1、35 11 2010 M11qv# SGeomatics and Information Scienceof Wuhan UniversityVol.35 No. 11Nov. 2010l :2010-09-15b “ :SE1 S “(40874010); 81 S “(2007GZC0474, 2008GQC0001, 2008GZS0041);qv o bWv L i 7b “( 080104);C SE L i 7b “(TJES0802); 3Sr 8 L i 7b “(DLLJ200506)bcI|: 1671-8860( 2010)11-1351-04DS :A总体最小二乘的迭代
2、解法鲁铁定1,2 周世健1,3(1 v o S, g 56|,344000)(2 qv,q g+ 129|,430079)(3 8 S, 2 g ,330029)K 1:针对总体最小二乘解算问题,应用测量平差中的间接平差原理推导了总体最小二乘的迭代逼近解算公式,通过与奇异值分解法进行比较,得出两种解算方法具有等价性b实验数据分析验证了算法的有效性b1oM:总体最小二乘;奇异值分解;迭代算法;测量平差mEs |: P207. 2 - : V ,Y f /L ! i4_ ,7“ cb 74HqK,4_a“ V ?ibD1) LZ Z 51US52 , 9 Tb98Kl=E %$#“ , Golub
3、Lan Loan ssE3b EZ ,D4-7) 98Kl= # p5,i %US5bD8) LB98Kl= E,“ 98Kl=E V %Kl= Z_ EB5byN,98Kl= # % Ll“ c 5 C Lilb W ,e V, D7M Tb1 98Kl= ss98Kl=,f :(A+ $A)X = L+ $L ( 1)_ (_ xZ 7 :$Lvec( $A ) 00 ,2L 00 2A In= R20 In 00 Im In( 2)T,vec( #)V U Mb| T(1)V UZ T T:( A+ EA) X = L+ e ( 3)V:A+ EA L + e # X- 1 =A L +
4、 E # X- 1 = 0 ( 4)T, E= EA eb V UK Hq4 :tr(E#ET ) = tr(EAETA + eeT) =vec( EA) Tvec(EA) + eTe = min ( 5)9v, N,l,. GIS bW s eM . Z: Z S/ D,199913 , +, ZM.HMQM 98Kl=ZE J .qv# S, 2010, 35( 2) :181-18414 Strang G. Linear Algebra and Its ApplicationsM .3rd ed. San Diego: Harcourt Brace Jovanovich,198815-
5、,Z. d9M .v :v v,2005BTe: ZM, q,p V 3,1V Y ) v bE-mail:An IterativeAlgorithmforTotalLeastSquaresEstimationL U T ieding1, 2 ZH OU Shijian 1, 3(1 School of Geoscience and Surveying Engineering,East China Institute of Technology,56 Xuefu Road, Fuzhou 344000,China)(2 School of Geodesy and Geomatics,Wuhan
6、 University,129 Luoyu Road, Wuhan 430079,China)(3 Jiangxi Academy of Sciences, Shangfang Road ,Nanchang, 330029,China)Abstract: Total least squares( TLS) approach aims at estimating a matrix of parameters froma linear model when there are errors in both the observation vector L and the data matrix A
7、.The authors derivedan iterativealgorithm to solve the TLS problem by using the principleofindirect adjustment. Compared with the method based on singular-value decomposition, theiterative algorithm coincides with the SVD algorithm. The calculated example has provedthat the iterative algorithm is validity and rationality.Keywords: TLS; singular-value decomposition; iterative algorithm; surveying adjustmentAboutthefirstauthor: LUTieding, associate professor, Ph. D candidate, majors in surveying data processing and geodesy.E-mail: tdlu ecit. edu. cn1354