar XKR car [2]. v is the vehicle velocity (me-ter/second). The values for the coefficients of rolling resistancef and the vehicle drag coefficient cw can be determined throughtwo simple coastdown tests. The calculations based on the testsare shown in Table I.

The climbing resistance and downgrade force is explained byFig. 8. The climbing resistance can be calculated by [1] FSt =G sin θ = mg sin θ, which includes the climbing and downgradeforce FSt. Thus, the rolling resistance force has to be alteredslightly. The rolling resistance now includes the cosine of theroad gradient, and can be rewritten as FRo = fmg(cos θ).

The running resistance force can also be obtained from acoastdown test. A coastdown test involves the vehicle being

Fig. 9. Process to find the resistance force model coefficients.

TABLE IIJAGUAR XKR VEHICLE MODEL PARAMETER VALUES

taken to a test track where it is driven up to a preset speed.The vehicle is, then, coasted down to a stop in the neutral gear.The test track needs to be flat to ensure that road gradient doesnot affect the results. Whilst the vehicle is coasting down toa stop, the forces acting against the motion of the vehicle arerolling resistance, aerodynamic drag, and mechanical drag. Thedata collected during this test is then, used to find a three-term approximation formula that models the combination of allthree resistance forces A + Bv + Cv2, where A,B, and C arethe coastdown equation coefficients. The coefficients have beenfound to be A = 207.2, B = 2.1085, and C = 0.5809 using aleast squares regression algorithm and the test data from JaguarCars Ltd. Fig. 9 shows the process used to find the parameters.

The coastdown test was carried out on a flat road. Clearly,the road gradient resistance is not considered by the coast-down resistance force model. Therefore, an extra section isadded to represent the influences of the road gradient. Thecomplete coastdown running resistance can be calculated byA + Bv + Cv2 + (mg sin θ). Based on the above model, thesecond version of the vehicle model should have the followingform, and Table II provides the parameter values for the Jaguar


Fig. 10. Actual acceleration versus estimated acceleration: standard vehiclemodel.

XKR car

ma=

Driveline force︷︸︸︷((Teµ)itid

r

)−

Brake force︷︸︸︷(bpkb) −

Running resistance force︷︸︸︷(a + bv + cv2 + (mg sin θ)) .

(2)The two vehicle models in (1) and (2) need to be tested

by simulation using the data collected from the test vehicle tovalidate their performance. While the test vehicle is travelingalong a road, the relevant data is logged that includes estimatedengine torque, vehicle velocity, gear position, brake pressure,torque converter slip, and road gradient. Note that for the dataof the gear position, the five forward gears are indicated bynumbers one to five. Number six indicates that the reverse gearhas been selected, and number seven indicates that a gear changeis in progress.

The gradient benchmark developed in Section II, now be-comes vital for the development and fine tuning of the vehiclemodel. The benchmark will run online together with the roadgradient estimation algorithm and the readings of the bench-mark system. The estimated road gradient will be compared totune the estimation algorithm. The vehicle models described in(1) and (2) are implemented in Simulink. The output of the ve-hicle model is an estimated acceleration at the first stage. Fig. 10shows the estimated acceleration versus the actual accelerationwhen the standard vehicle model (1) is adopted from one ofdifferent road tests.

From Fig. 10, the estimated acceleration appears to be anoffset of approximately 0.2 m/s2 from the actual accelerations.The error in the estimated acceleration appears mainly to bean offset. The vehicle model always seems to over estimate thelevel of acceleration, and under estimate the level of decelera-tion. This may be caused by the vehicle model overestimatingthe level of drive force, or an underestimate of the level of re-sistance acting against the vehicle. The effort has been made toidentify the possible reason for causing the offset errors. Thefirst consideration is that the system model may underestimatethe resistance force, so the tests have been carried out with theincreased rolling resistance coefficient f . But the increase of fdid not give a consistent compensation to the offset. The sec-

ond consideration is that the model may have over estimatedthe drive torque. So a negative torque offset is introduced intothe model. Again, this did not give the expected results. Furtherstudy indicated that the different compensation of f and torquefor different gear positions are required. The offset is caused byusing a fixed term in the vehicle model, which is only true forone gear position but causes the offset shifting for other gear po-sitions. However, the quantity of the compensation with respectto different gear positions is not known. Based on the analysis,a method is proposed, which is to introduce a variable terminto the vehicle model that will compensate for the accelerationoffset described by

a =Fdriveline − FR

m− η (3)

where η is the acceleration offset caused by driveline losses. Un-der a closer inspection, it is found that the offset varies slightlyfor each gear position. Therefore, the offset value needs to befound for each gear position, and the variable offset η will bea function of it to be represented by η(it). Genetic algorithms(GAs) are used to find and optimize the values of η(it) for sevendifferent gear positions in the project [7].

The search range is limited to 0 ∼0.6 based on the previousexperience and analysis. The binary coding is adopted for thistask, and the initial population is selected randomly within theprespecified limit. The fitness function is formed by the absolutemean error (AME) between the two accelerations, which isdefined by

AME

=∑

|actual acceleration − estimated acceleration|length (data)

(4)

where length(data) is the number of samples used to find themean error. The AME is used to assign a fitness value to eachstring, given by

fitness =1000

(1 + AME). (5)

Therefore, the objective of GAs in this particular task is tomaximize the fitness function. Five sets of test data are used forthis purpose; and for each set of data, the GAs identificationprocess is repeated 5 times with 50 generations. The best fittedvalues of η(it) found for both the standard vehicle model andthe coastdown vehicle model are listed in Table III.

B. Validation of the Vehicle Models

The model is then, validated using the data collected fromdifferent driving tests along different types of roads. The firstset of data is taken from some urban driving around the Whitleysite in Coventry, U.K. During this test, the vehicle is acceleratedand decelerated vigorously to introduce a lot of variation inorder to see how well the vehicle model reacts. Fig. 11(a) and(b) shows the vehicle velocity, gear position, brake pressure androad gradient data recorded from the CAN bus and gradientbenchmark during the first test run.

The data in Fig. 11 show that the vehicle is driven at relativelylow speeds. There is a lot of variation of the vehicle velocity,


TABLE IIIη(it) VALUES FOUND USING THE GENETIC ALGORITHMS

Fig. 11. Vehicle validation test data: urban driving.

and therefore, a lot of acceleration and deceleration. The vehiclestays in the lower gears, i.e., second and third gears. The actualacceleration and the estimated acceleration provided by the twovehicle models can be seen in Fig. 12. The average errors be-tween the actual and the estimated accelerations for the urbandriving test data are 0.0584 m/s2 for the vehicle model (1) and0.0504 m/s2 for the coastdown vehicle model (2).

Fig. 12. Estimated acceleration versus actual acceleration: urban driving.

The second set of test data is taken from a test run along amotorway. For this set of data, the vehicle is cruising along amotorway in just the fifth gear. There are minimal road gradientvariations and very little braking. The actual acceleration andthe estimated acceleration for both vehicle models can be seen inFig. 13. The average errors between the actual and the estimatedaccelerations for the motorway driving test data are 0.0543 m/s2

for the vehicle model (1) and 0.0440 m/s2 for the coastdownvehicle model (2).

The final set of validation data is taken from a test run alongsome hilly country roads. This is a combination of the previoustwo pieces of data. There is some low speed to reasonably highdriving with gears two to five being used. Some significant gra-dients are encountered during this run. The actual accelerationand the estimated acceleration for both vehicle models can beseen in Fig. 14.

The average errors between the actual and the estimated ac-celerations for the motorway driving test data are 0.2075 m/s2

for the vehicle model (1) and 0.1164 m/s2 for the coastdownvehicle model (2). From the validation data it can be seen thatthe coastdown vehicle model is the most accurate for all threetypes of roads. The coastdown vehicle model will be used forthe gradient estimation algorithm in the next stage.


Fig. 13. Estimated acceleration versus actual acceleration: motorway driving.

C. Structure of the Sensorless Gradient EstimationAlgorithm and Offline Test

Based on the vehicle model obtained in the previous sec-tion, the revised road-gradient estimation algorithm is shown inFig. 15.

From Section IV-B, the model can work out the differencebetween the actual acceleration/deceleration and the estimatedacceleration/deceleration for the vehicle traveling along a hor-izontal flat road. It is assumed that the acceleration differenceis caused by road gradient variations. Therefore, the road gra-dient should be proportional to the differences of accelerations.The proportional coefficient is identified using the test data, andthen, the longitudinal road gradient estimator is developed.

The estimation algorithm is tested offline using the data col-lected from the driving along urban, motorway, hilly roads. Testresults are summarized in Table IV.

From all the offline simulation, the proposed estimation algo-rithm is compared with the results obtained using the algorithmproposed in [9]. The proposed algorithm gives a better estima-tion than the method proposed by Ibamoto [9]. Combining thisvalue with the gradient benchmark accuracy of ±0.15◦ gives themaximum average error of±0.45◦ for the sensorless method de-veloped in the paper. Therefore, for all tests, the average error

Fig. 14. Estimated acceleration versus actual acceleration: hilly country roaddriving.

Fig. 15. Longitudinal road gradient estimator.

TABLE IVSUMMARY OF THE TEST RESULTS (DEGREES)


Fig. 16. Real-time execution of the algorithms and data collection.

Fig. 17. CAN data recorded: dual carriageway run.

is within the desired accuracy of ±1◦. Next stage is to validatethe algorithm online in real time.

V. ONLINE TEST OF THE SENSORLESS

ROAD-GRADIENT ALGORITHM

The test vehicle used for this project is a Jaguar XKR car.The data acquisition system is the same as the one described inSection III and shown in Fig. 16. During the online test, three setsof data are recorded: 1) the raw CAN bus data, i.e., wheel speed,gear position, etc; 2) the output of the road gradient estimationalgorithm; and 3) the output of the road gradient benchmarksystem.

The test vehicle is driven along a number of different types ofroads such as dual carriageways, urban roads, and hilly countryroads to test the accuracy and robustness of the road-gradientestimation algorithm in real time. The first set of online test datais taken from a dual carriageway run. Fig. 17 shows the vehiclevelocity, gear position, and brake pressure recorded during theonline test that indicates the vehicle cruising along with theACC operating. The ACC controller is constantly making minoradjustments to the vehicle velocity in order to maintain the setspeed or the required distance from the preceding vehicle. Theentire run was carried out in 5th gear, and the brakes were notapplied. Fig. 18 shows the results of the online test.

The second online test is taken from a drive along a reasonablyfast A-road. The road contains some reasonable road gradients

Fig. 18. Online test 1 results: dual carriageway run.

Fig. 19. CAN data recorded: hilly A-road.

from −2◦ to +4◦. The CAN data recorded during the test run isshown in Fig. 19.

Fig. 20 shows the results obtained from the road-gradient es-timation algorithm during the online test, which indicates thetest vehicle slowly accelerating from 10 to 20 m/s. The vehiclestays at a relatively constant velocity for approximately 50 s be-fore sharply decelerating when the vehicle comes to a crossroad.When the vehicle velocity drops below 8 m/s, the road gradientdata is ignored. During this online test, there are a few gearchanges presented as the vehicle accelerates and decelerates.

The third online test is taken from a run along a hilly countryroad. The data collected during this online test is shown inFig. 21. It shows the test vehicle traveling at a slower averagespeed than the two previous tests. There are a large number ofgear changes as the vehicle speeds up and slows down. Fig. 22shows the results obtained from the road-gradient estimationalgorithm.

The forth online test involves driving around urban roads.There are some significant gradient variations on these roads.The CAN data recorded during this online test is shown inFig. 23. The results obtained from the road-gradient estimationalgorithm are shown in Fig. 24.


Fig. 20. Online test 2 results: hilly A-road.

Fig. 21. CAN data recorded: hilly country road.

Fig. 22. Online test results: hilly country road driving.

The final set of online test data is taken from another runalong a dual-carriageway. The CAN data recorded during thisonline test is shown in Fig. 25. The results obtained from theroad-gradient estimation algorithm are shown in Fig. 26.

The statistical features for the online test results are summa-rized in Table V, which shows the maximum, average, andstandard deviation errors that are calculated when the esti-

Fig. 23. CAN data recorded: hilly urban roads.

Fig. 24. Gradients: hilly urban road driving.

Fig. 25. CAN data recorded: dual carriageway driving.

mated road gradient is compared to the gradient benchmark.The required accuracy for the estimated road gradient is ±1◦.The final column of Table V shows that the percentage of theestimated road-gradient data is within the required±1◦ accuracywith consideration of ±0.15◦ accuracy of gradient benchmarkmeasurement.


Fig. 26. Test results: dual carriageway driving.

TABLE VONLINE TEST RESULTS ANALYSIS

TABLE VICOMPARISON OF THE OFFLINE PERFORMANCE VERSUS

THE ONLINE PERFORMANCE

The results obtained from the online tests show that the road-gradient estimation algorithm performs very well online. Theperformance is very similar to the performance obtained duringthe offline tests. A comparison of the mean errors taken fromoffline tests and online tests is shown in Table VI. It shows thatthe online performance is as good as the offline simulations.The online results show that nearly the entire estimated roadgradient is within ±1◦ accuracy of the measured road gradient.When a large estimation error occurs, the estimation algorithmusually returns to the desired accuracy within 2 s. Therefore,the gradient estimation algorithm converges to the desired accu-racy reasonably quickly. The proposed road-gradient estimationalgorithm was proved to be robust enough to be used under anumber of different road conditions, while supplying reasonablyaccurate road-gradient information. This level of performanceis good enough to be used to provide road-gradient informationto other vehicle control algorithms.

VI. CONCLUSION

This paper presented a sensorless road-gradient estimationmethod, which was proved to be accurate and reliable enoughfor ACC systems. The method did not require any extra sensorsand hardware, so it is simple and cost effective. The estimationalgorithm was implemented in a rapid prototyping system, andtested online under different driving styles and road surfacepatterns. The test results showed that the method is successfuland reliable. The project cosponsor is satisfied with the testresults and the structure of the algorithm. This algorithm willbe integrated into other control algorithms at Jaguar Cars Ltd.The paper also presented a simple, efficient, and generic vehiclemodel to predict the acceleration if the vehicle travels along aflat road. The vehicle model is easy to be modified to representother type of cars or vehicles. So, the method developed in thispaper can be extended to be used in other vehicles if the requiredvariable measurements are available.

ACKNOWLEDGMENT

The authors would like to thank Dr. A. Dunoyer and Dr. M.Richardson from Jaguar Cars Ltd. for their support.

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Stephen Mangan received the B.Eng. degree in elec-trical engineering and computer science, in 2000, andthe Ph.D. degree in control and vehicle dynamicsfrom the Department of Electrical Engineering andElectronics, Liverpool University, Liverpool, U.K.

Currently, he is working on a micro-CHP productand other energy-efficiency projects at the EnergetixGroup plc, Capenhurst, U.K.

Jihong Wang (M’07) received the B.Eng. degreefrom Wuhan University of Technology, Wuhan,China, in 1982, the M.Sc. degree from ShandongUniversity of Science and Technology, Shandong,China, in 1985, both in automatic control, and thePh.D. degree in nonlinear uncertain system controlfrom Coventry University, Coventry, U.K., in 1995.

Currently, she is a Senior Lecturer with the De-partment of Electrical Engineering and Electronics,University of Liverpool, Liverpool, U.K. Her currentresearch interests include nonlinear system control,

system modeling and identification, power systems, energy-efficient systems,and applications of intelligent algorithms.

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