Application of Posteriori Estimation of a Stochastic Model on the Weighted Total Least Squares Problem

WANG Leyang; XU Guangyu

doi:10.13203/j.whugis20140275

Volume 41 Issue 2

Feb. 2016

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Geomatics and Information Science of Wuhan University > 2016 > 41(2): 255-261. > DOI: 10.13203/j.whugis20140275

WANG Leyang, XU Guangyu. Application of Posteriori Estimation of a Stochastic Model on the Weighted Total Least Squares Problem[J]. Geomatics and Information Science of Wuhan University, 2016, 41(2): 255-261. DOI: 10.13203/j.whugis20140275

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Application of Posteriori Estimation of a Stochastic Model on the Weighted Total Least Squares Problem

WANG Leyang^1,2,
XU Guangyu^1,3

1.
Application of Posteriori Estimation of a Stochastic Model on the Weighted Total Least Squares Problem1 Faculty of Geomatics, East China Institute of Technology, Nanchang 330013, China;
2.
Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, Nanchang 330013, China;
3.
School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China

Funds: The Project of Key Laboratory of Mapping from Space, NASG(K201502);The National Natural Science Foundation of China, Nos.41204003, 41161069, 41304020;National Department Public Benefit Research Foundation (Surveying,Mapping and Geoinformation), No. 201512026;Science and Technology Project of the Education Department of Jiangxi Province, Nos. KJLD12077, KJLD14049;The Project of Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, No.WE2015005;Scientific Research Foundation of ECIT, No. DHBK201113.

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Received Date: February 28, 2015
Published Date: February 04, 2016

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Abstract

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.
- weighted total least squares,
- variance components,
- line fitting,
- posteriori estimation

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