Variance component estimation for partial errors-in-variables models

详细信息    查看全文

• 作者：Leyang Wang ; Guangyu Xu
• 关键词：partial errors ; in ; variables model ; variance component estimation ; straight ; line fitting ; coordinate transformation
• 刊名：Studia Geophysica et Geodaetica
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：60
• 期：1
• 页码：35-55
• 全文大小：375 KB
• 参考文献：Adcock R.J., 1877. Note on the method of least squares. Analyst, 4, 183–184.CrossRef
  Amiri-Simkooei A.R. and Jazaeri S., 2012. Weighted total least squares formulated by standard least squares theory. J. Geod. Sci., 2, 113–124.
  Amiri-Simkooei A.R., 2013. Application of least squares variance component estimation to errorsin-variables models. J. Geodesy, 87, 935–944.CrossRef
  Amiri-Simkooei A.R. and Jazaeri S., 2013. Data-snooping procedure applied to errors-in-variables models. Stud. Geophys. Geod., 57, 426–441, DOI: 10.1007/s11200-012-0474-2.CrossRef
  Choi Y.J., Kim J.Y. and Sumg K.M., 1997. A robust algorithm of total least squares method. IEICE Trans. Fundam., 80, 1336–1339.
  De Moor B., 1993. Structured total least squares and L2 approximation problems. Linear Alg. Appl., 188–189, 163–207.CrossRef
  Fang X., 2011. Weighted Total Least Squares Solutions for Applications in Geodesy. Ph.D. Thesis. Leibniz University, Hannover, Germany.
  Fang X., 2014. A structured and constrained total least-squares solution with cross-covariances. Stud. Geophys. Geod., 58, 1–16, DOI: 10.1007/s11200-012-0671-z.CrossRef
  Gleser L.J., 1981. Estimation in a multivariate “errors in variables” regression model: large sample results. Ann. Statist., 9, 24–44.CrossRef
  Golub G.H. and Van Loan C., 1980. An analysis of the total least squares problem. SIAM J. Numer. Anal., 17, 883–893.CrossRef
  Helmert F.R., 1907. Die Ausgleichungsrechnung nach der Methode der kleinsten Quadrate. 2. Auflage. B.G. Teubner, Leipzig/Berlin, Germany (in German).
  Koch K.R., 1999. Parameter Estimation and Hypothesis Testing in Linear Models. Springer Verlag, Berlin, Germany.CrossRef
  Mahboub V., 2012. On weighted total least-squares for geodetic transformations. J. Geodesy, 86, 359–367.CrossRef
  Neri F., Saitta G. and Chiofalo S., 1989. An accurate and straightforward approach to line regression analysis of error-affected experimental data. J. Phys. E: Sci. Instr., 22, 215–217.CrossRef
  Rao C.R., 1971. Estimation of variance and covariance components- MINQUE theory. J. Multivar. Anal., 1, 257–275.CrossRef
  Schaffrin B. and Wieser A., 2008. On weighted total least-squares adjustment for linear regression. J. Geodesy, 82, 415–421.CrossRef
  Shen Y.Z., Li B.F. and Chen Y., 2011. An iterative solution of weighted total least-squares adjustment. J. Geodesy, 85, 229–238.CrossRef
  Sprent P., 1969. Models in Regression and Related Topics. Methuen, London, U.K.
  Teunissen P.J.G., 1984. A note on the use of Gauss’ formulas in non-linear geodetic adjustment. Stat. Descisions, 2, 455–466.
  Teunissen P.J.G., 1985. The Geometry of Geodetic Inverse Linear Mapping and Nonlinear Adjustment. Publications on Geodesy, New Series, 8(1). Netherlands Geodetic Commission, Delft, The Netherlands, 186 pp.
  Teunissen P.J.G., 1988. The nonlinear 2D symmetric Helmert transformation: an exact nonlinear least-squares solution. Bull. Geod., 62, 1–15.CrossRef
  Teunissen P.J.G., 1990. Nonlinear least-squares. Manus. Geod., 15, 137–150.
  Teunissen P.J.G. and Amiri-Simkooei A.R., 2008. Least-squares variance component estimation. J. Geodesy., 82, 65–82.CrossRef
  Wang L.Y., 2012. Research on theory and application of total least squares in geodetic inversion. Acta Geodaetica et Cartographica Sinica, 41, 629 (in Chinese).
  Wang L.Y., Xu C.J. and Lu T.D., 2010. Ridge estimation method in ill-posed weighted total least squares adjustment. Geomat. Inf. Sci. Wuhan Univ., 35, 1346–1350 (in Chinese with English Abstract).
  Wang L.Y. and Xu C.J., 2011. Total least squares adjustment with weight scaling factor. Geomat. Inf. Sci. Wuhan Univ., 36, 887–890 (in Chinese with English Abstract).
  Wang L.Y. and Xu C.J., 2013. Progress in total least squares. Geomat. Inf. Sci. Wuhan Univ., 38, 850–856 (in Chinese with English Abstract).
  Wang L.Y. and Yu D.D., 2014. Virtual observation method to ill-posed total least squares problem. Acta Geodaetica et Cartographica Sinica, 43, 575–581 (in Chinese with English Abstract).
  Welsch W., 1978. A posteriori Varianzenschatzung nach Helmert. Allgemeine Vermessungs-Nachrichten, 85, 55–63 (in German).
  Xu P.L., Liu J.N. and Shi C., 2012. Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis. J. Geodesy, 86, 661–675.CrossRef
  Xu P.L. and Liu J.N., 2014. Variance components in errors-in-variables models: estimability, stability and bias analysis. J. Geodesy, 88, 719–734.CrossRef
  Yu Z.L. and Chen H.M., 1989. On the accuracy evaluation in variance components estimation. Acta Geodaetica et Cartographica Sinica, 18, 219–226 (in Chinese with English Abstract).
  Zhang S.L., Tong X.H. and Zhang K., 2013. A solution to EIV model with inequality constraints and its geodetic applications. J. Geodesy, 87, 23–28.CrossRef
  Zhou Y.J., Kou X.Z., Zhu J.J., and Li J., 2014. A Newton algorithm for weighted total least-squares solution to a specific errors-in-variables model with correlated measurements. Stud. Geophys. Geod., 58, 349–375.CrossRef
  
• 作者单位：Leyang Wang (1) (2) (3)
  Guangyu Xu (1) (2) (3)
  
  1. Faculty of Geomatics, East China University of Technology, 330013, Nanchang, China
  2. Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, 330013, Nanchang, China
  3. Jiangxi Province Key Lab for Digital Land, 330013, Nanchang, China
  
• 刊物类别：Earth and Environmental Science
• 刊物主题：Earth sciences
  Geophysics and Geodesy
  Structural Geology
  Meteorology and Climatology
  
• 出版者：Springer Netherlands
• ISSN：1573-1626

文摘

An iterative algorithm for variance component estimation based on partial errors-invariables (PEIV) model is proposed. Correction of observation vector and random elements of the coefficient matrix is taken as one kind of posterior information. Variance components in the observation vector and the random elements of the coefficient matrix are estimated according to Helmert estimation method. During the estimating process, the correction factors are used to modify the initial weight matrix, so as to make it more accurate. At the same time, a method for determining correction factors is given. Through examples of linear fitting and numerical simulation experiment of coordinate transformation, the practical effect of this algorithm is verified. Keywords partial errors-in-variables model variance component estimation straight-line fitting coordinate transformation