Application of posteriori estimation of a stochastic model on the weighted total least squares problem

被引：0
|
作者：
Wang L. [1 ,2 ]
Xu G. [1 ,3 ]
机构：
[1] Faculty of Geomatics, East China Institute of Technology, Nanchang
[2] Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, Nanchang
[3] School of Geodesy and Geomatics, Wuhan University, Wuhan
来源：
Wuhan Daxue Xuebao (Xinxi Kexue Ban)/Geomatics and Information Science of Wuhan University | 2016年 / 41卷 / 02期
关键词：
Line fitting; Posteriori estimation; Variance components; Weighted total least squares;
D O I：
10.13203/j.whugis20140275
中图分类号：
学科分类号：
摘要：
Considering the situation that the weight matrix of observation vector and coefficient matrix may be inaccurate, an available algorithm is introduced in this paper, which is derived on the basis of combining the Helmert variance component estimation with a kind of fast weighted total least squares algorithm in the errors-in-variables models. And the derivative process of the fast weighted total least squares is described in detail and the comparison with three other algorithms is implemented in this paper. Using the fast weighted total least squares algorithm combining Helmert variance component estimation derived in this paper, the stochastic model and the unknown parameters of the functional model can be solved simultaneously. Three empirical examples, two straight line fitting and one linear parameter estimation, are also used to investigate the application of posteriori estimation of stochastic model on weighted total least squares problem. Results show that the algorithm is very effective. © 2016, Wuhan University. All right reserved.
引用
收藏
页码：255 / 261
页数：6
相关论文
共 13 条
  • [1] Schaffrin B., Wieser A., On Weighted Total Least-squares Adjustment for Linear Regression, Journal of Geodesy, 82, 7, pp. 415-421, (2008)
  • [2] Mahboub V., On Weighted Total Least-squares for Geodetic Transformations, Journal of Geodesy, 86, 5, pp. 359-367, (2012)
  • [3] Amiri-Simkooei A.R., Jazaeri S., Weighted Total Least Squares Formulated by Standard Least Sq-uares Theory, Journal of Geodetic Science, 2, 2, pp. 113-124, (2012)
  • [4] Cui X., Yu Z., Tao B., Et al., Generalized Surveying Adjustment (New Edition), (2005)
  • [5] Liu Z., Zhang S., Variance-covariance Component Estimation Method Based on Generalization Adjustment Factor, Geomatics and Information Science of Wuhan University, 38, 8, pp. 925-929, (2013)
  • [6] Wang L., Xu C., Zhang C., A Two-step Method to Determine Relative Weight Ratio Factors in Joint Inversion, Acta Geodaetica et Cartographica Sinica, 41, 1, pp. 19-24, (2012)
  • [7] Amiri-Simkooei A.R., Application of Least Squares Variance Component Estimation to Errors-in-Variables Models, Journal of Geodesy, 87, 10-12, pp. 935-944, (2013)
  • [8] Xu P., Liu J., Variance Components in Errors-in-Variables Models: Estimability, Stability and Bias Analysis, Journal of Geodesy, 88, 8, pp. 719-734, (2014)
  • [9] Neri F., Saitta G., Chiofalo S., An Accurate and Straightforward Approach to Line Regression Analysis of Error-affected Experimental Data, Journal of Physics E: Scientific Instruments, 22, 4, pp. 215-217, (1989)
  • [10] Wang L., Research on Theory and Application of Total Least Squares in Geodetic Inversion, (2011)
12