Weighted total least squares of universal EIV adjustment model

被引：0

作者：

Zeng W. ^{[1
]}

Fang X. ^{[1
]}

Liu J. ^{[1
,2
]}

Yao Y. ^{[1
]}

机构：

[1] School of Geodesy and Geomatics, Wuhan University, Wuhan

[2] Research Center of GNSS, Wuhan University, Wuhan

来源：

Cehui Xuebao/Acta Geodaetica et Cartographica Sinica | 2016年 / 45卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Nonlinear optimization; Precision; Universal EIV adjustment model; Weighted total least squares;

D O I：

10.11947/j.AGCS.2016.20150156

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper proposes the universal errors-in-variables (EIV) adjustment model based on the fundamental adjustment theory, which covers the parametric adjustment model, conditional adjustment model,conditional adjustment model with parameters and parametric adjustment model with constrains. Applying total least squares (TLS) principle, we deduce the weighted TLS (WTLS) algorithm and the approximated precision of the EIV model. The universal EIV adjustment model and its estimator of WTLS contribute to the integrity of theory of EIV model estimation. The proposed uniform WTLS algorithm is appropriate for programming in software, which can contribute to the geodetic application of the theory of the EIV model estimation. © 2016, Surveying and Mapping Press. All right reserved.

引用

页码：890 / 894and903

共 27 条

[1]

Error Theory and Foundation of Surveying Adjustment, (2003)

[2]

Van-Huffel S., Vandewalle J., The Total Least Squares Problem: Computational Aspects and Analysis, (1991)

[3]

Adcock R.J., Note on the Method of Least Squares, The Analyst, 4, 6, pp. 183-184, (1877)

[4]

Deming W.E., The Application of Least Squares, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Series 7, 11, 68, pp. 146-158, (1931)

[5]

Gerhold G.A., Least-squares Adjustment of Weighted Data to a General Linear Equation, American Journal of Physics, 37, 2, pp. 156-161, (1969)

[6]

Schaffrin B., Wieser A., On Weighted Total Least-squares Adjustment for Linear Regression, Journal of Geodesy, 82, 7, pp. 415-421, (2008)

[7]

Chen Y., Lu J., Performing 3D Similarity Transformation by Robust Total Least Squares, Acta Geodaetica et Cartographica Sinica, 41, 5, pp. 715-722, (2012)

[8]

Li B., Shen Y., Zhang X., Et al., Seamless Multivariate Affine Error-in-variables Transformation and Its Application to Map Rectification, International Journal of Geographical Information Science, 27, 8, pp. 1572-1592, (2013)

[9]

Wang L., Inversion of Crustal Strain Parameters Based on Total Least Squares, Journal of Geodesy and Geodynamics, 33, 3, pp. 106-110, (2013)

[10]

Xu P., Liu J., Shi C., Total Least Squares Adjustment in Partial Errors-in-variables Models: Algorithm and Statistical Analysis, Journal of Geodesy, 86, 8, pp. 661-675, (2012)

← 1 2 3 →