Acta Geodaetica et Cartographica Sinica >

2016 , Vol. 45 >Issue 4: 411 - 417

DOI: https://doi.org/10.11947/j.AGCS.2016.20150246

A Newton Algorithm for Multivariate Total Least Squares Problems

  • WANG Leyang ,
  • ZHAO Yingwen ,
  • CHEN Xiaoyong ,
  • ZANG Deyan
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  • 1. Faculty of Geomatics, East China University of Technology, Nanchang 330013, China;
    2. Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, Nanchang 330013, China;
    3. Jiangxi Province Key Lab for Digital Land, Nanchang 330013, ChinaAbstract

Received date: 2015-05-11

  Revised date: 2015-10-12

  Online published: 2016-04-28

Supported by

The National Natural Science Foundation of China(Nos.41204003;41161069;41304020;41464001);The National Department Public Benefit Research Foundation(Surveying,Mapping and Geoinformation)(No.201512026);The Natural Science Foundation of Jiangxi Province(No.20151BAB203042);The Science and Technology Project of the Education Department of Jiangxi Province(Nos.GJJ150595;KJLD12077;KJLD14049);The Found of Key Laboratory of Watershed Ecology and Geographical Environment Monitoring(No.WE2015005);The Scientific Research Foundation of ECIT(No.DHBK201113);Innovation Fund Designated for Graduate Students of Jiangxi Province(Nos.YC2015-S266;YC2015-S267);Innovation Fund Designated for Graduate Students of ECIT(No.DHYC-2015005);The Found of the Key Laboratory of Mapping from Space, NASG(No.K201502)

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Abstract

In order to improve calculation efficiency of parameter estimation, an algorithm for multivariate weighted total least squares adjustment based on Newton method is derived. The relationship between the solution of this algorithm and that of multivariate weighted total least squares adjustment based on Lagrange multipliers method is analyzed. According to propagation of cofactor, 16 computational formulae of cofactor matrices of multivariate total least squares adjustment are also listed. The new algorithm could solve adjustment problems containing correlation between observation matrix and coefficient matrix. And it can also deal with their stochastic elements and deterministic elements with only one cofactor matrix. The results illustrate that the Newton algorithm for multivariate total least squares problems could be practiced and have higher convergence rate.

Key words： multivariate total least squares; Newton method; propagation of cofactor; affine transformation

Cite this article

WANG Leyang , ZHAO Yingwen , CHEN Xiaoyong , ZANG Deyan . A Newton Algorithm for Multivariate Total Least Squares Problems[J]. Acta Geodaetica et Cartographica Sinica, 2016 , 45(4) : 411 -417 . DOI: 10.11947/j.AGCS.2016.20150246

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