基于目标航迹的引导误差校正方法研究.pdf

文章编号：1002-2082(2023)05-1088-07基于目标航迹的引导误差校正方法研究路大举1,2，张大勇3，曾砾堂4，张凯1，杨浩1，张佩宇4（1.中国工程物理研究院应用电子学研究所，四川绵阳，621900；2.中国工程物理研究院研究生院，四川绵阳，621900；3.中国工程物理研究院流体物理研究所，四川绵阳，621900；4.95972 部队，甘肃酒泉，735300）摘摘 要：要：在探测目标尺寸小且距离远时，由于光电系统的视场角很小，有效的目标前级引导是光电系统跟瞄目标的前提。目标引导的本质是将大地坐标系下的目标点转换至光电系统局部坐标系下，转换过程中引入一系列旋转和平移参数，其准确程度决定了最终的目标引导精度。提出基于无人机航迹的光电系统引导误差校正方法，通过围绕光电系统周围无人机航迹数据，求解引导数据计算过程中坐标变换的最优参数，进而提高目标引导精度。在本项目搭建的实验装置上实现了方位引导标准方差小于 0.052，俯仰引导标准方差小于 0.04，最大误差不超过 0.7。目标前级引导的引导精度越高，光电系统捕获目标速度越快，对于提高目标处置相应速度具有重要意义。关键词：关键词：目标引导；引导误差；目标探测中图分类号：TN953+.5文献标志码：ADOI：10.5768/JAO202344.0503005Guidance error correction method based on target trackLUDaju1,2，ZHANGDayong3，ZENGLitang4，ZHANGKai1，YANGHao1，ZHANGPeiyu4（1.InstituteofAppliedElectronics,ChinaAcademyofEngineeringPhysics,Mianyang621900,China；2.GraduateSchool,ChinaAcademyofEngineeringPhysics,Mianyang621900,China；3.InstituteofFluidPhysics,ChinaAcademyofEngineeringPhysics,Mianyang621900,China；4.Unit95972ofPLA,Jiuquan735300,China）Abstract：Whenthesizeofthedetectiontargetissmallandisinthefardistance,duetothesmallfieldofviewofthephotoelectricsystem,theeffectivepre-stagetargetguidanceisthepremiseforthephotoelectricsystemtotrackandpointthetarget.Theessenceoftargetguidanceisconvertingthetargetpointunderthegeodeticcoordinatesystemintothelocalcoordinatesystemofthephotoelectricsystem.Sinceaseriesofrotationalandtranslationalparameterswillbeintroducedinthisconversionprocess,theaccuracyoftheseparameterswilldeterminetheultimatetargetguidanceaccuracy.Aguidanceerrorcorrectionmethodwasproposedforthephotoelectricsystem,namelyacquisition-tracking-pointing(ATP)system,basedonunmannedaerialvehicle(UAV)track,which used the track data around ATP system to solve optimal parameters for coordinateconversionintheprocessofcomputingtargetguidancedata,therebytoimprovethetargetguidanceaccuracy.Experimental device built for this project achieves the following results:the azimuth guidance standardvarianceisbetterthan0.052,theelevationguidancestandardvarianceisbetterthan0.04,andthemaximumerrordoesnotexceed0.7.Theresultsalsoshowthatthehighertheaccuracyofpre-stageguidance,thefasterthetargetacquisitionspeedofATPsystem,whichisofgreatsignificanceforimprovingthecorrespondingspeedofthetargetdisposal.Key words：targetguidance；guidanceerror；targetdetectionIntroductionThe ATP is an important technical means toaccuratelytrackandpointthetarget,butwhenthesizeofthedetectiontargetissmallandisinthefardistance,收稿日期：2022-11-04；修回日期：2023-08-02基金项目：中国工程物理研究院创新基金（C-2021-CX20210023）作者简介：路大举（1981），男，硕士，副研究员，主要从事光学探测和激光测量技术研究。E-mail：通信作者：杨浩（1988），男，硕士，副研究员，主要从事指挥控制和智能化技术研究。E-mail：第44卷第5期应用光学Vol.44No.52023年9月JournalofAppliedOpticsSep.2023the field of view(FOV)of the photoelectric systembecomesverysmall,whichrequiresaneffectivepre-stageguidancetoallowthetargettofallintotheFOVof ATP,then to achieve capturing,tracking andpointing.Effective pre-stage target guidance is thepremisefortheATPtotrackandpointthetarget1-4.The essence of target guidance is a series of linearcoordinateconversions,thatis,thetargetpointunderthegeodeticcoordinatesystemcanbeconvertedintothe local coordinate system of the ATP5-7.Since aseriesofrotationalandtranslationalparameterswillbeintroducedinthisconversionprocess,theaccuracyofthese parameters will determine the ultimate targetguidanceaccuracy.Aguidanceerrorcorrectionmethodis proposed for the ATP based on unmanned aerialvehicle(UAV)track,whichcoversalltheUAVtrackdatafromdifferentpositionsaroundtheATPtosolveoptimal parameters for coordinate conversion in theprocessofcomputingtargetguidancedata,therebythetargetguidanceaccuracyisimproved.Thesmallertheerror of the pre-stage target guidance,the faster thetarget acquisition speed of ATP,which is of greatsignificanceforimprovingthecorrespondingspeedofthetargetdisposal.1 Principles for target guidance1.1 Target guidance scenarioAsshowninFigure1,thepositionofthetargetisexpressedbythelongitude,latitudeandheightinthegeodeticcoordinates,andthepointingoftheATPisexpressedbytheazimuth,pitchandslantdistanceinitslocalcoordinates.ThepurposeofguidanceistomaketheFOVofATPpointingtothetarget,anditsprocesscan be described as the conversion of the longitude-latitude-height position of target under the geodeticcoordinatesintothelocalcoordinatesoftheATP.ZXYLocal coordinatesof ATPAzimuthpitchslant distanceLongitudeheightTargetEarthlatitudeFig.1 Schematic diagram of target guidance scenario1.2 Target guidance mathematic modelAsshowninFigure2,thecalculationprocessoftarget guidance data is divided into 4 steps duringcoordinateconversion8-10.Targets geodetic position:(Lt,Bt,Ht)WGS84 ellipsoid parameters:radius of long axis rE,flat rate fATP geodetic position:(Lz,Bz,Hz)INS measurement attitude:(,)Installation relationship between theINS and the ATP:(0,0,0)Translation between the positioningantenna and the origin of the ATPcoordinates:(X0,Y0,Z0)ATPs correction value of pitch zero:E0Targets vector in ECEF:(X1,Y1,Z1)Targets flat earth position:(X2,Y2,Z2)Targets INS position:(X3,Y3,Z3)Targets position in the ATPlocal coordinate system:(At,Et,Ht)Fig.2 Calculation process during coordinate conversionThecalculationprocessofeachstepisasfollows.1）Convertingthegeodeticpositionofthetargetintotheearth-centeredearth-fixed(ECEF)coordinatesThe calculation process of converting the longi-tude(L),latitude(B),and height(H)into the ECEFcoordinatesisasshowninformula(1):XECEF=(rE1(2f f2)sin2B+H)cosBcosLYECEF=(rE1(2f f2)sin2B+H)cosBcosLZECEF=(rE(1 f)21(2f f2)sin2B+H)sinB（1）rEwhereistheradiusofthelongaxisofearth,fistheflat rate of earth,and the values of which can beobtainedbyqueryingtheWGS84ellipsoidparameters.Thetargetposition(Lt,Bt,Ht)andATPposition(Lz,Bz,Hz)areputintoformula(1),respectively,anditiscalculatedtogainthetargetposition(Xt,Yt,Zt)andATPposition(Xz,Yz,Zz)intheECEFcoordinates,thenthetargetpositionissubtractedfromtheATPpositionto obtain the target vector(X1,Y1,Z1)in the ECEFcoordinates.2）ConvertingthetargetvectorintotheflatearthcoordinatesThe calculation process of converting the targetvector into the flat earth coordinates is as shown in应用光学2023，44（5）路大举，等：基于目标航迹的引导误差校正方法研究1089formula(2):X2Y2Z2=Tz(2)Ty(2Bz)Tz(Lz)X1Y1Z1（2）where T is the rotational matrix,and the rotationalmatrixaroundthe(X,Y,Z)axisisasfollows:Tx=1000sincos0cossin,Ty=sin0cos010cos0sin,Tz=sincos0cossin00013）Convertingtheflatearthpositionofthetargetintotheinertialnavigationsystem(INS)coordinatesThecalculationprocessofconvertingtheflatearthposition of the target into the INS coordinates is asshowninformula(3):X3Y3Z3=Ty()Tx()Tz()X2Y2Z2（3）where T is the rotational matrix,and is theazimuth,pitch and roll attitude angles of the INSmeasurement,respectively.4）ConvertingtheINSpositionofthetargetintothelocalpolarcoordinatesofATPThe calculation process of converting the INSpositionofthetargetintothelocalpolarcoordinatesofATP is as shown in formula(4)and formula(5),respectively.First,it is converted into the localrectangularcoordinatesofATPbyusingformula(4),thenitisconvertedintothepolarcoordinatesbyusingformula(5):X4Y4Z4=Ty(0)Tx(0)Tz(0)X3Y3Z3X0Y0Z0（4）where(X0,Y0,Z0)isthetranslationbetweentheINSfixandtheoriginoftheATPcoordinates,and(0,0,0)istherotationbetweentheINSandtheATPcoordinates.A=tan1(X4Y4)E=sin1(Z4D)+E0D=X24+Y24+Z24（5）Where(A,E,D)isthelocalpolarcoordinateofthetargetpositionofATP,Aisthetargetazimuth,Eisthetargetpitch,Disthetargetdistance,andE0isthepitchzerocorrectionoftheATP.2 Source of errorFromthemathematicalmodeloftheguidance,wecanseethatthetargetguidanceerrorsourcesarefromthefollowings:thepre-stagetargetdetectionerror,thepositionerroroftheATP,theattitudeangleerroroftheINS measurement,the calibration error of theinstallation relationship between the INS coordinatesandtheATPcoordinates(i.e.,installationerror),andthepitchcoderzerocalibrationerroroftheATP(i.e.,pitchzeroerror)4.Inaddition,ittakestimefromthetargetdetectiontosendthesolvedguidancedatatotheATP,thustheATPcertainerrorisproducedduetothedelayofthereceivedguidancedata,andthiserroriscalleddelayerror.Intheaboveerrors,thepre-stagetargetdetectionerror,thepositionmeasurementerroroftheATP,andtheattitudepositionerroroftheINSmeasurementaredetermined by the inherent performance of themeasuring equipment.The delay error is mainlyaffectedbythedelayofthesystemsignaltransmission.For a stable guidance system,the delay is generallymorestable,anditcanbeobtainedbytheATPtimeofreceivingtheguidancedataminusthetimeofthetargetdetectionatthepre-stage,andcompensatedbyderivingtheguidancedata.Theinstallationerrorandpitchzeroerrordependon the calibration method and the measurementaccuracyofthecalibrationdata.Therefore,itismainlyaimedtoimprovetheguidanceaccuracybystudyingtheinstallationrelationshipbetweentheINScoordinates and the ATP coordinates,as well as thepitchzerocalibrationmethodoftheATP.3 Calibration of guidance parameters3.1 ATPs pitch zero calibration methodAsshowninFigure3,theATPsrotatingZ-axisand X-axis of the rotating plane form a rectangularcoordinatesystem,wherethepitchangleEshouldbezero when the ATPs pointing is parallel with the1090应用光学第44卷第5期rotatingplane.However,whentheATPisinstalled,theactual pointing of its pitch coders zero position Ecannotbecoincided.Therefore,therewillalwaysbeanerrorE0.ZXparallel with the rotating planeATPs pointing when pitch E is zeroE0EEPitch angle E when the ATPs pointing isFig.3 Schematic diagram of pitch zero errorFigure4showstheprincipleoftheATPspitchzerocalibration.First,theATPispointedtothetargetandapitchvalueE1,thentheATPisrotatedby180aroundtheZ-axis,theATPspitchangleisadjustedtillafteroverheadandpointtothetargetagain,andanotherpitchvalueE2isreadatthismoment.Bygeometricrelationships,thecalculationformula(6)fortheATPspitchzerocorrectionE0canbeestablished:E0=E1+E21802（6）ZXTargetE1E2OE0E0Fig.4 Schematic diagram of pitch zero calibrationThiscalibrationmethodhasahighaccuracyoftheATPspitchzerocorrection,whichcanbeashighasananglerepresentedbyonepixelunitoftheATP.3.2 Calibration of installation relationship betweenINS and ATPTheATPandthepre-stagedetectionsystemarerequired to simultaneously detect a moving UAVtarget,whilelettheUAVsflighttrackscoverallthedirections of the ATP as much as possible,and thetarget tracks detected by the ATP as well as thatdetectedbythepre-stagedetectionsystemarerecordedasPA,E,DandS,respectively.Theformula(7)isusedtoobtainthetargetstrackcoordinatePundertheATPslocalcoordinates,andtheconversionofform-ula(1),formula(2)andformula(3)isusedtoobtainthetargetstrackcoordinateSunderthetargetsINScoordinates,whereSisaN3dimensionalmatrix11-15.Pn=DncosEnsinAncosEncosAnsinEnT，n=1,2,N（7）TheconversionbetweenSandPisarotationalandtranslationalrelationship.Let betheconversionalmatrix,thenthemathematicalrelationshipbetweenHandPisasshowninformula(8):P=SI=H（8）N1H=SIN4where I is the unit vector of the dimension,Histhedimensionalmatrix,istheconversionalmatrixof43,andexpressedasfollows:=a1b1c1a2b2c2a3b3c3A0B0C0(0,0,0)Thefirstthreelinesof arerotationalparameters,the fourth line is a translational parameter.Therotational parameters in can also be expressed byasfollows:a1a2a3b1b2b3c1c2c3=Ty(0)Tx(0)Tz(0)SincethepurposeoftheguidanceistopointtheATPtothetarget,thetargettrackPdetectedbytheATP in the closed-loop can be used as a referencecriterionfortheguidancedatasolution.Thecalibrationofinstallationrelationshipistheprocessofsolvingtheparameters of conversion from the targets pre-stagedetection track S to the ATPs detection track P.Therefore,the calibration of installation relationshipcan be converted to a math problem of solving theoptimalconversionalmatrixinformula(8).ThesmallerthedifferenceoftargetpositiondatabetweenthetargetguidancedataandATPdetection,thehigherguidanceaccuracy.Basedonthisprinciple,weuseJ()tomeasuretheguidanceerror,whichcanbeexpressedasformula(9):J()=N1(PnSn1)2=(PH)T(PH)（9）whereJ()isasecondaryfunctionof,andthemath应用光学2023，44（5）路大举，等：基于目标航迹的引导误差校正方法研究1091problemcanbesimplifiedassolvingthe whenJ()isminimum.Expandingformula(9),wehave:J()=(PTP2PTH+THTH)（10）Thederivativeissubstitutedintoformula(10)toobtain:J()=2HTP+2HTH（11）J()bWhenthederivativeiszero,thevalueofisminimum,sotheoptimal canbesolved.b=(HTH)1HTP（12）bFor the rotational and translational conversionparametersobtainedthroughthismethod,becausethesolution process uses a large number of UAV trackpointscoveringallthedirectionsaroundtheATPtofitthe calculation,the random error of the pre-stagedetectionandtheATPhaslessimpacton.Therefore,the obtained installation relationship parametersbetweentheINSandtheATPhasaconsiderablyhighaccuracy.4 Validation experiment4.1 Experimental designAs shown in Figure 5,the device used for theexperimentwasmainlycomposedof5parts:theATP,theINS,aUAV,aradiostation,andacontrolsystem.GPSantennaControl systemRadio stationUAVpositionUAVATPINSFig.5 Schematic diagram of experimental deviceTheATPwasusedtotrackandpointtheflyingUAVandacquiretheUAVsflighttrack.TheINSisused to measure the geodetic coordinates of theexperimentaldeviceandtheATPsazimuth,pitch,androllattituderelativetothehorizontalcoordinates.Asthetargetfordetection,theUAVfliedaroundtheATP,and at the same time,its own position data wastransmittedtothecontrolsystemviatheradiostationasthepositionforpre-stagedetection.ThemainfunctionofthecontrolsystemwastoguidetheATPtotrackandpoint the UAV,and record the ATPs tracking andpointingtracks,theUAVstrack,andthepositionandattitudedatameasuredbytheINS.The experimental site was selected at anunobstructed open area.The UAV should change itsheight and distance during flight to avoid its trackbeinginanear-sameplane.4.2 Experimental resultsReferring to the ATPs pitch zero calibrationmethod described in section 3.1,when the ATPpointing at the static target,we read the pitch angleE1=0.9.Then the ATP was horizontally rotated by180,thepitchanglewasadjustedtillafteroverheadandpointedtothesamepointoftargetagain,andthepitchangleE2=180.3wasread.Theformula(6)wasusedtocalculateandobtainthecorrectedvalueofthepitchzeroE0=0.6.DuringthecalibrationexperimentoftheinstallationrelationshipbetweentheINSandtheATP,thefrequenciesoftheacquiredpre-stagedetectiondataofthetargetandtheATPsdetectiondatawereboth20Hz,theflighttimeoftheUAVwasabout23min,and11000setsofvaliddatawereacquiredfromtheflighttrack.Thevaliddatawasdefinedwhenthepre-stagedetectiondataofthetargetwasnormalandtheATP was in a closed-loop state with respect to thetarget.Inthissectionofvaliddata,theUAVsflighttrackwasasshowninFigure6,wherethecirclewasthepositionoftheATP,andthecurvewastheUAVsflighttrack.1 6001 4001 2001 00080060040020002002 0001 000 50005001 000 1 500 2 0001 500Y/mX/mFig.6 UAVs flight track around ATPThelongitude,latitude,andheightoftheATPsposition measured by the INS were 104.731 95,1092应用光学第44卷第5期b31.530 62,550.24 m,respectively.The azimuth,pitch,and roll attitudes of the ATP relative to thehorizon when measured in static conditions were317.93,0.08,1.12,respectively.Based on theabove data and using the installation relationshipcalibrationmethoddescribedinsection3.2,thedirectrotationalandtranslationalparametermatrixoftheINS and the ATP coordinates was calculated andobtainedasf