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(jì)（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(jià)尚未全面了解一個(gè)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(jià)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(diǎn)分布和變換模型。轉(zhuǎn)換模型和點(diǎn)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(diǎn)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(diǎn)分布;轉(zhuǎn)換模型一、介紹所有公共點(diǎn)點(diǎn)的信息組成信號。然而,測量技術(shù)的精度不足,計(jì)算模型的缺點(diǎn),和地殼運(yùn)動(dòng)和變化等造成的噪聲也變成一個(gè)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(diǎn)上。在計(jì)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(gè)原因,一個(gè)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(gè)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(jià)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(diǎn)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(diǎn)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(diǎn)個(gè)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(bào)告并沒有全面調(diào)查證明仿真能力可行和有價(jià)值。因此本文的目的是:(1)是引入全面質(zhì)量評價(jià)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(diǎn)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(diǎn)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(diǎn)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(diǎn)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(diǎn)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(gè)“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(gè)“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(jià)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(jì)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(cuò)誤之間的關(guān)系。殘差值取決于矩陣,這是由設(shè)計(jì)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?yàn)樗从沉溯斎脲e(cuò)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(jì)和測試在實(shí)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(gè)對角元素被認(rèn)為是第i個(gè)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(shí)。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(dòng),然后內(nèi)在可靠性一個(gè)確定的范圍被體現(xiàn)作為可控的數(shù)值,如下:(6)這個(gè)控制值表示在一次觀測中對于一個(gè)觀測值來說一個(gè)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(gè)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(gè)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(shí)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(shí)，它會(huì)被與相比,以決定它是否會(huì)被檢測作為一個(gè)粗差。B．仿真指標(biāo)當(dāng)考慮數(shù)據(jù)轉(zhuǎn)換的可靠性時(shí),這個(gè)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(jià)值的。4)精度精度表現(xiàn)了從一個(gè)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(jì)在計(jì)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(diǎn)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(gè)數(shù)據(jù)集被用來量化轉(zhuǎn)換的精度。如果所有公共點(diǎn)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(huì)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(huì)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(diǎn)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(diǎn)與用于生成模型獲得的點(diǎn)一致,則該轉(zhuǎn)換是可擴(kuò)展的?？蓴U(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(diǎn)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(gè)點(diǎn)轉(zhuǎn)換為坐標(biāo)系統(tǒng)2中單個(gè)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(shí)驗(yàn)和討論A.數(shù)據(jù)和方法在這項(xiàng)研究中,在中國安陽城共計(jì)30個(gè)公共點(diǎn)的空間直角坐標(biāo),每個(gè)點(diǎn)同時(shí)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(diǎn)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(gè)GCPs在右下角的圖2a中被選擇作為一個(gè)在較小