Acta Geodaetica et Cartographica Sinica >

2015 , Vol. 44 >Issue 8: 866 - 876

DOI: https://doi.org/10.11947/j.AGCS.2015.20130701

Complex Total Least Squares Adjustment

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  • 1. Faculty of Geomatics, East China Institute of Technology, Nanchang 330013, China;
    2. Jiangxi Province Key Laboratory for Digital Land, Nanchang 330013, China;
    3. Key Laboratory of Watershed Ecology and Geographical Environment Monitoring, NASG, Nanchang 330013, China

Received date: 2013-10-02

  Revised date: 2014-12-25

  Online published: 2015-09-02

Supported by

The National Natural Science Foundation of China(Nos.41204003;41161069;41304020);Natural Science Foundation of Jiangxi Province(No.20132BAB216004);Science and Technology Project of the Education Department of Jiangxi Province(Nos.GJJ13456;KJLD12077;KJLD14049);Key Laboratory of Geo-informatics of State Bureau of Surveying and Mapping(No.201308);The National Department Public Benefit Research Foundation(Surverying, Mapping and Geoinfor mation)(No.201512026) Scientific Research Foundation of ECIT(No.DHBK201113)

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Abstract

On the basis of complex least squares adjustment method (CLSAM), the theory of complex total least squares adjustment method (CTLSAM) is proposed. The algorithms of complex total least squares and complex LS-TLS method are derived. Through two examples, the complex LS method under the adjustment criterions that minimize the sum of squares of the module of observation vector residual (adjustment criterion 1) and the sum of squares of the real part and imaginary part of the observation vector (adjustment criterion 2), the complex TLS method under the adjustment criterions that minimize the sum of squares of the module of observation vector and coefficient matrix residual (adjustment criterion 3)and the sum of squares of the real part and imaginary part of the observation vector and coefficient matrix residual (adjustment criterion 4) are compared and analyzed respectively. The results of two examples show that the CLSAM under the adjustment criterion 1 is more reasonable than the adjustment criterion 2; the CTLSAM under the adjustment criterion 3 is more accurate than the adjustment criterion 4; the CTLSAM under the adjustment criterion 3 is better than the CLSAM under the adjustment criterion 1 when the coefficient matrix contains stochastic noise.

Key words： complex; total least squares; mixed total least squares; least squares; adjustment criterion

Cite this article

WANG Leyang, YU Dongdong, LÜ Kaiyun . Complex Total Least Squares Adjustment[J]. Acta Geodaetica et Cartographica Sinica, 2015 , 44(8) : 866 -876 . DOI: 10.11947/j.AGCS.2015.20130701

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