畢業(yè)論文坐標(biāo)轉(zhuǎn)換中英文翻譯

word文檔可自由復(fù)制編輯本科畢業(yè)設(shè)計（論文）中英文對照翻譯院（系部）專業(yè)名稱年級班級學(xué)生姓名指導(dǎo)老師XXX年X月XAbstractStudiesonqualityevaluationofcoordinatetransformationhavenotyettocomprehensivelyinvestigatethesimulationabilityandreliabilityofatransformation.Thispaperpresentsacomprehensivequalityevaluationsystem(QES)forcoordinatetransformationthatincludesthetestingofreliabilityandsimulationability.TheproposedQESwasusedtotestandevaluatetransformationsusingtypicalcommonpointdistributionsandtransformmodels.Boththetransformationmodelanddistributionofcommonpointsarefactorsintheeffectivenessofatransformation.TheperformancesoftypicalcommonpointdistributionsandtransformmodelsaredemonstratedusingtheproposedQES.Keywords：coordinatetransformation;QES;reliability;simulationreliability;commonpointdistribution;transformmodel =1\*ROMANI.INTRODUCTIONInformationaboutcommonpointsconsistsofsignals.However,noisecausedbyinadequaciesintheprecisionofsurveyingtechniques,byshortcomingsincomputationalmodels,andbyvariationsduetocrustalmovements,etc.alsobecomeincorporated.Thisnoisecanshowsystematicorrandomcharacteristics,orcanevenappearatsomepointsasgrosserrors.Duringcomputations,randomerrorscanbeexposedasresiduals,whilesystematicerrorscanbesimulatedbysuitabletransformationmodels.Incontrast,grosserrorsareabsorbedinparametersthatresultinremarkabledistortionofthetransformation.Forthisreason,anoptimaltransformationmusthavetheabilitytosimulatesignalsandsystematicerrors(simulationability)andalsotodetectanddefendagainstgrosserrors(reliability).Precisionisgenerallyconsideredtobeauniqueindicatorthatreflectsthequalityofatransformation(WellsandVanicek1975;Appelbaum1982;Featherstoneetal.1999).Chenetal.(2005)proposedanumberofsimulationindicatorsforevaluationoftheperformanceofatransformation.Youetal.(2006)usedleast-squarescollocationtoeliminatenoisefromcommonpoints,butfoundthattheresultingisotropicalcovariancewasoftennotcorrect.Hakanetal.(2006)investigatedtheeffectofcommonpointdistributiononreliabilityofadatatransformation.Theyestablishedthattheredundancynumbersindatatransformationweredeterminedbythedistributionofcommonpointsintheareathattheybounded.Guietal(2007)presentedaBayesianapproachthatallowedgrosserrordetectionwhenpriorinformationoftheunknownparameterswasavailable.However,theseexistingreportsonevaluationofthequalityofcoordinatetransformationdidnotcomprehensivelyinvestigateeitherthesimulationabilityorthereliabilityofthetransformationbeingstudied.Theobjectivesofthispaperweretherefore:(1)tointroduceacomprehensivequalityevaluationsystem(QES)forcoordinatetransformationthatwouldincludetestsofsimulationabilityandreliability;(2)toanalyzetheeffectsofcommonpointdistributionandthetransformationmodelonsimulationabilityandreliability;and(3)toinvestigateperformanceoftypicalcommonpointdistributionsandtransformationmodelsusingtheproposedQES.Section2providesanintroductiontotheQESthatisproposedforcoordinatetransformation.Transformationswithtypicalcommonpointdistributionsandtransformmodelsarethentestedandevaluatedinsection3.Lastly,section4presentsconclusions.II.THEPROPOSEDMETHODFig.1.FlowchartofproposedQES.Fig.1showstheflowchartfortheproposedQES.Inthispaper,boththedistributionofcommonpointsandthetransformationareconsideredtobethedeterminingfactors,whilereliabilityandsimulationabilityarethemainindicatorsusedforevaluation.Ifperformancesofcandidatedistributionsandmodelsarebothabletosatisfycertainchosencriteria,thenan“optimum”transformationappears.Otherwise,othercandidatesareintroducedfortestingperformancesoftheindicators.Thus,Fig.1isalsotheflowchartthatleadstoan“optimum”transformation.Whenreliabilityistakenintoconsideration,theinvestigationofsimulationabilityprovesbothfeasibleandvaluable.Thereliabilityindicatorsconsistofredundantobservationcomponents(ROC)andinternalandexternalreliabilities(LiandYuan2002),whilethesimulatedindicatorsconsistofprecision,extensibility,anduniqueness.A.ReliabilityIndicators1)RedundantObservationComponentsThegenerallinearizedGauss-Markovmodelisexpressedasfollows:(1)Here,listhevectorofobservations,Visthevectorofresiduals,Aisthelinearizeddesignmatrix,andistheapproximationofunknownparameters.Itsnormalequationisasfollows: (2)Here,.Then:(3)Eq.3describestherelationshipbetweenresidualsandtheinputerrors.Residualsdependonthematrix,whichisdecidedbythedesignmatrixAandtheweightmatrixP.Thisrepresentsthegeometricalconditionofanadjustment,termedthereliabilitymatrix,becauseitreflectstheeffectofinputerrorsonresiduals.Sincethereliabilitymatrixisindependentofobservations,theadjustmentcanbedesignedandtestedpriortofieldobservation.Thetraceofisequaltotheredundantobservationnumberr,soitsithdiagonalelementisconsideredtobetheithredundantobservationcomponent,asfollows:,.(4)Ingeneral,.2)InternalReliabilityTheinternalreliabilityreferstothemarginaldetecTablegrosserrorwithsignificancelevelandpowerfunction,asfollows:,(5)Whereisthenon-centralityparameterofnormaldistributioncausedbygrosserror.reflectstheabilitytodetectgrosserrorincertainobservations.Asmallerinnerreliabilitywillleadtothedetectionofmoregrosserrors.IftheprecisioncomponentisremovedfromEq.5,thenapurescaleofinnerreliabilityispresentedasthecontrollablevalue,asfollows:(6)Thiscontrollablevalueindicateshowmanytimeslargeragrosserrorinacertainobservationmustbe,comparedtoitsstandarddeviation,sothatcanitbedetectedatleastwithconfidencelevel0andthepoweroftests0.Thisvalueisindependentoftheobservationunit.3)ExternalReliabilityExternalreliabilityreflectstheeffectsofundetectedgrosserrorsonadjustment(includingallunknowncoefficients,etc.).Giventhatthereisjustonegrosserrorandthatalloftheobservationsareuncorrelated,theeffectvectorofundetectedgrosserrorsincertainobservationsonunknownscanbededucedfromEq.2.Itsmoduleisasfollows:(7)Therearemanytheoreticalmethods,butinpractice,thedatasnoopingmethodpresentedbyBaarda(1976)isoftensuccessivelyusedtodetectgrosserrorsandtofinddubiTableobservations.Itsgeneralizedmodelisasfollows:(8)and;whereisthestandardizedresidual.When~,itwillbecomparedwith,whichdecideswhetheritwillbedetectedasagrosserror.4)PrecisionPrecisionindicatesthedifferencebetweenthetransformedcoordinatesfromonereferencesystemandtheknowncoordinatesinanotherreferencesystem.Theresidualsbetweenthetransformedandtheknowncoordinatesaregenerallyconsideredtorepresentprecision.Mathematicalexpectationandstandarddeviationhavebeenwidelyusedinstatisticstoexpressprecisionofacalculation,shownasfollows:(9)(10)wherexirepresentstransformedcoordinates,Xirepresentsknowncoordinates,nisthenumberofcommonpoints;ismathematicalexpectationandstdisstandarddeviation.However,thisdoesnotprovidethedistributionofresiduals.Arandomselectionof75%ofallavailabledataisusedtogenerateatransformationmodel,whiletheother25%areusedtotestthemodel(WuChenetal.2005).Theresidualsfrombothdatasetsareusedtoquantifytheprecisionofthetransformation.Ifallcommonpointsavailableareusedtogeneratethemodel,withoutleavingdatafortestingthemodel,theresultwillonlyshowhowwellthemodelfitstheexistingdata.Theprecisionofthetransformationmaybemisleading,resultinginnoclearindicationofhowwellthetransformationwillperformwithindependentdata.5)ExtensibilityExtensibilityrequiresthatthetransformationmodelobtainedfromagivendistributionofcommonpointswillbeapplicablebeyondtheboundariesofthedistribution,withincertainprecisionlimits.Ifthetransformationprecisionwiththesurroundingpointsiscomparabletothatobtainedforthepointsusedtogeneratethemodel,thistransformationisextensible.Extensibilityisimportanttoatransformation.Ifnodataareavailableoutsidethedistributionforgeneratingcorrespondingtransformationparameters,anumberofcommonpointsintheinteriorofthedistributionneedtobeselectedtogeneratetheseparameters.Predictionorcheckingtransformationsbeyondtheboundariesofthedistributionisdoneinasimilarmanner.6)UniquenessUniquenessrequires:(1)thateachpointincoordinatesystem1transformstoasingleuniquecoordinateinsystem2;(2)thatdifferenttransformationsusedindifferentregionsagreeattheboundaryofadjoiningregions.B.SimulationIndicatorsWhenthereliabilityistakenintoconsiderationfordatatransformation,theissuebecomesamatterofdistortionsratherthanofgrosserrors.Theinvestigationofitssimulationabilitybecomesbothfeasibleandvaluable.III.EXPERIMENTSANDDISCUSSIONSA.DataandMethodsInthisstudy,atotalof30GCPsinthecityofAnyangChina,withcoordinatesinboththeWGS84andXi’an80coordinatesystem(asshowninFig.2a),areusedtoprovideseveraltypicalcommonpointdistributions.CoordinatesoftheGCPsinWGS84areobtainedbytertiaryGPScontrolsurveying.UTMsareusedtotransformtheseintoaplanecoordinatesystem.CoordinatesoftheGCPsinXi’an80areobtainedbytriangularsurveying.The15GCPsinthelowerrightofFig.2aareselectedasanewdistributionofcommonpointsinasmallerarea(asshowninFig.2b).SomeGCPsaresoclosetoeachotherthattheycannotbedistinguishedeasilyineitherofthesmall-scalemapsshowninFig.2aandFig.2b.Typicaltransformationmodelsusedinthesetypesofexperimentshaveincludedanalytictransformation,planesimilaritytransformation,andpolynomialtransformation.Inanalytictransformation,thecoordinatesintheplanesystemmustfirstbetransformedintoageodeticcoordinatesystem,andthenintoarectangularspacecoordinatesystem.Theparametersofa3DtransformationmodelbetweentworectangularspacecoordinatesystemsarethengeneratedbycommonpointstransformedfromXi’an80andWGS84.Inthecurrentpaper,weuseMolodenskitransformationwith3parametersandHelmerttransformationwith7parametersas3Dtransformationmodels.Giventhatthecoordinateinthesourcesystemis,andthetransformedcoordinateinthetargetsystemis,theMolodenskitransformationandHelmerttransformationareshownasEq.11andEq.12,respectively:(11)(12) Here,[dXdYdZ]Tisthetranslationvectorbetweentheoriginsofthetwosystems,Misrelativescalefactorbetweentwosystems,andRX,RY,RZaretherotationparametersfromthesourcesystemtothetargetsystem.Planesimilaritytransformationandquadraticpolynomialtransformationcanbeimplementedwhenbothsystemsareplanecoordinatesystems.Giventhatthecoordinatesinsourcesystemare[XSYSZS],andthetransformedcoordinatesinthetargetsystemare[XTYT]T,planesimilaritytransformationandpolynomialtransformationareshownasinEq.13andEq.14,respectively. (13) whereistherotationanglebetweentwosystems,isthecoordinateoftheoriginofthesourcesysteminthetargetsystem,anddSrepresentstheincrementofscalebetweenthetwosystems,asfollows: ,(14) Here,areparametersofpolynomialtransformation. InFig.3a,thedistributionsofROCsandinternalreliabilitiesaremaintainedevenly,withnosuddendisruptions.Althoughthedistributionofexternalreliabilitiesbecomessomewhatsteeper,theactualvaluesremainsmall.InFig.3b,thedistributionsofallreliabilityindicatorsbecomesteeper;buttheyallstillmaintainarelativelysmallvalue.InFig.3c,distributionsofallreliabilityindicatorsarethesteepest;inparticular,theexternalreliabilitiesatsomepointsaremuchgreaterthanareothers.Inotherwords,itbecomesmoredifficulttodetectandtoeliminategrosserrors,andmoreerrorsmaybeabsorbedwithintheparametersatthesepoints.Theeffectsofdifferenttransformationmodelsonreliabilityofatransformationclearlyindicatethatrigorousanalyticaltransformationprovidesbetterreliability.Fig.4followssimilarrules.However,distributionsofreliabilityindicatorsineachpanearenowallworsethanB.TestingReliabilityFigures3and4showtheeffectsofcommonpointdistributionandtransformationmodelsonthereliabilityofacoordinatetransform.Toconservethenumberofpages,onlyexperimentsonmoretypicalmodelssuchastheHelmerttransformation,planesimilaritytransformation,andquadraticpolynomialtransformation,areshownandcomparedbelow.IntheFigures,theROC,internalreliability,andexternalreliabilityarecalculatedandshownasbarsateachpoint,givensignificancelevel,powerfunction,andthenon-centralityparameter.Fig.4.ReliabilityindicatorsgeneratedbytypicaltransformationmodelswithcommonpointsshowninFig.2barethoseinthecorrespondingpanesinFig.3.ComparingFig.1aandFig.1b,thenumberofcommonpointsinFig.2bbecomesfewerandthedistributionofcommonpointsalsobecomesmoreuneven.Fig.3andFig.4showthattheredundancynumbersanddistributionofcommonpointsarekeyfactorsthatimpingeonreliabilityindicators.Adistributionofcommonpointsthatprovideshighredundancynumbersthereforeleadstoreliableestimationsforresidualsandparametersoftransformationmodels.Bothtransformationmodelsanddistributionsofcommonpointsaredeterminingfactorsforthereliabilityofatransformation.Forthisreason,investigationofbothfactorsshouldbecarriedoutinordertoensureareliabletransformation. C.TestingSimulationAbilityToinvestigatethesimulationabilityofthetransformationmodelsshownanddiscussedinsection3.1,twoexperimentsweredevelopedandimplemented.First,totestprecisionoftypicaltransformationmodels,arandomselectionof3/4oftheGCPsshowninFig.2awasusedtogenerateparametersoftransformationmodels.TheremainingGCPswereusedasdatapointsfortestingthemodel.TheseresultsareshowninTableI.Secondly,totesttheextensibilityoftypicaltransformationmodels,thecommonpointsshowninFig.2bwereusedtogenerateparametersoftransformationmodels,whileotherpointsofthetotal30GCPsshowninFig.2awereusedascheckpoints.TheseresultsareshowninTableII.Thepointsusedtogenerateparametersaredesignatedasfittedpointsinthispaper.TableI.comparestheprecisionoftypicaltransformationmodelsandthestatisticsofresidualsgeneratedbythesemodels,withthecommonpointsshowninFig.2a.Theresultingperformanceoftypicaltransformationmodelsontransformationprecisionismeaningfulforfurtherexperimentsandapplications.Residualsatfittedpointsgeneratedbyaquadraticpolynomialaresmallerthanthosegeneratedbyaplanesimilaritytransformation;however,residualsatcheckpointsgeneratedbyaquadraticpolynomialarelargerthanthosegeneratedbyaplanesimilaritytransformation.Thus,thetransformationmodelthatadequatelyfitsthepointsusedtogenerateparametersmaynotperformwellatotherpoints.Thisverifiestheneedtosetcheckpoints.TableII.showstestsofextensibilityoftypicaltransformmodelsusingthefittedpointsshowninFig.2bandthecheckpointsofthe30GCPsshowninFig.2a,minusthelowerleft15pointsshowninFig.2b.Inthispaper,theratiobetweenRMSEoffittedpointsandthatofthecheckpointsisusedtoquantifytheextensibilityoftypicaltransformmodels,andisdesignatedastheextensibilityratio.BasedontheextensibilityratioofthetypicaltransformmodelsshowninTableII,planesimilaritytransformationappearstohavethebestextensibility.TheHelmertandMolodenskitransformationsalsoperformwell,whiletheperformanceofthepolynomialmodelsisworse.Theextensibilityratioincreasesdramaticallywiththeexponentofpolynomialmodels.TheresultsshowninTableI.provethatalltransformationmodelssatisfythefirstrequirementofuniqueness,asgoodprecisioncannotbegeneratedbymodelswithoutone-to-oneprojection.Extensibilityofatransformationmodeldeterminesitsabilitytosatisfythesecondrequirementofuniqueness,astheextensibilityratiodetermineshowwelldifferenttransformationsagreeattheboundaryofadjoiningregions.AlthoughthenumberofcommonpointsusedtogenerateparametersinTableIislargerthanthatinTableII,theresidualsoffittedpointsshowninTableIIarebetterthanthoseshowninTableI.ThisisbecausethedensityofcommonpointsinFig.2bisgreaterthanthatshowninFig.2a.Therefore,thedistributionofcommonpointsalsodeterminesthesimulationabilityofaIV.CONCLUSIONSSimulationabilityandreliabilityarecrucialtoanytransformation.However,existingreportsonqualityevaluationofcoordinatetransformationhavenotyetcomprehensivelyinvestigatedthesimulationabilityandreliabilityofatransformationortheeffectsofcommonpointdistributionandtransformmodelsontheseabilities.ThispaperpresentsacomprehensiveQESforcoordinatetransformationthatincludesthetestingofcommonpointdistributions.Italsocomparestransformationmodelsbasedonreliabilityindicatorsandsimulationindicatorsanddiscussestheseindicatorsindetail.TheexperimentsanddiscussionsadequatelysupportthevalidityandfeasibilityoftheproposedQES.WiththisQES,transformationswithtypicalcommonpointdistributions,aswellastransformationmodels,havebeentestedandevaluated.Boththetransformationmodelandthedistributionofcommonpointsareimportantfactorsthatdeterminethereliabilityandsimulationabilityofagiventransformation.Thus,investigationofbothofthesefactorsshouldbecarriedout,inordertoensureareliableandprecisetransformation.TheperformancesoftypicalcommonpointdistributionsandtransformationmodelsusingtheproposedQESshowthatitisworthpursuinginfurtherexperimentsandapplications.摘要研究坐標(biāo)轉(zhuǎn)換的質(zhì)量評價尚未全面了解一個轉(zhuǎn)換的仿真能力和可靠性。本文提出一種坐標(biāo)轉(zhuǎn)換綜合素質(zhì)評價體系(QES),包括可靠性測試和仿真能力測試。擬議中的QES被用來測試和評估轉(zhuǎn)換使用典型的公共點分布和變換模型。轉(zhuǎn)換模型和點分布都是影響轉(zhuǎn)換的有效性的因素。使用擬議的QES能展示典型的公共點分布和轉(zhuǎn)換模型的優(yōu)劣。關(guān)鍵字:坐標(biāo)轉(zhuǎn)換;QES;可靠性;仿真可靠性;公共點分布;轉(zhuǎn)換模型一、介紹所有公共點點的信息組成信號。然而,測量技術(shù)的精度不足,計算模型的缺點,和地殼運(yùn)動和變化等造成的噪聲也變成一個總和。這噪音可以表示系統(tǒng)的隨機(jī)特性,或甚至可以作為粗差出現(xiàn)在一些公共點上。在計算中,隨機(jī)誤差可以體現(xiàn)為殘差,當(dāng)系統(tǒng)誤差能被合適的轉(zhuǎn)換模型模擬。相反,粗差被參數(shù)吸收導(dǎo)致轉(zhuǎn)換的顯著的扭曲。出于這個原因,一個最佳的轉(zhuǎn)換,必須有信號仿真能力和系統(tǒng)誤差仿真能力以及檢測和抵御粗差(可靠性)。精度普遍被認(rèn)為是一個獨(dú)特的指標(biāo),反映了坐標(biāo)轉(zhuǎn)換的質(zhì)量(Wells和Vanicek1975;Appelbaum1982;費(fèi)瑟斯通.1999年)。為了評價的坐標(biāo)轉(zhuǎn)換的性能，陳etal(2005)提出了一系列模擬指標(biāo)。Youetal.(2006)在點處使用最小二乘法消除噪聲,但是發(fā)現(xiàn)產(chǎn)生的各向同性的協(xié)方差往往是不正確的。Hakanetal.(2006)調(diào)查公共點分布對數(shù)據(jù)轉(zhuǎn)換可靠性的影響。在他們限定的區(qū)域內(nèi)，他們在數(shù)據(jù)轉(zhuǎn)換中建立了冗余公共點個數(shù)。Guietal(2007)提出了一種貝葉斯方法,允許粗差的偵測當(dāng)未知的參數(shù)主要信息沒有被利用之前。然而,這些現(xiàn)有的坐標(biāo)變換的質(zhì)量評估報告并沒有全面調(diào)查證明仿真能力可行和有價值。因此本文的目的是:(1)是引入全面質(zhì)量評價體系(QES)進(jìn)行坐標(biāo)變換,包括仿真能力和可靠性的測試;(2)是分析公共點分布的影響和轉(zhuǎn)換模型的仿真能力和可靠性,(3)是研究對典型的公共點分布和坐標(biāo)轉(zhuǎn)換模型使用擬議的QES轉(zhuǎn)換模型性能的表現(xiàn)。第2節(jié)介紹了坐標(biāo)變換的擬議的QES。在第三節(jié)對典型的公共點分布和坐標(biāo)轉(zhuǎn)換模型進(jìn)行了測試和評估。最后,在第四節(jié)給出結(jié)論。二、擬議的方法圖1擬議的QES的流程圖 圖1展示了擬議的QES的流程圖。在這篇論文中，公共點的分布和坐標(biāo)轉(zhuǎn)換模型被認(rèn)為是決定性的因素，而可靠性和仿真能力是評估的主要指標(biāo)。如果公共點的分布和轉(zhuǎn)換模型的表現(xiàn)都能夠滿足被選定的標(biāo)準(zhǔn),那么這就是一個“最佳”轉(zhuǎn)換。否則,其他候選的方法被引入了用于測試其表現(xiàn)。因此,圖1的流程圖也能產(chǎn)生一個“最佳”轉(zhuǎn)換。當(dāng)考慮到可靠性的問題，對仿真能力的研究變得可行又有價值?？煽啃灾笜?biāo)由冗余觀測值組成(ROC)和內(nèi)部和外部可靠性組成(Li和Yuan2002),而仿真指標(biāo)包括精度、可擴(kuò)展性和獨(dú)特性。A．可靠性指標(biāo)1)冗余觀測值一般的線性化高斯-馬爾可夫模型表示如下:(1)上式中,是觀測向量,V是殘差向量,是線性化設(shè)計矩陣,是未知參數(shù)的近似。它們的正式的方程如下:(2)在式中,.所以:(3)等式3描述了殘差和輸入錯誤之間的關(guān)系。殘差值取決于矩陣,這是由設(shè)計矩陣A和權(quán)重矩陣P決定的。這代表了幾何條件調(diào)整,被稱為可靠性矩陣,因為它反映了輸入錯誤對殘差的影響。由于可靠性矩陣是獨(dú)立于觀測值的，對它的調(diào)整可以被設(shè)計和測試在實地觀測之前。而矩陣的跡等于多余的跟蹤觀測數(shù)r,所以它的第i個對角元素被認(rèn)為是第i個多余觀測值,如下: ，(4)一般來說,.2)內(nèi)部可靠性內(nèi)部可靠性指的是邊緣檢測粗差和顯著性水平和冪函數(shù),如下:,(5)當(dāng)因粗差導(dǎo)致不符合正態(tài)分布參數(shù)時。反映了檢測某些觀測誤差的粗差的能力。更小的內(nèi)部可靠性將導(dǎo)致更多的粗差被檢測。如果精確的成分從等式(5)中移動,然后內(nèi)在可靠性一個確定的范圍被體現(xiàn)作為可控的數(shù)值,如下:(6)這個控制值表示在一次觀測中對于一個觀測值來說一個粗差超過其標(biāo)準(zhǔn)偏差的倍數(shù)。所以它以最小置信區(qū)間和置信水平被檢測出來。這兩個數(shù)是獨(dú)立于觀測過程而存在的。3)外部可靠性外部可靠性反映了在調(diào)整中未檢測出粗差的效果(包括所有的無效的，等等)。所有的不相關(guān)的觀測值下只有一個粗差，其影響效果向量在確定的觀測值下能在公式(2)下被推導(dǎo)出來。其公式如下：(7)有許多理論方法,但在實踐中,Baarda(1976)提出的數(shù)據(jù)監(jiān)聽方法總值通常是先后用于檢測粗差和發(fā)現(xiàn)可疑的觀測值。其廣義模型如下: (8)式中，；上式中是標(biāo)準(zhǔn)的偏差值。當(dāng)~時，它會被與相比,以決定它是否會被檢測作為一個粗差。B．仿真指標(biāo)當(dāng)考慮數(shù)據(jù)轉(zhuǎn)換的可靠性時,這個問題就不僅僅只是涉及到粗差了。其仿真能力的研究就變得可行和有價值的。4)精度精度表現(xiàn)了從一個參考系統(tǒng)轉(zhuǎn)換被轉(zhuǎn)換的坐標(biāo)和另一參考系統(tǒng)中已知坐標(biāo)之間的差異。已知的坐標(biāo)和轉(zhuǎn)換坐標(biāo)之間的殘差通常被認(rèn)為是精度的代表。數(shù)學(xué)期望和方差已經(jīng)廣泛應(yīng)用于統(tǒng)計在計算中表達(dá)精度,表示如下:(9)(10)其中代表轉(zhuǎn)換坐標(biāo),代表已知坐標(biāo),是公共點的數(shù)量,是數(shù)學(xué)期望和是方差。然而,這并不提供殘差的分布信息。隨機(jī)選擇75%的所有可用的數(shù)據(jù)用于生成轉(zhuǎn)換模型,而另25%是被用于測試模型(陳吳etal.2005)。殘差的兩個數(shù)據(jù)集被用來量化轉(zhuǎn)換的精度。如果所有公共點可用來生成模型,無需留下數(shù)據(jù)用來測試模型,結(jié)果將只顯示模型符合現(xiàn)有的數(shù)據(jù)。轉(zhuǎn)換的精度可能會被結(jié)果誤導(dǎo),導(dǎo)致沒有明確的體現(xiàn)轉(zhuǎn)換用獨(dú)立數(shù)據(jù)將會有怎樣的表現(xiàn)。5)可擴(kuò)展性可擴(kuò)展性要求轉(zhuǎn)換模型在一定的精度范圍內(nèi)獲得從給定的公共點分布將能適用的邊界之外的分布。如果轉(zhuǎn)換精度與周圍的點與用于生成模型獲得的點一致,則該轉(zhuǎn)換是可擴(kuò)展的。可擴(kuò)展性對于坐標(biāo)轉(zhuǎn)換來說是很重要的。如果沒有在分布之外的可用的數(shù)據(jù)用于生成相應(yīng)的轉(zhuǎn)換參數(shù),則需要選擇一定數(shù)量內(nèi)部公共點分布用于生成這些參數(shù)。預(yù)測或檢查邊界之外分布的轉(zhuǎn)換坐標(biāo)是以類似的方式完成的。6)獨(dú)特性獨(dú)特性要求:(1)在坐標(biāo)系統(tǒng)1中的每個點轉(zhuǎn)換為坐標(biāo)系統(tǒng)2中單個的獨(dú)特的坐標(biāo);(2)在不同地區(qū)使用不同的轉(zhuǎn)換而在相鄰的邊界地區(qū)則具有一致性。三、實驗和討論A.數(shù)據(jù)和方法在這項研究中,在中國安陽城共計30個公共點的空間直角坐標(biāo),每個點同時擁有在WGS84和80西安坐標(biāo)系下坐標(biāo)(如圖2所示),用于提供幾種典型公共點分布。WGS84下空間直角坐標(biāo)的都是通過三級的GPS控制測量獲得。并使用UTMs投影將這些坐標(biāo)轉(zhuǎn)化為平面直角坐標(biāo)。西安80系下空間直角坐標(biāo)均由三角控制測量得到。15個GCPs在右下角的圖2a中被選擇作為一個在較小