2.4Theleast-Squaresadjustment主講人：LiSimengtheknowledgeoftheleast-Squaresadjustmentthesentenceanalysis01WhatIsGeomaticsCONTENTS目錄PARTONEWhatIsGeomatics01WhatIsGeomaticsMathematicalModel數(shù)學(xué)模型AdjustmentMethods調(diào)整方法(1)theknowledgeoftheleast-SquaresadjustmentWhatIsGeomatics(1)theknowledgeoftheleast-SquaresadjustmentMathematicalModelAfunctionalmodeldescribesthegeometricorphysicalcharacteristicsofthesurveyproblem.Inadjustmentcomputationsafunctionalmodelisanequationthatrepresentsordefinesanadjustmentcondition,Itmusteitherbeknown,orassumed.WhatIsGeomatics(1)theknowledgeoftheleast-SquaresadjustmentThedeterminationofvariances,andsubsequentlytheweightsoftheobservations,isknownasthestochasticmodelinaleast-squaresadjustmentwhichdescribesthestatisticalpropertiesofalltheelementsorrepresentsawaytoenterinformationabouttheprecisionoftheobservationsinvolvedinthefunctionalmodel.Theimportanceofthestochasticmodelisoftenoverlookedandundervalued.WhatIsGeomatics(1)theknowledgeoftheleast-SquaresadjustmentAdjustmentMethodsTherearetwoadjustmentmethods:theconditionalandparametricadjustments.Conditionaladjustment：WhatIsGeomatics(1)theknowledgeoftheleast-SquaresadjustmentIntheconditionaladjustment,geometricconditionsareenforced,upontheobservationsandtheirresiduals,Sotheconditionaladjustmentiscalleddirectadjustment.Examplesofconditionaladjustmentare:(1)thesumofanglesinapolygonis(n-2)·180°,wherenisthenumberofanglesinthepolygon;(2)thesumoftheanglesinthehorizonatanystationequals360°;(3)inaclosedtraverse,thealgebraicsumofthedeparturesshouldequalthedifferencebetweentheXcoordinatesatthebeginningandtheendingstationsofthetraverse,similarly,thealgebraicsumofthelatitudesshouldequalthedifferencebetweentheYcoordinatesatthebeginningandtheendingstationsofthetraverse.WhatIsGeomatics(1)theknowledgeoftheleast-SquaresadjustmentTheparametricadjustment:Whenperformingaparametricadjustment,observationsareexpressedinitemsofunknownparametersthatwerenevermeasureddirectly.Sotheparametricadjustmentissometimescalledindirectionadjustment,inwhichthecorrectionsarestatedasfunctionsofindirectlydeterminedvaluesofparametersofthemeasurements.Forexample,thewell-knowncoordinateequationsareusedtomodelthemeasuredangles,directionanddistancesinatraverse.Theadjustmentyieldsthemostprobablevaluesforthecoordinates(parameters),whichinturnenablethemostprobablevaluesfortheadjustedobservationstobecomputed.WhatIsGeomatics(2)Thesentenceanalysis.1.Thedeterminationofvariances,andsubsequentlytheweightsoftheobservations,isknownasthestochastic/st??k?st?k/modelinaleast-squaresadjustmentwhichdescribesthestatisticalpropertiesofalltheelementsorrepresentsawaytoenterinformationabouttheprecisionoftheobservationsinvolvedinthefunctionalmodel.本句的主語為Thedeterminationofvariances,andsubsequentlytheweightsoftheobservations,其中variances,andsubsequentlytheweightsoftheobservations一起做determination邏輯上的賓語。Which引導(dǎo)的定語從句修飾限定先行詞thestochastic/st??k?st?k/model）（隨機(jī)模型），which在定于從句中做主語。譯文：在最小二乘平差中,確定方差和觀測值的權(quán)稱為隨機(jī)模型。這種隨機(jī)模型描述了所有元素(觀測值)的統(tǒng)計特性,或者說它描述了函數(shù)模型中的觀測值所具有的精度信息。WhatIsGeomatics(2)Thesentenceanalysis.Therefore,parametricadjustmentisbecomingverypopular,whichgenerallyleadstolargersystemsofequationsbutisstraightforwardinitsdevelopmentandsolutionand,asaresult,iswellsuitedtoc