Error Correction of Measured Unstructured Road Profiles...

Research ArticleError Correction of Measured Unstructured Road ProfilesBased on Accelerometer and Gyroscope Data

Jinhua Han Xiaoqiang Yang Huanliang Li and Hongxin Cui

Engineering Institute PLA University of Science and Technology Nanjing 210007 China

Correspondence should be addressed to Xiaoqiang Yang 3113593699qqcom

Received 25 October 2016 Accepted 27 December 2016 Published 24 January 2017

Academic Editor Francesco Franco

Copyright copy 2017 Jinhua Han et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper describes a noncontact acquisition system composed of several time synchronized laser height sensors accelerometersgyroscope and so forth in order to collect the road profiles of vehicle riding on the unstructured roads A method of correctingroad profiles based on the accelerometer and gyroscope data is proposed to eliminate the adverse impacts of vehicle vibration andattitudes change Because the power spectral density (PSD) of gyro attitudes concentrates in the low frequency band a methodcalled frequency division is presented to divide the road profiles into two parts high frequency part and low frequency part Thevibration error of road profiles is corrected by displacement data obtained through two times integration of measured accelerationdata After building the mathematical model between gyro attitudes and road profiles the gyro attitudes signals are separated fromlow frequency road profile by the method of sliding block overlap based on correlation analysisThe accuracy and limitations of thesystem have been analyzed and its validity has been verified by implementing the system on wheeled equipment for road profilesrsquomeasuring of vehicle testing ground The paper offers an accurate and practical approach to obtaining unstructured road profilesfor road simulation test

1 Introduction

Road profile is the most important external excitation ofthe ground vehicle which influences vehicle ride comfortoperational stability driving reliability fatigue life of compo-nents and so forth [1ndash3] Therefore providing accurate roadprofile for vehicle reliability testing and simulation has beenan important research content in this field

The actual roads can be divided into structured andunstructured roads The structured roads generally refer tothe well-structured pavements with flat road surface andregular edge such as the expressway and urban roads Theunstructured roads generally refer to the less structuredroads with high roughness including the nonpaved roadssuch as gravel road and sand road ldquobad roadrdquo whose roaddegree is E or below E and road cover is damaged roadlessroad and strengthened test pavement Currently road profilemeasuring concentrates on the structured roads mainlymeasured by the Highway Department Moreover lots ofstructured road profile models have been built up and can besimulated and reconstructed accurately [4 5] However with

regard to the unstructured roads there is no standardizedroad profile to utilize because of the potential complexityFurthermore the unstructured road profile has evident non-Gaussian characteristics largely due to a large number ofhigh amplitude excitations [6] The characterization of thestructured road profile based on the assumption of stationaryrandom andGaussian is difficult to be applied to the unstruc-tured roads [7] Therefore an in situ acquisition operation ofunstructured roads is always needed before performing anyroad simulation

Since the 1960s a lot of studies had been done formeasuring road profiles and many kinds of measuringdevices had been invented [8ndash11] which contain Level andRod Multiwheel Profilograph BPR Roughometer InertialProfiler Laser Profiler and so forth But they are alwaysdifficult to simultaneously consider the measuring speedand accuracy Nowadays the most commonly used noncon-tact profilometers can measure the road profile with prettyhigh accuracy [12 13] Nonetheless this system may notbe applicable for the unstructured road profile measuringdue to the following reasons [14] The road profile mainly

HindawiMathematical Problems in EngineeringVolume 2017 Article ID 5670697 11 pageshttpsdoiorg10115520175670697

2 Mathematical Problems in Engineering

Laser height sensor Accelerometers

GPS

Camera

Gyroscope Displacement sensor

SoMat eDAQ

Figure 1 Road profile acquisition system of the vehicle

depends on the relative displacement between the sensorand the road surface measured by the sensor (laser infraredor ultrasonic) mounted on the vehicle The obtained finaldisplacement could represent the road profile only when thevehicle is not excessively interrupted and maintains steadywhile driving through the road Obviously this hypothesis isnot true for unstructured roads because of the bumpiness ofthe unstructured road which result in severe vibration andattitudesrsquo change of the vehicle and the major variation in thevehicle speed [15 16]

To solve the problem a laser measuring system forthe unstructured road is proposed to realize the fast mea-surement of the road profiles vibration acceleration andgyro attitudes of the vehicle To improve the accuracy ofthe measured road profiles an error correction methodbased on measured acceleration and gyro attitudes data isdiscussed in detail Aiming at the characteristic that the PSDof vehicle attitudes concentrates in the low frequency bandthe measured road profile can be divided into high frequencypart and low frequency part by the method of frequencydivision Then the vibration error of the measured roadprofile is corrected by displacement data obtained throughtwo times integration of measured acceleration data Theattitude error of the measured road profile is correctedby signal separation based on sliding block overlap andcorrelation analysis The proposed acquisition system hasbeen used in the unstructured road profile measurement ofvehicle testing ground and its validity has been evaluated inthe paper

2 Laser Road Profile Acquisition System

For the reliability simulation of the vehicle the 2D profilecurve in the direction of the vehicle wheelsrsquo orbit is generallyused as the research object A road profile acquisition systemis shown in Figure 1 which integrates the gyro attitudesGPS vibration acceleration and displacement measuringThe system can be used tomeasure road profiles of structuredroads (asphalt road expressway etc) and unstructured roads

(gravel road cross-country path strengthen-road etc) Thetest vehicle is an 8 times 8 wheeled vehicle with independentsuspension [17] which could reduce the impact of the roadprofiles to the vehicle and improve ride comfort Howeverthe vehiclersquos attitude change is inevitable when driving on theunstructured roads Generally the frequencies of sensors arehigh enough for the acquisition The sampling frequenciesof acceleration and road profile data are 1 kHz while thesampling frequency of gyro attitudes is 200Hz

The road profile acquisition system consists of a HBMSoMat eDAQ System (data acquisition and record) a RMSStrapdown Platform System (mounted in the center of thevehicle andmeasuring vehiclersquos attitudes change) two groupsof Datron HF-500C laser height sensors (measuring the rel-ative displacement between sensor and road surface ie theroad profile) ten groups of ENDEVCO 7596 accelerometers(measuring the vibration acceleration of laser sensors and thespindles of the vehicle) some groups of cable displacementsensors (measuring displacement of the spindles) an ordi-naryGPSmodule (measuring the longitude latitude altitudeand speed of the vehicle) an AXIS P1311 webcam (recordingvideo information of testing roads) and so forth As shownin Figure 2 the laser height sensors and accelerometers arecounted on the brackets that are fixed on both sides of thefront of the vehicle

3 Error Correction of Road Profiles

The road profile includes the large-scale signal that is fromlow frequency to high frequency the laser height sensorcould barely measure the signals of all frequency bands Inaddition the devices of the acquisition system are fixed on thevehicle the road profilesmeasured by laser sensors aremostlyhigh frequency and short wavelength signals (the wavelengthis less than the wheelbase of testing vehicle) Therefore themeasuring frequency band is divided into several sectionsFor the low frequency and long wavelength part of roadprofile that the laser sensor cannot measure (the frequencyis generally lower than 01Hz) a Global Positioning System

Mathematical Problems in Engineering 3

Datron HF-500C

Laser height sensor

Left bracket

ENDEVCO 7596accelerometer

Figure 2 The mounted sensors of the acquisition system (leftbracket)

(GPS) receiver supplemented with Real Time Kinematics(RTK) technology can easily measure the road profile withcentimeter level accuracy and has been widely used in roadprofile measurement [18 19]

For the short wavelength signals above 01 Hz that thelaser sensor can measure they are also divided into twoparts due to the PSD of the vehicle attitudes [20] Tocorrect the errors of road profile caused by the vibrationand attitudes change of the testing vehicle the vibrationacceleration and gyro attitudes are measured For the roadprofile with frequency below 3Hz (01 Hzsim3Hz) the error iscorrected by themeasured gyro attitudes For the road profilewith frequency above 3Hz (gt3Hz) the error is correctedby displacement data obtained by two times integration ofmeasured acceleration data Finally the final corrected roadprofile is obtained by combining the corrected low frequencypart and the corrected high frequency part its specificcalculation process is shown in Figure 3 Each filteringfrequency can be adjusted according to the actual need in thecalculation process

31 Division Frequency Determined The division frequencyof measured road profiles is mainly determined by the gyroattitudes frequency band and the road frequency band Theroad frequency band depends on vehicle forward speed Vand the wavelengths of road profile The wavelengths of roadprofile are mainly concentrated within a certain range Itis hypothesized that 1205821 and 1205822 are the lower and upper ofthe wavelengths respectively Then the frequencies of roadwavelengths measured by the laser sensor can be expressedas

119891119871 = V1205822

119891119867 = V1205821

(1)

Therefore to divide the gyro attitudes frequency and roadfrequency ofmeasured road profile the division frequency119891119889should be lower than the road frequency band [119891119871 119891119867] andhigher than the gyro attitudes frequency band [119891119886 119891119887] whichcan be expressed as

119891119887 lt 119891119889 lt 119891119871 = V1205822 (2)

32 Acceleration Integration To correct the vibration errordue to the movement of laser sensor along with the testingvehicle the displacement is calculated by two times integra-tion of measured acceleration data

As shown in Figure 4 the measured acceleration signalshould be preprocessed first including singularity removedamp detrend and band-pass filtering in order to improve mea-suring accuracy Then the vibration velocity is obtained byacceleration integration Finally the vibration displacementis obtained by velocity integration after band-pass filteringScilicet the vibration displacement is the vibration error ofroad profileTherefore the vibration error of road profile canbe corrected by subtracting the vibration displacement

33 Mathematics Description of Gyro Attitude To realize theerror correction of measured road profile due to the vehiclersquosattitudes change the mathematical model between vehiclersquosattitudes and road profile should be established first afteranalyzing the relation between them Due to the relativityof motion the corresponding coordinate system should beintroduced in the gyro attitudes measurement The gyroattitudes measured by strapdown gyroscope in this paper arethe geometric angles of the body coordinate system (BCS)119900119909119887119910119887119911119887 relative to the geographic coordinate system (GCS)119900119909119905119910119905119911119905TheBCS 119900119909119887119910119887119911119887 denotes the coordinate systemfixedon the testing vehicle that its origin is located at the centerof the vehicle 119900119909119887 points to forward along the longitudinalaxis of the vehicle 119900119910119887 points to left along the horizontal axisof the vehicle and 119900119911119887 is perpendicular to the 119900119909119887119910119887 planeand points to up along the vertical axis of the vehicle TheGCS 119900119909119905119910119905119911119905 denotes the coordinate system that its origin isalso located at the center of the vehicle 119900119909119905 points to east119900119910119905 points to north and 119900119911119905 points to sky along the verticaldirection according to the right-hand rule

The gyro attitudes of the testing vehicle include threeparameters [21] yaw angle 120574 pitch angle 120579 and roll angle 120593They denote the rotation angle of the vector around the 119909 119910and 119911 axes respectively According to the right-hand rule theinverse rotation is clockwise

As shown in Figure 5 in the case of the invariant of thecoordinate origin the GCS 119900119909119905119910119905119911119905 is used as the referencecoordinate system Then the BCS 119900119909119887119910119887119911119887 is obtained aftertriple rotation according to the order of 119911 minus 119910 minus 119909 Its specificconversion process is as follows

119900119909119905119910119905119911119905 120574997888997888rarr119900119911119905 11990011990910158401199101015840119911119905 120579997888997888rarr1199001199101015840

11990011990911988711991010158401199111015840 120593997888997888rarr119900119909119887 119900119909119887119910119887119911119887 (3)


Two-integralalgorithm

Signal separationalgorithm

High frequencyroad profiles

High frequency correctionroad profiles

Low frequency correctionroad profiles

Final correctionroad profiles

Integraldisplacement

Low frequencyroad profiles

Gyro attitudes

Band-pass filter

Gyro attitudes(200 Hz)

Measured laser road profiles(1000 Hz)

Vibration acceleration(1000 Hz)

High-pass filter High-pass filter Low-pass filter High-pass filter

Resampling(200 Hz)

(gt01 Hz) (gt3 Hz) (le3 Hz) (gt01 Hz)

(01Hz le f le 3Hz)

Figure 3 The calculation flow chart of correcting road profile

Then the transformation relation from the BCS 119900119909119887119910119887119911119887to the GCS 119900119909119905119910119905119911119905 is shown as follows

[[[[[

119909119905119910119905119911119905

]]]]]

= C119905119887[[[[[

119909119887119910119887119911119887

]]]]]

(4)

where [119909119905 119910119905 119911119905]119879 and [119909119887 119910119887 119911119887]119879 denote the coordi-nate of the laser sensor in the GCS 119900119909119905119910119905119911119905 and the BCS119900119909119887119910119887119911119887 respectively C119905119887 denotes the rotational transforma-tion matrix also called the strapdown matrix

The emphasis of realizing the sensor coordinate transfor-mation between different coordinate systems is the solutionof the strapdown matrix C119905119887 Therefore the obtained strap-down matrix C119905119887 according to the order of 119911 minus 119910 minus 119909 can beexpressed as

C119905119887 = C119911120574C119910120579C119909120593 = [[[[[

cos 120574 minus sin 120574 0sin 120574 cos 120574 0

0 0 1]]]]]

[[[[[

cos 120579 0 sin 1205790 1 0

minus sin 120579 0 cos 120579]]]]]

[[[[[

1 0 00 cos120593 minus sin1205930 sin120593 cos120593

]]]]]

=[[[[[[[

cos 120579 cos 120574 sin120593 sin 120579 cos 120574 minus cos120593 sin 120574 cos120593 sin 120579 cos 120574 + sin120593 sin 120574cos 120579 sin 120574 sin120593 sin 120579 sin 120574 + cos120593 cos 120574 cos120593 sin 120579 sin 120574 minus sin120593 cos 120574

minus sin 120579 sin120593 cos 120579 cos120593 cos 120579

]]]]]]]

(5)


Acceleration signal Singularity removed amp detrend

Band-pass filtering First-order integral Velocity signal

Band-pass filtering Second-order integral Displacement signal

Figure 4 The flow chart of acceleration integration

where C119911120574 denotes the rotational transformation matrixaround the 119911-axis with rotation angle 120574 C119910120579 denotes therotational transformation matrix around the 119910-axis withrotation angle 120579 C119909120593 denotes the rotational transformationmatrix around the 119909-axis with rotation angle 120593

The research of road profile is concerned with the roadroughness that is perpendicular to the ground Scilicetthe main external excitation of the testing vehicle is thedisplacement of the road in the 119911-axis direction along thedirection of the vehicle rather than in the 119909-axis or 119910-axisdirection Thus substituting (5) into (4) can be expressed as

119911119905 = [minus sin 120579 sin120593 cos 120579 cos120593 cos 120579] [[[

119909119887119910119887119911119887

]]]

(6)

When the change of the gyro attitudes angles 120593 120579 and 120574is small (6) can be simplified as

119911119905 = minus120579 sdot 119909119887 + 120593 sdot 119910119887 + 119911119887 (7)

Thus the error of measured road profile caused by thegyro attitudes is given by

Δ119911 = 119911119905 minus 119911119887 = minus120579 sdot 119909119887 + 120593 sdot 119910119887 (8)

As shown in (8) the measured road profiles are mainlyaffected by the pitch angle 120579 and roll angle 120593 the yaw angle 120574has almost no influence on them Due to the relatively largevalues of 119909119887 and 119910119887 (up to several meters) the small changesof vehiclersquos attitudes can cause large error of the measuredroad profiles Therefore the error of measured road profilescaused by vehiclersquos attitudes must be corrected based on thecalculation result of (8)

34 Error Correction Based on Signal Separation Accordingto (8) the relation between the vehiclersquos attitudes and theerror of road profile Δ119911 can be approximately regarded aslinear Hence the measured road profile can be regarded asthe linear mixture of true road and vehiclersquos attitude signalsThe error correction of measured road profile due to vehiclersquosattitudes change can be regarded as the signal separationof mixed signal [22] The mixed and separation process of

xb x998400xt

120579

120579

120574

120574

yt

y998400

yb

120593

120593

o

zt

z998400

zb

Figure 5 Coordinate transformation diagram

measured road profiles is shown in Figure 6 1199091 denotes thetrue road profile that is unseparated signal The additivemixed signal 119910 = 1199091 + 1199092 measured by the laser height sensor1198791 consists of signals 1199091 and 1199092 that are obtained through theunknown transmission channel 1198671 2 denotes the vehiclersquosattitudes measured by gyroscope 1198792 located in the center ofthe vehicle Then the mixed signal 119910 is separated to obtainthe accurate road profile based on the observed signal 119910 andthe reference signal 2

The signal separation algorithm in this paper is based onthe assumption of linear mixture However the signal mixinghas a certain nonlinearity in fact To satisfy the assumptionof linear mixture as much as possible a method called slidingblock overlap is proposed to correct the low frequency roadprofile The correction steps are shown as follows

Step 1 (signals acquisition) The low frequency road profile119910 and vehiclersquos attitudes (pitch angle 120579 roll angle 120593 and yawangle 120574) are measured and calculated firstThen according to(8) the reference signal 2 = minus120579 sdot 119909119887 + 120593 sdot 119910119887 is obtained


Sensor 1Observed signal

Signalseparation

Sensor 2Reference signal

Road profile

Gyro attitude

T1x1

x2x2

T2

H1

y = x1 + x2

x2 = A2x2(n + m2)x1(n)

x2(n)

Figure 6 The mixed and separation process of measured road profiles

i minus 1i

i + 1

1 s 1 s 5 s 1 s 1 s 5 s 1 s 1 s 5 s 1 s 1 s

Figure 7 The schematic diagram of the data segmentation

Step 2 (estimation of the time shift 1198982 by cross-correlationfunction) The cross-correlation function is a description ofthe correlation between random signal 2 and 119910 at differenttime According to the properties of the cross-correlationfunction when 1198771199102(120591) takes the maximum value at 120591 = 1205911the time shift 1198982 = 1205911 of the signals is determined

Step 3 (signal sliding segmentation and overlap) Theschematic diagram of the data segmentation is shown inFigure 7 The testing data of the time length 119879 is dividedinto 119873 segments of the equal length 1199051 Then there are 119873 minus 1overlapping segments of the equal length 1199052 Data segmentnumber 119873 and length 119905 can be adjusted according to theactual situation in order to achieve the best effectThe relationof the parameters is shown by

119873 sdot 1199051 + (119873 minus 1) sdot 1199052 = 119879 (9)

After completing the time shift of Step 2 the signalsliding segmentation and overlap of measured road profile119910 and reference attitudes 2 are accomplished according tothe above method Then the 119894 segment of measured roadprofile 119910 and reference attitudes 2 are recorded as 119910119894 and 2119894respectively

Step 4 (amplitude adjustment) The amplitude of the vehiclersquosattitude signal will change during the process of mixinginto the road profile Therefore the amplitude adjustment isrequired to keep the reference signal 2 in the same amplitudeas themixed signal119910 To reduce the nonlinearity error ampli-tude adjustment is performed for each data segment Theamplitude of reference signal 2119894 after amplitude adjustmentcan be computed as

1198601015840119909119894 = (119860119909119894 minus 119898119909119894) 119889119910119894119889119909119894 + 119898119909119894 (10)

where119860119909119894 denotes the amplitudes of references signal 2119894119898119909119894denotes the mean values of references signal 2119894 119889119909119894 and 119889119910119894

denote the mean square errors (MSE) of references signal 2119894andmixed signal 119910119894 respectivelyThen the adjusted referencesignal 10158402119894 has the same amplitude and distribution as themixed signal 119910119894Step 5 (segment error correction) The true road profile 1199091119894can be computed from

1199091119894 = 119910119894 minus 10158402119894 (11)

Step 6 (smooth connection of segmental data) The correctedsegmented road profile is connected in a time sequenceFor the data overlap part the arithmetic mean is applied toreduce the difference within the data connection Moreoverfor the data connection adaptive correction method basedon local signal baseline adjustment is used to realize smoothconnection of segmental data [23] Then the low frequencyroad profile is corrected and obtained by the above steps

Step 7 (signal merging) After correcting the low frequencyand high frequency road profile the final corrected roadprofile is obtained by combining the low frequency and highfrequency corrected road profile

4 Application

By using the acquisition system shown in Figure 1 all roadsignals had been acquired during the testing vehicle ridingthrough the unstructured proving ground (PG) roads ofBeijing vehicle testing ground which include Ripple TracksBelgian Road Cobblestone Tracks Washboards Body TwistLane and Potholes Road The original collected signalsmainly include road profiles (with frequency of 1 kHz)vibration acceleration (with frequency of 1 kHz) and gyroattitudes (with frequency of 200Hz) Then some preprocess-ing methods including the identification and correction ofabnormal errors the extraction of signal trends and digitalfiltering are implemented to the original collected signals


150mm

Figure 8 The Belgian Road in picture

minus100minus60minus20

2060

100

Hei

ght (

mm

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

5 10 15 20 25 30 35 40 45 500Time (s)

minus100minus50

050

100

Hei

ght (

mm

)

(b)

Figure 9 Measured road profiles of Belgian Road (a) The left wheel (b) the right wheel

[24] The Belgian Road is a typical unstructured road andman-made test road whose characteristics are determinedWhen driving on the Belgian Road the testing vehiclebumps violently which can cause randomvibration of rollingpitching and vertical direction Therefore the Belgian Roadis expressed as an example to verify the validity and accuracyof the error correction algorithm mentioned above in thispaperThe average vehicle speed is about 185 kmh (514ms)during the testing Figure 8 shows the Belgian Road inpicture The average length of the cobbles in the directionof testing vehicle travel is about 150mm Figure 9 givesthe road profiles corresponding to two wheels measured bylaser height sensors Figure 10 presents the vehiclersquos attitudesmeasured by strapdown gyroscope

41 Frequency Division of Measured Road Profiles As men-tioned above the vehiclersquos attitudes mainly affect the lowfrequency band of measured road profiles which is about01 Hzsim20HzTherefore the road profile is divided into highfrequency part (gt3Hz) and low frequency part (01 Hzsim3Hz)by frequency division As shown in Figure 11 is the highfrequency and low frequency road profile of right wheel

42 Acceleration Integration As shown in Figure 12 theintegral velocity and displacement signal are obtained byacceleration integration measured by accelerometer fixed onthe right bracket (Figure 2) The error of measured roadprofile caused by vehicle vibration is mainly concentratedin plusmn05mm (except for the individual) and the impact isabout 2 Due to the relative displacement between thesensor and the road surface measured by laser height sensorthe corrected high frequency road profile can be computedby subtracting integral displacement from the original highfrequency road profile Thus the impact of vehicle vibrationto road profile acquisition is removed

Table 1 Correlation coefficients between road profiles and gyroattitudes

Correlation coefficients Roll 120593 Pitch 120579 Yaw 120574Original signal(119891 gt 01Hz)

Left road profile minus04518 07421 01886Right road profile 05677 07943 01933

High frequency signal(119891 gt 3Hz)Left road profile 00610 00037 minus00114Right road profile minus00531 00069 00184

Low frequency signal(01Hz le 119891 le 3Hz)Left road profile minus04905 07765 02169Right road profile 05919 08201 02181

43 Correlation Analysis As mentioned previously the gyroattitudes have great influence on the road profile measuringHowever the impacts of yaw angle 120574 pitch angle 120579 and rollangle120593 on the road profilemeasuring are different Generallythe impact size between gyro attitudes and road profile canbe analyzed by correlation coefficient 120588119883119884 The correlationcoefficient 120588119883119884 between signals 119883 and 119884 is between minus1 and1 When 120588119883119884 = 0 119883 and 119884 are not relatedWhen |120588119883119884| = 1 119883and 119884 are completely related When |120588119883119884| gt 08 119883 and 119884 arehighly related When |120588119883119884| lt 03 119883 and 119884 are lowly relatedWhen 03 le |120588119883119884| le 08 119883 and 119884 are moderately relatedThegreater the absolute value of 120588119883119884 the higher the correlationbetween 119883 and 119884

To analyze the relation between measured road profileand gyro attitudes the correlation coefficients between themare computed and shown in Table 1 The pitch angle 120579and roll angle 120593 have a high correlation with the measured


minus050

05Ro

ll (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

minus1minus05

005

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus1minus05

005

1

Yaw

(∘)

(c)

Figure 10 Measured vehiclersquos attitudes of Belgian Road (a) The roll angle (b) the pitch angle and (c) the yaw angle

5 10 15 20 25 30 35 40 45 500Time (s)


010203040

Hei

ght (

mm

)

(a)


2060

100

Hei

ght (

mm

)5 10 15 20 25 30 35 40 45 500

Time (s)

(b)

Figure 11 Road profile after frequency division (right wheel) (a) The high frequency part (b) the low frequency part

road profile which verifies the validity of (8) Besides thecorrelation coefficients between gyro attitudes and highfrequency road profile are close to zero This means that theyare basically not related The impact of vehiclersquos attitudes onroad profile measuring is mainly concentrated in the lowfrequency band (le3Hz) which verifies the feasibility of thefrequency division methodTherefore the impact of vehiclersquosattitudes to road profile acquisition can be removed only bycorrecting the low frequency road profile

44 Error Correction As shown in Figure 2 the laser heightsensor and accelerometer are fixed on the bracket in frontof the testing vehicle The distances from the sensors to thevehicle center in each direction are 119909 = 4500mm 119910 =1300mm and 119911 = 1050mm The curves of low frequencyroad profile and pitch angle 120579 are shown in Figure 13According to the comparison the low frequency road profileand pitch angle 120579 have the same change trend which meanshigh correlation between them

Known from Section 3 of the paper the error of vehiclersquosattitudes to measured road profile Δ119911 is computed as (8)Then the error correction is completed according to the stepsmentioned in Section 34 The corrected low frequency roadprofile is explicitly shown in Figure 14 The large wave ofroad profile caused by vehiclersquos attitudes iswell removedThenthe final corrected road profile is obtained by combining lowfrequency road profile after removing attitudesrsquo impact andhigh frequency road profile after removing vibration impactas shown in Figure 15The amplitude of road profile decreasesfrom about 50mm to 20mm which is more consistent withthe real road features of the Belgian Road in vehicle testingground

Table 2 RMS comparison of road profile before and after correc-tion

Road profile RMS (mm)Original Corrected

High frequency 92798 92793Low frequency 353676 150620Final 361104 182179

For comparison the RootMean Square (RMS) of the roadprofiles before and after error correction are calculated andshown in Table 2 By the error correction method raised inthis paper the RMS of road profile reduces from 361104mmto 182179mm Obviously the validity of the error correctionmethod can be verified easily by comparing Figures 9 and 15

To further analyze the validity of the error correctionmethod proposed in the paper the space road spectrum isintroduced for comparison According to standard ISODIS8608 and GBT 7031-2005 the model and grading methodbased on the PSD of the road roughness were worked outThe fitting expression of the road PSD using power functioncan be shown as

119866119889 (119899) = 119866119889 (1198990) ( 1198991198990)minus119882 (12)

where 119899 denotes the space frequency in mminus1 1198990 = 01mminus1denotes the reference space frequency 119866119889(1198990) denotes theroad roughness coefficient which is the value of PSD at 1198990in m3 119882 denotes the frequency index (the general value is2)


minus2000

200

Acc (

mm

s2)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

5 10 15 20 25 30 35 40 45 500Time (s)

minus100

10

Vel (

mm

s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus101

Disp

(mm

)

(c)

Figure 12 Acceleration integration (right wheel) (a) Acceleration (b) integral velocity and (c) integral displacement


2060

100

Hei

ght (

mm

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)


0206

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)

Figure 13 Comparison of low frequency road profile and pitch angle (right wheel) (a) The low frequency road profile (b) the pitch angle

5 10 15 20 25 30 35 40 45 500Time (s)

minus40minus30minus20minus10

010203040

Hei

ght (

mm

)

Figure 14 Low frequency road profile after correction (right wheel)

5 10 15 20 25 30 35 40 45 500Time (s)

minus80

minus60

minus40

minus20

0

20

40

60

80

Hei

ght (

mm

)

Figure 15 Final corrected road profile (right wheel)


CorrectedAcquisitionStandard

EDC

F

AB

Y 2399e minus 006

X 6623

100 10110minus110minus2

10minus810minus710minus610minus510minus410minus310minus210minus1100

Gd

(n) (

m2m

minus1)

minus1)n (m

Figure 16 Space PSD of the road profiles 119866119889(119899)

However the road profile measured in this paper is timedomain displacement 119863(120591) The time domain road profile119863(120591) should transform into space domain displacement119863(119878)based on the distance history 119878(120591) which is obtained byvehicle speed V(120591) integration measured by GPS moduleThen the space domain spectrum 119866119889(119899) of road profile iscalculated through Fast Fourier Transform (FFT) based on119863(119878) as shown in Figure 16

In Figure 16 six standard road spectra from Grade A toGrade F according to ISODIS 8608 have been plotted asreferences The space PSD of corrected and acquisition roadprofile have also been plotted for comparison Besides it isnoted that the peak at a space frequency of 6623 cyclesmetercorresponds to the wavelength of about 150mm which is theaverage length of the cobbles It can be concluded that inthe whole interested frequency range the error correctionmethod raised in the paper shows its advantage by obtaininga more accurate PSD as removing the vehicle vibration andattitudes impacts The proposed method can adapt variousunstructured road profile measuring and correcting andprovides accurate road spectra for road simulation test

5 Conclusions

The acquisition system integrated by laser height sensorsaccelerometers and strapdown gyroscope can be easilymounted and quickly deployed on a testing vehicle to acquirethe road profile for road simulationWith the vibration accel-eration history and the vehiclersquos attitude history respectivelyobtained by the accelerometers and strapdown gyroscopethe measured road profiles can be accurately corrected bythe frequency division and sliding block overlap calibrationmethod The validity of the method has been verified byapplying to measure and correct the road profile of theBelgian Road

However the proposed method is limited by vehiclespeed straight-line driving long-wave of road and so forthVehicle rapid cornering will affect the accuracy of gyroattitude measurement The gyro attitudes frequency band

and road frequency band of measured road profiles will bedifficult to divide due to the improper vehicle speed and long-wave of road Therefore the vehicle speed and testing roadsection should be determined before the testing to improvethe applicability of the proposed method

Though the method proposed in this paper is onlyverified under the Belgian Road situation the method isapplicable for measuring of other kinds of roads after properamendments especially for unstructured roads due to theirlarge range vehicle vibration and attitudes change whichare easy to be measured by sensors Moreover aided withhigh precision GPS receiver for low frequency road profilemeasuring (lt01Hz) the method can also be applicable tothe road profile measuring and Noise Vibration Harshness(NVH) assessment with wider bandwidth and higher accu-racy requirement

Abbreviations

PSD Power spectral densityGPS Global Positioning SystemRTK Real Time KinematicsGCS Geographic coordinate systemBCS Body coordinate systemPG Proving groundRMS Root Mean SquareFFT Fast Fourier TransformNVH Noise Vibration Harshness

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by Weapon and Equipment Explo-ration Research Project (no 7131255)


References

[1] K Reza-Kashyzadeh M J Ostad-Ahmad-Ghorabi and AArghavan ldquoInvestigating the effect of road roughness on auto-motive componentrdquo Engineering Failure Analysis vol 41 no 3pp 96ndash107 2014

[2] P E Uys P S Els and M Thoresson ldquoSuspension settings foroptimal ride comfort of off-road vehicles travelling on roadswith different roughness and speedsrdquo Journal of Terramechanicsvol 44 no 2 pp 163ndash175 2007

[3] G Li and TWang ldquoInfluence of long-waved road roughness onfatigue life of dump truck framerdquo Journal of Vibroengineeringvol 16 no 8 pp 3862ndash3878 2014

[4] M N Tautan S Miclos D Savastru and A Stoica ldquoLongitudi-nal road profile reconstruction from dual laser scansrdquoOptoelec-tronics and Advanced Materials Rapid Communications vol 8no 7 pp 622ndash625 2014

[5] W R Graham F LiuM P F Sutcliffe andM Dale ldquoCharacter-isation and simulation of asphalt road surfacesrdquoWear vol 271no 5-6 pp 734ndash747 2011

[6] V Rouillard ldquoStatistical models for nonstationary and non-Gaussian road vehicle vibrationsrdquo Engineering Letters vol 17no 4 pp 1ndash11 2009

[7] N Cong J Shang and Y Ren ldquoUnstructured road spectrum120572-stable distribution parameters interval estimation and recon-struction based on moving block bootstrap methodrdquo Journal ofMechanical Engineering vol 49 no 4 pp 106ndash113 2013

[8] Y Du C Liu D Wu and S Jiang ldquoMeasurement of internatio-nal roughness index by using Z-axis accelerometers and GPSrdquoMathematical Problems in Engineering vol 2014 Article ID928980 10 pages 2014

[9] P Johannesson K Podgorski and I Rychlik ldquoModelling rou-ghness of road profiles on parallel tracks using roughnessindicatorsrdquo International Journal of Vehicle Design vol 70 no2 pp 1ndash28 2016

[10] D J Wilson B Jacobsen andW Chan ldquoThe effect of road rou-ghness (and test speed) onGripTestermeasurementsrdquo ResearchReport 523 NZ Transport Agency Wellington New Zealand2013

[11] M Yousefzadeh S Azadi and A Soltani ldquoRoad profile esti-mation using neural network algorithmrdquo Journal of MechanicalScience and Technology vol 24 no 3 pp 743ndash754 2010

[12] A Cigada F Mancosu S Manzoni and E Zappa ldquoLaser-tri-angulation device for in-line measurement of road texture atmedium and high speedrdquo Mechanical Systems and Signal Pro-cessing vol 24 no 7 pp 2225ndash2234 2010

[13] P Kumar P Lewis C P Mcelhinney and A A Rahman ldquoAnalgorithm for automated estimation of road roughness frommobile laser scanning datardquo Photogrammetric Record vol 30no 149 pp 30ndash45 2015

[14] N Cong J Shang Y Ren and Y Guo ldquoVehicle unpaved roadresponse spectrum acquisition based on accelerometer andGPSdatardquo Sensors (Switzerland) vol 12 no 8 pp 9951ndash9964 2012

[15] M L Westphalen B L Steward and S Han ldquoTopographicmapping through measurement of vehicle attitude and ele-vationrdquo Transactions of the American Society of AgriculturalEngineers vol 47 no 5 pp 1841ndash1849 2004

[16] V Zuraulis L Levulyte and E Sokolovskij ldquoThe impact of roadroughness on the duration of contact between a vehicle wheeland road surfacerdquo Transport vol 29 no 4 pp 431ndash439 2014

[17] C Gohrle A Schindler A Wagner and O Sawodny ldquoRoadprofile estimation andpreview control for low-bandwidth active

suspension systemsrdquo IEEEASMETransactions onMechatronicsvol 20 no 5 pp 2299ndash2310 2014

[18] A Farah ldquoDigital road profile using kinematic GPSrdquo ArtificialSatellites vol 44 no 3 pp 95ndash101 2010

[19] C Mekik and M Arslanoglu ldquoInvestigation on accuracies ofreal time kinematic GPS for GIS applicationsrdquo Remote Sensingvol 1 no 1 pp 22ndash35 2009

[20] B R Davis and A G Thompson ldquoPower spectral density ofroad profilesrdquo Vehicle System Dynamics vol 35 no 6 pp 409ndash415 2001

[21] SWang ldquoResearch on laser Gyro strapdown attitude amp headingroad-spectrum measurement systemrdquo Doctor Paper NationalUniversity of Defense Technology Changsha China 2006

[22] T J Ulrych M D Sacchi and J M Graul ldquoSignal and noiseseparation art and sciencerdquoGeophysics vol 64 no 5 pp 1648ndash1656 1999

[23] H M Duan Y Ma F Shi K B Zhang and F Xie ldquoSmoothconnection method of segment test data in road surfaceprofile measurementrdquo in Proceedings of the 4th InternationalConference on Machine Vision (ICMV rsquo11) pp 83491ndash83497Singapore 2011

[24] H-M Duan F Xie K-B Zhang Y Ma and F Shi ldquoMethods ofsignal pre-processing with massive road surface measurementdatardquo Journal of Vibration amp Shock vol 30 no 8 pp 101ndash1172011

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Laser height sensor Accelerometers

GPS

Camera

Gyroscope Displacement sensor

SoMat eDAQ

Figure 1 Road profile acquisition system of the vehicle

depends on the relative displacement between the sensorand the road surface measured by the sensor (laser infraredor ultrasonic) mounted on the vehicle The obtained finaldisplacement could represent the road profile only when thevehicle is not excessively interrupted and maintains steadywhile driving through the road Obviously this hypothesis isnot true for unstructured roads because of the bumpiness ofthe unstructured road which result in severe vibration andattitudesrsquo change of the vehicle and the major variation in thevehicle speed [15 16]

To solve the problem a laser measuring system forthe unstructured road is proposed to realize the fast mea-surement of the road profiles vibration acceleration andgyro attitudes of the vehicle To improve the accuracy ofthe measured road profiles an error correction methodbased on measured acceleration and gyro attitudes data isdiscussed in detail Aiming at the characteristic that the PSDof vehicle attitudes concentrates in the low frequency bandthe measured road profile can be divided into high frequencypart and low frequency part by the method of frequencydivision Then the vibration error of the measured roadprofile is corrected by displacement data obtained throughtwo times integration of measured acceleration data Theattitude error of the measured road profile is correctedby signal separation based on sliding block overlap andcorrelation analysis The proposed acquisition system hasbeen used in the unstructured road profile measurement ofvehicle testing ground and its validity has been evaluated inthe paper

2 Laser Road Profile Acquisition System

For the reliability simulation of the vehicle the 2D profilecurve in the direction of the vehicle wheelsrsquo orbit is generallyused as the research object A road profile acquisition systemis shown in Figure 1 which integrates the gyro attitudesGPS vibration acceleration and displacement measuringThe system can be used tomeasure road profiles of structuredroads (asphalt road expressway etc) and unstructured roads

(gravel road cross-country path strengthen-road etc) Thetest vehicle is an 8 times 8 wheeled vehicle with independentsuspension [17] which could reduce the impact of the roadprofiles to the vehicle and improve ride comfort Howeverthe vehiclersquos attitude change is inevitable when driving on theunstructured roads Generally the frequencies of sensors arehigh enough for the acquisition The sampling frequenciesof acceleration and road profile data are 1 kHz while thesampling frequency of gyro attitudes is 200Hz

The road profile acquisition system consists of a HBMSoMat eDAQ System (data acquisition and record) a RMSStrapdown Platform System (mounted in the center of thevehicle andmeasuring vehiclersquos attitudes change) two groupsof Datron HF-500C laser height sensors (measuring the rel-ative displacement between sensor and road surface ie theroad profile) ten groups of ENDEVCO 7596 accelerometers(measuring the vibration acceleration of laser sensors and thespindles of the vehicle) some groups of cable displacementsensors (measuring displacement of the spindles) an ordi-naryGPSmodule (measuring the longitude latitude altitudeand speed of the vehicle) an AXIS P1311 webcam (recordingvideo information of testing roads) and so forth As shownin Figure 2 the laser height sensors and accelerometers arecounted on the brackets that are fixed on both sides of thefront of the vehicle

3 Error Correction of Road Profiles

The road profile includes the large-scale signal that is fromlow frequency to high frequency the laser height sensorcould barely measure the signals of all frequency bands Inaddition the devices of the acquisition system are fixed on thevehicle the road profilesmeasured by laser sensors aremostlyhigh frequency and short wavelength signals (the wavelengthis less than the wheelbase of testing vehicle) Therefore themeasuring frequency band is divided into several sectionsFor the low frequency and long wavelength part of roadprofile that the laser sensor cannot measure (the frequencyis generally lower than 01Hz) a Global Positioning System


Datron HF-500C

Laser height sensor

Left bracket






119891119871 = V1205822

119891119867 = V1205821

(1)


119891119887 lt 119891119889 lt 119891119871 = V1205822 (2)






119900119909119905119910119905119911119905 120574997888997888rarr119900119911119905 11990011990910158401199101015840119911119905 120579997888997888rarr1199001199101015840

11990011990911988711991010158401199111015840 120593997888997888rarr119900119909119887 119900119909119887119910119887119911119887 (3)










Gyro attitudes

Band-pass filter





Resampling(200 Hz)


(01Hz le f le 3Hz)



[[[[[

119909119905119910119905119911119905

]]]]]

= C119905119887[[[[[

119909119887119910119887119911119887

]]]]]

(4)



C119905119887 = C119911120574C119910120579C119909120593 = [[[[[


0 0 1]]]]]

[[[[[

cos 120579 0 sin 1205790 1 0

minus sin 120579 0 cos 120579]]]]]

[[[[[


]]]]]

=[[[[[[[



]]]]]]]

(5)









119909119887119910119887119911119887

]]]

(6)


119911119905 = minus120579 sdot 119909119887 + 120593 sdot 119910119887 + 119911119887 (7)





xb x998400xt

120579

120579

120574

120574

yt

y998400

yb

120593

120593

o

zt

z998400

zb







Signalseparation


Road profile

Gyro attitude

T1x1

x2x2

T2

H1

y = x1 + x2

x2 = A2x2(n + m2)x1(n)

x2(n)


i minus 1i

i + 1

1 s 1 s 5 s 1 s 1 s 5 s 1 s 1 s 5 s 1 s 1 s




119873 sdot 1199051 + (119873 minus 1) sdot 1199052 = 119879 (9)



1198601015840119909119894 = (119860119909119894 minus 119898119909119894) 119889119910119894119889119909119894 + 119898119909119894 (10)



1199091119894 = 119910119894 minus 10158402119894 (11)



4 Application



150mm



2060

100

Hei

ght (

mm

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

5 10 15 20 25 30 35 40 45 500Time (s)

minus100minus50

050

100

Hei

ght (

mm

)

(b)













minus050

05Ro

ll (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

minus1minus05

005

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus1minus05

005

1

Yaw

(∘)

(c)


5 10 15 20 25 30 35 40 45 500Time (s)


010203040

Hei

ght (

mm

)

(a)


2060

100

Hei

ght (

mm

)5 10 15 20 25 30 35 40 45 500

Time (s)

(b)










119866119889 (119899) = 119866119889 (1198990) ( 1198991198990)minus119882 (12)



minus2000

200

Acc (

mm

s2)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

5 10 15 20 25 30 35 40 45 500Time (s)

minus100

10

Vel (

mm

s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus101

Disp

(mm

)

(c)



2060

100

Hei

ght (

mm

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)


0206

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)


5 10 15 20 25 30 35 40 45 500Time (s)


010203040

Hei

ght (

mm

)


5 10 15 20 25 30 35 40 45 500Time (s)

minus80

minus60

minus40

minus20

0

20

40

60

80

Hei

ght (

mm

)




EDC

F

AB

Y 2399e minus 006

X 6623



Gd

(n) (

m2m

minus1)

minus1)n (m




5 Conclusions





Abbreviations


Competing Interests


Acknowledgments



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Datron HF-500C

Laser height sensor

Left bracket






119891119871 = V1205822

119891119867 = V1205821

(1)


119891119887 lt 119891119889 lt 119891119871 = V1205822 (2)






119900119909119905119910119905119911119905 120574997888997888rarr119900119911119905 11990011990910158401199101015840119911119905 120579997888997888rarr1199001199101015840

11990011990911988711991010158401199111015840 120593997888997888rarr119900119909119887 119900119909119887119910119887119911119887 (3)










Gyro attitudes

Band-pass filter





Resampling(200 Hz)


(01Hz le f le 3Hz)



[[[[[

119909119905119910119905119911119905

]]]]]

= C119905119887[[[[[

119909119887119910119887119911119887

]]]]]

(4)



C119905119887 = C119911120574C119910120579C119909120593 = [[[[[


0 0 1]]]]]

[[[[[

cos 120579 0 sin 1205790 1 0

minus sin 120579 0 cos 120579]]]]]

[[[[[


]]]]]

=[[[[[[[



]]]]]]]

(5)









119909119887119910119887119911119887

]]]

(6)


119911119905 = minus120579 sdot 119909119887 + 120593 sdot 119910119887 + 119911119887 (7)





xb x998400xt

120579

120579

120574

120574

yt

y998400

yb

120593

120593

o

zt

z998400

zb







Signalseparation


Road profile

Gyro attitude

T1x1

x2x2

T2

H1

y = x1 + x2

x2 = A2x2(n + m2)x1(n)

x2(n)


i minus 1i

i + 1

1 s 1 s 5 s 1 s 1 s 5 s 1 s 1 s 5 s 1 s 1 s




119873 sdot 1199051 + (119873 minus 1) sdot 1199052 = 119879 (9)



1198601015840119909119894 = (119860119909119894 minus 119898119909119894) 119889119910119894119889119909119894 + 119898119909119894 (10)



1199091119894 = 119910119894 minus 10158402119894 (11)



4 Application



150mm



2060

100

Hei

ght (

mm

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

5 10 15 20 25 30 35 40 45 500Time (s)

minus100minus50

050

100

Hei

ght (

mm

)

(b)













minus050

05Ro

ll (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

minus1minus05

005

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus1minus05

005

1

Yaw

(∘)

(c)


5 10 15 20 25 30 35 40 45 500Time (s)


010203040

Hei

ght (

mm

)

(a)


2060

100

Hei

ght (

mm

)5 10 15 20 25 30 35 40 45 500

Time (s)

(b)










119866119889 (119899) = 119866119889 (1198990) ( 1198991198990)minus119882 (12)



minus2000

200

Acc (

mm

s2)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

5 10 15 20 25 30 35 40 45 500Time (s)

minus100

10

Vel (

mm

s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus101

Disp

(mm

)

(c)



2060

100

Hei

ght (

mm

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)


0206

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)


5 10 15 20 25 30 35 40 45 500Time (s)


010203040

Hei

ght (

mm

)


5 10 15 20 25 30 35 40 45 500Time (s)

minus80

minus60

minus40

minus20

0

20

40

60

80

Hei

ght (

mm

)




EDC

F

AB

Y 2399e minus 006

X 6623



Gd

(n) (

m2m

minus1)

minus1)n (m




5 Conclusions





Abbreviations


Competing Interests


Acknowledgments



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


















Gyro attitudes

Band-pass filter





Resampling(200 Hz)


(01Hz le f le 3Hz)



[[[[[

119909119905119910119905119911119905

]]]]]

= C119905119887[[[[[

119909119887119910119887119911119887

]]]]]

(4)



C119905119887 = C119911120574C119910120579C119909120593 = [[[[[


0 0 1]]]]]

[[[[[

cos 120579 0 sin 1205790 1 0

minus sin 120579 0 cos 120579]]]]]

[[[[[


]]]]]

=[[[[[[[



]]]]]]]

(5)









119909119887119910119887119911119887

]]]

(6)


119911119905 = minus120579 sdot 119909119887 + 120593 sdot 119910119887 + 119911119887 (7)





xb x998400xt

120579

120579

120574

120574

yt

y998400

yb

120593

120593

o

zt

z998400

zb







Signalseparation


Road profile

Gyro attitude

T1x1

x2x2

T2

H1

y = x1 + x2

x2 = A2x2(n + m2)x1(n)

x2(n)


i minus 1i

i + 1

1 s 1 s 5 s 1 s 1 s 5 s 1 s 1 s 5 s 1 s 1 s




119873 sdot 1199051 + (119873 minus 1) sdot 1199052 = 119879 (9)



1198601015840119909119894 = (119860119909119894 minus 119898119909119894) 119889119910119894119889119909119894 + 119898119909119894 (10)



1199091119894 = 119910119894 minus 10158402119894 (11)



4 Application



150mm



2060

100

Hei

ght (

mm

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

5 10 15 20 25 30 35 40 45 500Time (s)

minus100minus50

050

100

Hei

ght (

mm

)

(b)













minus050

05Ro

ll (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

minus1minus05

005

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus1minus05

005

1

Yaw

(∘)

(c)


5 10 15 20 25 30 35 40 45 500Time (s)


010203040

Hei

ght (

mm

)

(a)


2060

100

Hei

ght (

mm

)5 10 15 20 25 30 35 40 45 500

Time (s)

(b)










119866119889 (119899) = 119866119889 (1198990) ( 1198991198990)minus119882 (12)



minus2000

200

Acc (

mm

s2)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

5 10 15 20 25 30 35 40 45 500Time (s)

minus100

10

Vel (

mm

s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus101

Disp

(mm

)

(c)



2060

100

Hei

ght (

mm

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)


0206

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)


5 10 15 20 25 30 35 40 45 500Time (s)


010203040

Hei

ght (

mm

)


5 10 15 20 25 30 35 40 45 500Time (s)

minus80

minus60

minus40

minus20

0

20

40

60

80

Hei

ght (

mm

)




EDC

F

AB

Y 2399e minus 006

X 6623



Gd

(n) (

m2m

minus1)

minus1)n (m




5 Conclusions





Abbreviations


Competing Interests


Acknowledgments



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

















119909119887119910119887119911119887

]]]

(6)


119911119905 = minus120579 sdot 119909119887 + 120593 sdot 119910119887 + 119911119887 (7)





xb x998400xt

120579

120579

120574

120574

yt

y998400

yb

120593

120593

o

zt

z998400

zb







Signalseparation


Road profile

Gyro attitude

T1x1

x2x2

T2

H1

y = x1 + x2

x2 = A2x2(n + m2)x1(n)

x2(n)


i minus 1i

i + 1

1 s 1 s 5 s 1 s 1 s 5 s 1 s 1 s 5 s 1 s 1 s




119873 sdot 1199051 + (119873 minus 1) sdot 1199052 = 119879 (9)



1198601015840119909119894 = (119860119909119894 minus 119898119909119894) 119889119910119894119889119909119894 + 119898119909119894 (10)



1199091119894 = 119910119894 minus 10158402119894 (11)



4 Application



150mm



2060

100

Hei

ght (

mm

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

5 10 15 20 25 30 35 40 45 500Time (s)

minus100minus50

050

100

Hei

ght (

mm

)

(b)













minus050

05Ro

ll (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

minus1minus05

005

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus1minus05

005

1

Yaw

(∘)

(c)


5 10 15 20 25 30 35 40 45 500Time (s)


010203040

Hei

ght (

mm

)

(a)


2060

100

Hei

ght (

mm

)5 10 15 20 25 30 35 40 45 500

Time (s)

(b)










119866119889 (119899) = 119866119889 (1198990) ( 1198991198990)minus119882 (12)



minus2000

200

Acc (

mm

s2)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

5 10 15 20 25 30 35 40 45 500Time (s)

minus100

10

Vel (

mm

s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus101

Disp

(mm

)

(c)



2060

100

Hei

ght (

mm

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)


0206

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)


5 10 15 20 25 30 35 40 45 500Time (s)


010203040

Hei

ght (

mm

)


5 10 15 20 25 30 35 40 45 500Time (s)

minus80

minus60

minus40

minus20

0

20

40

60

80

Hei

ght (

mm

)




EDC

F

AB

Y 2399e minus 006

X 6623



Gd

(n) (

m2m

minus1)

minus1)n (m




5 Conclusions





Abbreviations


Competing Interests


Acknowledgments



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Signalseparation


Road profile

Gyro attitude

T1x1

x2x2

T2

H1

y = x1 + x2

x2 = A2x2(n + m2)x1(n)

x2(n)


i minus 1i

i + 1

1 s 1 s 5 s 1 s 1 s 5 s 1 s 1 s 5 s 1 s 1 s




119873 sdot 1199051 + (119873 minus 1) sdot 1199052 = 119879 (9)



1198601015840119909119894 = (119860119909119894 minus 119898119909119894) 119889119910119894119889119909119894 + 119898119909119894 (10)



1199091119894 = 119910119894 minus 10158402119894 (11)



4 Application



150mm



2060

100

Hei

ght (

mm

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

5 10 15 20 25 30 35 40 45 500Time (s)

minus100minus50

050

100

Hei

ght (

mm

)

(b)













minus050

05Ro

ll (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

minus1minus05

005

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus1minus05

005

1

Yaw

(∘)

(c)


5 10 15 20 25 30 35 40 45 500Time (s)


010203040

Hei

ght (

mm

)

(a)


2060

100

Hei

ght (

mm

)5 10 15 20 25 30 35 40 45 500

Time (s)

(b)










119866119889 (119899) = 119866119889 (1198990) ( 1198991198990)minus119882 (12)



minus2000

200

Acc (

mm

s2)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

5 10 15 20 25 30 35 40 45 500Time (s)

minus100

10

Vel (

mm

s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus101

Disp

(mm

)

(c)



2060

100

Hei

ght (

mm

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)


0206

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)


5 10 15 20 25 30 35 40 45 500Time (s)


010203040

Hei

ght (

mm

)


5 10 15 20 25 30 35 40 45 500Time (s)

minus80

minus60

minus40

minus20

0

20

40

60

80

Hei

ght (

mm

)




EDC

F

AB

Y 2399e minus 006

X 6623



Gd

(n) (

m2m

minus1)

minus1)n (m




5 Conclusions





Abbreviations


Competing Interests


Acknowledgments



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










150mm



2060

100

Hei

ght (

mm

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

5 10 15 20 25 30 35 40 45 500Time (s)

minus100minus50

050

100

Hei

ght (

mm

)

(b)













minus050

05Ro

ll (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

minus1minus05

005

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus1minus05

005

1

Yaw

(∘)

(c)


5 10 15 20 25 30 35 40 45 500Time (s)


010203040

Hei

ght (

mm

)

(a)


2060

100

Hei

ght (

mm

)5 10 15 20 25 30 35 40 45 500

Time (s)

(b)










119866119889 (119899) = 119866119889 (1198990) ( 1198991198990)minus119882 (12)



minus2000

200

Acc (

mm

s2)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

5 10 15 20 25 30 35 40 45 500Time (s)

minus100

10

Vel (

mm

s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus101

Disp

(mm

)

(c)



2060

100

Hei

ght (

mm

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)


0206

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)


5 10 15 20 25 30 35 40 45 500Time (s)


010203040

Hei

ght (

mm

)


5 10 15 20 25 30 35 40 45 500Time (s)

minus80

minus60

minus40

minus20

0

20

40

60

80

Hei

ght (

mm

)




EDC

F

AB

Y 2399e minus 006

X 6623



Gd

(n) (

m2m

minus1)

minus1)n (m




5 Conclusions





Abbreviations


Competing Interests


Acknowledgments



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










minus050

05Ro

ll (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

minus1minus05

005

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus1minus05

005

1

Yaw

(∘)

(c)


5 10 15 20 25 30 35 40 45 500Time (s)


010203040

Hei

ght (

mm

)

(a)


2060

100

Hei

ght (

mm

)5 10 15 20 25 30 35 40 45 500

Time (s)

(b)










119866119889 (119899) = 119866119889 (1198990) ( 1198991198990)minus119882 (12)



minus2000

200

Acc (

mm

s2)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

5 10 15 20 25 30 35 40 45 500Time (s)

minus100

10

Vel (

mm

s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus101

Disp

(mm

)

(c)



2060

100

Hei

ght (

mm

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)


0206

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)


5 10 15 20 25 30 35 40 45 500Time (s)


010203040

Hei

ght (

mm

)


5 10 15 20 25 30 35 40 45 500Time (s)

minus80

minus60

minus40

minus20

0

20

40

60

80

Hei

ght (

mm

)




EDC

F

AB

Y 2399e minus 006

X 6623



Gd

(n) (

m2m

minus1)

minus1)n (m




5 Conclusions





Abbreviations


Competing Interests


Acknowledgments



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










minus2000

200

Acc (

mm

s2)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)

5 10 15 20 25 30 35 40 45 500Time (s)

minus100

10

Vel (

mm

s)

(b)

5 10 15 20 25 30 35 40 45 500Time (s)

minus101

Disp

(mm

)

(c)



2060

100

Hei

ght (

mm

)

5 10 15 20 25 30 35 40 45 500Time (s)

(a)


0206

1

Pitc

h (∘

)

5 10 15 20 25 30 35 40 45 500Time (s)

(b)


5 10 15 20 25 30 35 40 45 500Time (s)


010203040

Hei

ght (

mm

)


5 10 15 20 25 30 35 40 45 500Time (s)

minus80

minus60

minus40

minus20

0

20

40

60

80

Hei

ght (

mm

)




EDC

F

AB

Y 2399e minus 006

X 6623



Gd

(n) (

m2m

minus1)

minus1)n (m




5 Conclusions





Abbreviations


Competing Interests


Acknowledgments



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











EDC

F

AB

Y 2399e minus 006

X 6623



Gd

(n) (

m2m

minus1)

minus1)n (m




5 Conclusions





Abbreviations


Competing Interests


Acknowledgments



References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










References

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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