TLS与LS数据处理方法对比研究

©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(2007)04-74-03:P207+11:ATLSLS3,,3:20060927:(1982),,,:(,430074):(TLS),,,,,,,:,,,,,:;;;1,,,,,[1],,,,Mikhail,,(TLS)70,,,[2]2A+ASVD,xe2=min(1)b+erange(A)3L2,e2=mi=1e2iArange(A)={bRn:b=AxxRn},ebb+eA,b,A[3],bA(TLS),TLS,(A+E)x=b+e(2)(2)([-b|A]+[-e|E])1x=0(3a)(B+D)z=0(3b)B=[-b|A],D=[-e|E],z=1x,(3):zDF=min(4)(b+e)range(A+E),Frobenius[9]DF=(mi=1nj=1djj)1/2(5)47©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(3):TLS:DRm(n+1)B+D(,z=0)SVDB=UV3(6):12min(m,n+1)0mn+1,(3),,TLSTLS(3),mn+1,[4]TLS,nn+1,TLS,^x=1v(1,n+1)v(2,n+1)v(n+1,n+1)(7),v(i,n+1)Vn+1iB(),TLS12kk+1n+1viSc=span{k+1,,n+1},,TLSx=yiai(8),vi=[ai/yi],yi,ai,i=k+1,,n+1,ai0,^xn+1-k,vk+1,,vn+1,,:[5]311TLSGolubandVanLoan(1980)4[6](1)BSVD,U3BV=diag(1,,n+1),V(2)pn+1+p+1n+1P,0(3)V1=[vp+1,,vn+1]V,HouseholderQV1Q=0y,(4)=0,TLS;,xTLS=y/312(SVD-TLS)(1)BSVD,V(2)Bp(3)S(p)=pj=1n+1-pi=12jvij(vij)3vik=[v(i,k),v(i+1,k),v(i+p,k)]T(p+1)(p+1)S(p)(4)S(p)S-(p),^xi=S-(p)(i+1,1)/S-(p)(1,1)(i=1,,p)^xi(i=1,,p)4TLSLS(1),1,A,B,C,D,P1,P2,P3,P4,4,111/mXYA53743.13661003.826B47943.00266225.854C40049.22953782.790D36924.72861027.086P148580.27460500.498P248681.38955018.290P343767.18857968.614P440843.31864867.981,:L1=5760.7132m,L2=5187.3387m,L3=7838.8726m,L4=5483.1580m,L5=5731.8220m,L6=8720.1288m,571TLSLS©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=5598.6018m,L8=7494.8989m,L9=7493.2662m,L10=5438.4036m,L11=5487.0595m,L12=8884.5594m,L13=7228.3699m(2)P1,P2,P3,P4,,2,1,,;2,,,2:1:113,L1=5760.706m,L2=5187.342m,L3=7838.880m,L4=5483.158m,L5=5731.788m,L6=8720.162m,L7=5598.570m,L8=7494.881m,L9=7493.323m,L10=5438.382m,L11=5487.073m,L12=8884.587m,L13=7228.367m2:113,L1=5761.706m,L2=5186.342m,L3=7837.880m,L4=5484.158m,L5=5730.788m,L6=8721.162m,L7=5597.570m,L8=7493.881m,L9=7492.323m,L10=5437.382m,L11=5488.073m,L12=8883.587m,L13=7229.367m52,:(/m)21212P148580.274048580.274148580.275148580.273448580.273960500.498060500.498260500.497160500.498160500.4979P248681.389048681.388948681.390048681.388948681.389155018.290055018.290255018.291155018.290155018.2987P343767.188043767.187943767.188943767.188143767.188157968.614057968.614057968.613157968.613957968.6142P440843.318040843.317840843.316940843.317940843.318264867.981064867.980864867.980964867.980764867.9813:(1)1011mm,21mm2,:,,,,(2)12011mm:,,,,6,,,,,,,,,,,[1]..:,1996.[2],..,1996.5,213[3]..,1993.9,243[4]M.WeiG.Majda,Ontheaccuracyoftheleastsquaresandthetotalleastsquaresmehtods,Number.Math,1994,267278[5],.TLSLS.,2003.11,254[6]..:,1994.(95)67©1994-2009ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[1].,:,1991[2].,:,1995[3].Excel2000,:,1999CalculateandOutputSectionDatainExcelAutomaticlyBieJianXiao(WuhanMunicipalEngineeringDesign&ResearchInstituteco.ltd,Wuhan430015,China)Abstract:Insurveyingsectiondataweusuallysurveysuperelevationbylevellinginstrumentandlevellingstaff,measuredistancebybandtape,andcalculatesectiondataonreadingsandbackelevation.Finallyweneedtoinputsec2tiondatatoelectronicfileinfixedform.Inthecourseofcalculatingandinputtingitnotonlymakesmistakesinfigureandform,butalsoinefficient.Thispaperexplainshowtomakeatemplateinexceltocalculateandoutputsectiondataauto2maticly,thustheaboveproblemcanbesettled.Keywords:Excel;sectiondata;calculate;output(76)OntheComparativeStudyofLSandTLSWanBaoFeng,ChengXinWen,OuLong(InstituteofEngineering,ChinaUniversityofGeosciences,Wuhan430074,China)Abstract:Thetotalleastsquares(TLS),whichisakindofdataprocessingmethoddevelopedinrecentyears,hasalreadycausedoftheattentionofvariousfieldsspecialist,butthearticleabouttheapplicationoftotalleastsquaresmeth2odinadjustmenthasbeenseldomseen.Thetotalleastsquaresmethodcantakeboththeerrorsofcoefficientmatrixandtheerrorsofmeasurementsintoconsideration,soitcanmakeadjustmentmoreaccurate,reliabilityhigher.Thistexthasintroducedthebasicprinciplesofleastsquaresandtotalleastsquaresseparatelyatfirst,thendesignedtwokindsofschemesnamelyunderthesituationthattheerrorofthecoefficientmatrixisverylittleandgreater,thendealtwithtwokindsofschemeswithleastsquaresandtotalleastsquaresseparately.Atlasttheconclusionis:inthesituationthatthecoefficientmatrixerrorisverylittle,twokindsofmethodsbothcanreachtheprecisiontorequire,andinthesituationthatthecoefficientmatrixerrorisbigger,totalleastsquarescanreachtheprecisiontorequire,leastsquarescannotreachtherequirementofprecision.Inaword,totalleastsquaresisbetterthanleastsquares.Keywords:Totalleastsquares;Singularvaluedecomposition;LeastsquaresCoefficientmatrix591Excel