On total least squares for quadratic form estimation

被引：18

作者：

Fang, Xing ^{[1
]}

Wang, Jin ^{[2
]}

Li, Bofeng ^{[3
]}

Zeng, Wenxian ^{[1
]}

Yao, Yibin ^{[1
]}

机构：

[1] Wuhan Univ, Sch Geodesy & Geomat, Wuhan 430072, Peoples R China

[2] Beijing Univ Technol, Beijing Key Lab Traff Engn, Beijing, Peoples R China

[3] Tongji Univ, Coll Surveying & Geoinformat, Shanghai 200092, Peoples R China

来源：

STUDIA GEOPHYSICA ET GEODAETICA | 2015年 / 59卷 / 03期

基金：

中国国家自然科学基金;

关键词：

total least squares; quadratic forms; high power structured errors-in-variables homogeneous equation; deformation monitoring; ELLIPSES; BIAS;

D O I：

10.1007/s11200-014-0267-x

中图分类号：

P3 [地球物理学]; P59 [地球化学];

学科分类号：

0708 ; 070902 ;

摘要：

The mathematical approximation of scanned data by continuous functions like quadratic forms is a common task for monitoring the deformations of artificial and natural objects in geodesy. We model the quadratic form by using a high power structured errors-in-variables homogeneous equation. In terms of Euler-Lagrange theorem, a total least squares algorithm is designed for iteratively adjusting the quadratic form model. This algorithm is proven as a universal formula for the quadratic form determination in 2D and 3D space, in contrast to the existing methods. Finally, we show the applicability of the algorithm in a deformation monitoring.

引用

页码：366 / 379

页数：14

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