41 3 Vol.41,No.3 2012 6 ActaGeodaeticaetCartographicaSinica Jun.,2012 WANG Tao,ZHANG Yongsheng,ZHANG Yan,etal.AirborneLinearCCDSensorGeometricCalibrationBasedonSel-calibration[J]. ActaGeodaeticaetCartographicaSinica,2012,41(3):393-400.(. CCD [J].,2012,41(3):393-400.) CCD, 450052 AirborneLinearCCDSensorGeometricCalibrationBasedonSel-calibration WANGTao,ZHANGYongsheng,ZHANGYan,FANDazhao InstituteoSurveyingandMapping,InormationEngineeringUniversity,Zhengzhou450052,China Abstract:Thesel-calibrationbundleblockadjustmenttechniquebasedontheadditionalparametersisappliedto theairbornelinearccdsensorgeometriccalibration.takingtheads40sensororexample,theintegratedsensor imagingrelationshipisanalyzedirstly,andthenthegpsobservationsmodel,theimu misalignmentanglemodel areintroduced.thesel-calibrationbundleblockadjustmentmodelorthecalibrationissetup.uponthedetailed investigationontheimagingerorproperties,thesuitablesensorcalibrationparametermodelisbuiltup.finaly theads40dataonthetestieldisusedorthecalibrationexperiments.experimentalresultsprovethatthegeometric calibrationmethodiscorectandeective,whichcansigniicantlyimprovethemeasuringaccuracyandthereliability. Keywords:airbornelinearCCDsensor;sel-calibrationbundleblockadjustment;ADS40;geometriccalibration : CCD ADS40,, GPS IMU ; CCD ; ADS40, : CCD ; ;ADS40; :P237 :A :1001-1595(2012)03-0393-08 : (41001262); (K201004); (Y201001) 1 CCD ADS40(airbornedigitalsensor) EuroSDR, CCD, POS(positioning and orientationsystem), [2-9] ADS40, [10] Leica [1] CCD, POS Leica ; [11 16] [17] ; ADS40 ORIMA,, CCD,
394 June2012Vol.41No.3AGCS htp: xb.sinomaps.com ADS40 熿 X A 燄熿 X s 燄熿 u燄, GPS IMU Y A = Y s +R v, 燀 ZA 燅燀 Zs 燅燀 w燅, ADS40 (1) 2 ADS40 ADS40 GPS/ IMU ( 1) 2 GPS GPS IMU Fig.2 Positioningprincipleoaerialsystem withgps IMU ( X b,y b,z b ) ( X c,y c,z c ), GPS, GPS, [19] GPS, GPS ; IMU, (1), IMU 熿 X A 燄熿 X s 燄熿 u燄熿 a X 燄熿 b X 燄 GPS IMU Y A = Y s +R v + a Y +(t-t 0 ) b Y IMU 燀 ZA 燅燀 Zs 燅燀 w燅燀 az 燅燀 bz 燅 IMU GPS (2),GPS,t 0 ;a X a y a Z b X b y b Z GPS ;IMU, u ν w GPS, CCD 熿 v XA 燄 GPS IMU 熿 Δφ 燄熿 ΔX s 燄熿 Δu 燄 v YA =A Δω + ΔY s +R Δv + 燀 v Z A 燅燀 Δk 燅燀 ΔZ s 燅燀 Δw 燅 熿 Δa X 燄熿 Δb X 燄 Δa Y +(t-t 0 ) Δb Y - 燀 Δa Z 燅燀 Δb Z 燅 燀 ZA 燅燀 ZA 燅 1 GPS/IMU,A GPS X A Y A Z A Fig.1 Aerialphotographysystem equipped with GPS/IMU 熿 X A 燄 φ ω κ, Y A [18] 2.1 GPS 燀 ZA 燅 2 GPS A (2) GPS S-uvw (u,v,w), V GPS= 珚 At+Rr+Dd-L GPS (4) GPS,V GPS 熿 X A Y A 燄熿 + X A Y A 燄 (3)
3 : CCD 395 GPS ;t,δx Δy ;r ;d ; 珚 A t ;R r ;D d ;L GPS GPS V X =Bd+At+Ca-L X V C=E dd-l C P X P C (9) V A=E aa-l A PA 烎 [20] 2.2 IMU,V X V C V A (ω, φ,κ) ;d = R AT,IMU (Ω,Φ,Κ) [ ΔX ΔY ΔZ ] R IMU,IMU (e x,e y,e z ) ;t= [ Δφ Δω Δκ ΔX s ΔY s ΔZ ] T s R MIS R AT R IMU R MIS ; a = [ a 1 a 2 a 3 ] ;A R AT=R IMUR MIS (5) B C t d a ;E d E a R IMU=R ATR T MIS (6) ;L X L C L A ; ω-φ-κ P X P C P A Ω Φ 3.2 (Ω,Φ,Κ) POS Ω = -arctan(r 23 /r 33 ) Φ= arcsin(r 13 ) (7) Κ = nπ-arctan(r 12 /r 11 ) 烎, K r 12 r 11 n (7) IMU 3,,,, GPS/IMU GPS/IMU, GPS, (9) V X =Bd+At+Ca-L X P X V C=E dd-l C P C, (10) V A=E aa-l A P A V GPS= 珚 At+Rr+Dd-L GPS PGPS 烎,r ;d 3.1 ; 珚 A R D GPS t r d GPS x+δx= - a1 X-X r ; IMU s +b 1 ( Y-Y s ) +c 1 ( Z-Z s ) a 3 ( X-X s ) +b 3 ( Y-Y s ) +c 3 ( Z-Z s ) (7), y+δy=, k 90 (7) - a2 X-X s +b 2 ( Y-Y s ) +c 2 ( Z-Z s ) r 11 0, r a 3 ( X-X s ) +b 3 ( Y-Y s ) +c 3 ( Z-Z s) 烎, (8)
396 June2012Vol.41No.3AGCS htp: xb.sinomaps.com GPS IMU IMU a ω 熿 ω燄熿 ωimu 燄熿燄熿燄 φ = φ IMU + a φ + b φ (t-t 0 ) (11) 燀 κ 燅燀 κimu 燅燀 aκ 燅燀 bκ 燅,(a ω,a φ,a κ,b ω,b φ,b κ ) IMU (10) (11), b ω V X =Bd+At+Ca-L X V C=E dd-l C V A=E aa-l A P X P C P A V GPS= 珚 At+Rr+Dd-L GPS V INS= 珚 A It+Qq+Ee-L INS P GPS P INS 烎,q ;e ; 珚 A I Q E IMU t q e 4 CCD 3 CCD Fig.3 TranslationandrotationothreelinearCCDin ocalplane CCD, CCD,,CCD CCD 3 CCD p() r =r 2 p 2 2 槡 1+p 2 (14) x y,,, Δx d=p1 ( r 2 +2 珚 x 2 ) 珚 +2p2 x 珔 y珚 4.1 Δyd=2p1 x 珔 y+p2 r 2 +2 珔 (15) 2 ( y ) 烎,p1 p2, ( x p,y p ) x y Δx p Δyp Δx=k 1r 3 +k 2r 5 +k 3r 7 + (12), Δ, x y, dx =- Δ ( x-x ) p Δx r=k 1 珚 xr 2 +k 2 珚 xr 4 +k 3 珚 xr 6 + Δyr=k 1 珔 yr 2 +k 2 珔 yr 4 +k 3 珔 (13) yr 6 + 烎 dy=- Δ (16) ( y-y p ) 烎, x= 珚 ( x-x 0 ), y= 珔 ( x-y 0 ),r 2 = 珚 x 2 + 珔 y 2, p, ( x 0,y 0 ) ;k 1 k 2 k 3
3 : CCD 397 Δx =Δx p - Δ x+ 珚 ( k 1r 2 +k 2r 4 +k 3r 6 ) x+ 珚 p1 ( r 2 +2 珚 x 2 ) 珚 +2p2 x 珔 y Δy =Δyp- Δ y+ 珔 ( k 1r 2 +k 2r 4 +k 3r 6 ) y+ 珔 珚 2p1 x 珔 y+p2 r 2 +2 珔 2 ( y ) 烎 (17) r 2 = ( x-x p ) 2 2 + ( y-y p ) x= 珚 ( x-x p ) y= 珔 ( y-y p ) (18) 4.2 CCD 4 CCD,x,y CCD ( ),N p CCD ( px,p y ), dx ( p,dy p )x y 7 CCD ( dpx,dp y ) y N p,x Fig.7 Figureosinglelenswithmulti-CCD 1 dpx=dx p (19) dpy=n p dy } x 4 CCD Δy =(Δyp+dyc)- Δ y+ 珔 Fig.4 LinearCCDpixelsizechangeeect ( k 1r 2 +k 2r 4 +k 3r 6 ) 珔珚 y+2p1 x y+ 珔 CCD p2 ( r 2 +2 珔 y 2 ) + 珔 ys y x y dx c dyc, 5 Fig.5 5 CCD y x TranslationolinearCCDalongxaxisandy axisrespectively dx θ= 珔 ysinθ (20) dyθ= y- 珔 ycosθ= 珔珔 y ( 1-cos θ ) 烎 dyθ x 6 CCD Fig.6 RotationolinearCCDinocalplane CCD, y p, CCD y x Δx = ( Δx p +dx c )- Δ x+ 珚 ( k 1r 2 +k 2r 4 +k 3r 6 ) 珚 x+p1 ( r 2 +2 珚 x ) 2p2 珚 x 珔 y+ 珔 ysinθ 2 + 烎 (21),dx c dyc Δx p Δyp ;θ CCD ;s y ADS40 ( 7) CCDj,j=1,2, ( 3 ),dx cj dycj Δx pj Δypj θj s yj, CCD θ,dx θ dyθ CCD Δx j =Δx pj - Δ x+ 珚 ( k 1r 2 +k 2r 4 +k 3r 6 ) x+ 珚, 6, p1 ( r 2 +2 珚 x 2 ) 珚 +2p2 x y+ 珔珔 ysinθj Δy j =Δypj- Δ y+ 珔 ( k 1r 2 +k 2r 4 +k 3r ) 珚 2p1 x 珔 y+p2 ( r 2 +2 珔 y 2 ) + 珔 ys yj 6 y+ 珔 烎 (22)
398 June2012Vol.41No.3AGCS htp: xb.sinomaps.com 5 5.1 2009 8 Δx Δy ADS40 3, cama camb 600m 1000m 5.3 3000m, GSD 0.06m 0.10m 0.30m A B C A B C A 4 2, 1 67 ; B 4 2 43 ; C 7 4, A B 71 2 5.2 ADS40 5.4 1 A B (22) 1: A B C, ( cam0) POS,, ; 2 cam0 cama 3:, (22) 1: cama camb cam0 2: cama camb cam0, camb 3 ; 2: A B 8 GSD ; 3, ; cama camb A B 1 A B Tab.1 BundleadjustmentresultsodataAandBsets m GCP X Y Z GCP X Y Z 3 0.108 0.166 0.163 3 0.032 0.043 0.051 A B 5 0.067 0.158 0.126 5 0.024 0.039 0.047 9 0.064 0.160 0.125 9 0.023 0.034 0.046 3 0.089 0.207 0.221 3 0.039 0.062 0.082 5 0.084 0.198 0.211 5 0.037 0.055 0.077 9 0.087 0.126 0.205 9 0.036 0.045 0.074 2 A B C Tab.2 DirectgeopositioningresultsodataA,BandCsets A B C X Y Z X Y Z X Y Z cam0 0.235 0.200 0.349 0.304 0.417 0.523 0.814 0.763 1.258 cama 0.164 0.121 0.132 0.146 0.244 0.201 0.249 0.354 0.723 camb 0.155 0.102 0.128 0.137 0.242 0.190 0.256 0.322 0.686
3 : CCD 399 3 A B Tab.3 NormalblockadjustmentresultsocalibrateddataAandBsets m A B cama camb GCP GCP X Y Z X Y Z 3 0.037 0.051 0.062 3 0.044 0.069 0.101 5 0.028 0.041 0.052 5 0.041 0.062 0.089 9 0.023 0.034 0.053 9 0.042 0.053 0.089 3 0.035 0.047 0.055 3 0.042 0.064 0.091 5 0.029 0.038 0.051 5 0.039 0.056 0.087 9 0.021 0.034 0.048 9 0.037 0.044 0.089 Fig.8 8 A B C DirectgeopositioningresultsodataA,B andcsets : (1)ADS40, X (5) 2.71~3.91 GSD,Y 2.54~ 4.17 GSD,Z 4.19~5.78 GSD :, ; GPS IMU,ADS40 (2) 1, CCD,5, ;, ADS40 9, A X Y Z 1.0 2.6 2.1 GSD 0.4 0.6 0.8 GSD B 0.9 1.3 2.0 GSD 0.4 0.5 0.7 GSD Y ;,, (3) cama camb A B,,,camB cama Z 3.6 GSD, 1.8 GSD, X 1.2~1.8 GSD,Y 1.3~1.7 GSD (4) cama camb A B, cam0,, ADS40 POS ;,, [1] SANDAU R,BRAUNECKERB,DRIESCHER H,etal. Design Principles othe LH Systems ADS40 Airborne DigitalSensor[C] ProceedingsoInternationalArchives o Photogrammetry and Remote Sensing. Amsterdam: IAPRS,2000:258-265. [2] CRAMER M.A EuropeanNetworkonCameraCalibration
400 June2012Vol.41No.3AGCS htp: xb.sinomaps.com [J].PhotogrammetricEngineeringand RemoteSensing, 2004,70 (12):1328-1334. [3] CRAM ER M.Calibrationand ValidationoDigital AirborneCameras [C] ProceedingsotheInternational Calibration and Orientation Workshop EuroCOW 2006. Casteldeels:[s.n.],2006. [4] CRAMER M.TheEuroSDR ApproachonDigitalAirborne CameraCalibrationandCertiication [C] Proceedingso theinternationalarchivesothephotogrammetry,remote SensingandSpatialInormationSciences.Beijing:IAPRS, 2008:1753-1758. [5] MOSTAFA M R.DigitalMulti-sensorSystems-calibration andperormance Analysis[C] Proceedingso OEEPE WorkshopIntegrated Sensor Orientation.Hannover:[s. n.],2001:17-18. [6] PACEY RE,WALKER AS,SCHEIDT M.Calibrationo AnalogueandDigitalAirborneSensorsatLH Systems[C] Proceedingsothe1999ASPRSAnnualConerence.Port- land:[s.n.],1999:950-956. [7] PETRIE G A, WALKER S.Airborne DigitalImaging Technology:aNew Overview [J].ThePhotogrammetric Record,2007,22(119):203-225. [8] HONKAVARRA E,AHOKAS E,HYYPPA J,et al.geometrictestfieldcalibrationodigitalphotogram- metricsensors[j].isprsjournalophotogrammetryand RemoteSensing,2006,60(6):387-399. [9] DOERSTELC,ZEITLER W.GeometricCalibrationothe DMC:MethodandResults[C] ProceedingsoPecora15/ LandSateliteInormationIV/ISPRSCommissionI/FIEOS 2002Conerence.[S.l.]:IAPRS,2002:324-333. [10] TEMPELMANN U,HINSKEN L,RECKE U.ADS40 Calibrationand VeriicationProcess[C] Proceedingso Optical3D MeasurementTechniquesConerence.Zurich: [s.n.],2003:48-54. [11] KOCAMANS,CASELLA V,FRANZINIM,etal.The TriangulationAccuracyoADS40ImageryoverThePavia Testsite[C] Proceedingso WG 4 Airborne Digital PhotogrammetricSensorSystems Workshop.Newcastle: [s.n.],2007:12-17. [12] CASELLA V,FRANZINIM,KOCAMAN,etal.Trian- gulation and Sel-calibration othe ADS40Imagery:a CaseStudyoverthePaviaTestSite[C] Proceedingso the8th Conerenceon Optical3D Measurement Tech- niques.zurich:[s.n.],2007:223-232. gulationoads40threelineimagesusingunitquaternion [C] ProceedingsotheInternational Archivesothe Photogrammetry,RemoteSensingandSpatialInormation Sciences.Beijing:IAPRS,2008:573-578. [14] CRAMER M.TheADS40 Vaihingen/EnzGeometric PerormanceTest[J].ISPRSJournaloPhotogrammetry andremotesensing,2006,60(6):363-374. [15] CRAMER M.DigitalCameraCalibration[R].Frankurt: EuroSDR,2009. [16] KOCAMANS,ZHANG L,GRUEN A.Sel-calibrating TriangulationoAirborneLinearArrayCCDCameras[C] Proceedings o the EuroCOW 2006 International CalibrationandOrientation Workshop.Casteldeels:[s. n.],2006:25-27. [13] LIUJun,WANG Donghong,ZHANG Yongsheng.Trian- [17] TU Xinru,XU Miaozhong,LIU Li.TheGeometric Calibrationo Airborne Three-line-scanner ADS40[J]. ActaGeodaeticaetCartographicaSinica,2011,40(1):78-83(. ADS40 [J].,2011,40(1):78-83.) [18] YUAN Xiuxiao.ThePrincipleandApplicationoGPS- supported AerialTriangulation[M].Beijing:Surveying and MappingPress.2001:35-40.(.GPS [M]. :,2001: 35-40.) [19] FRIESSP.AerotriangulationwithGPS-Methods,Experi- ences,exception[c] ProceedingsothePhotogrammet- ricweek91.stutgart:[s.n.],1999. [20] LIUJun,AStudyonthePositioningTheoryoAirborne LineCCDImagerySupportedbyGPS/IMU[D].Zhengzhou: Inormation Engineering University,2007:41-42.(. GPS/IMU CCD [D]. :,2007:41-42.) :2011-05-31 :2011-08-03 ( : ) : (1975 ) Firstauthor:WANG Tao (1975 ),male,phdcandidate, associateproessor,majorsinaerospacephotography positioningandremotesensingimageprocessing. E-mail:wangtaoynl@163.com