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Generalized total least squares prediction algorithm for universal 3D similarity transformation

作者:Wang, B (Wang, Bin)^{[ 1,2 ]} ; Li, JC (Li, Jiancheng)^{[ 1 ]} ; Liu, C (Liu, Chao)^{[ 3 ]} ; Yu, J (Yu, Jie)^{[ 4 ]}

ADVANCES IN SPACE RESEARCH

卷: 59

期: 3

页: 815-823

子辑: 1DOI: 10.1016/j.asr.2016.09.018

出版年: FEB 1 2017

会议名称

会议: 7th China Satellite Navigation Conference (CSNC)

会议地点: Changsha, PEOPLES R CHINA

会议日期: MAY 18-20, 2016

摘要

Three dimensional (3D) similarity datum transformation is extensively applied to transform coordinates from GNSS-based datum to a local coordinate system. Recently, some total least squares (TLS) algorithms have been successfully developed to solve the universal 3D similarity transformation problem (probably with big rotation angles and an arbitrary scale ratio). However, their procedures of the parameter estimation and new point (non-common point) transformation were implemented separately, and the statistical correlation which often exists between the common and new points in the original coordinate system was not considered. In this contribution, a generalized total least squares prediction (GTLSP) algorithm, which implements the parameter estimation and new point transformation synthetically, is proposed. All of the random errors in the original and target coordinates, and their variance-covariance information will be considered. The 3D transformation model in this case is abstracted as a kind of generalized errors-in-variables (EIV) model and the equation for new point transformation is incorporated into the functional model as well. Then the iterative solution is derived based on the Gauss-Newton approach of nonlinear least squares. The performance of GTLSP algorithm is verified in terms of a simulated experiment, and the results show that GTLSP algorithm can improve the statistical accuracy of the transformed coordinates compared with the existing TLS algorithms for 3D similarity transformation. (C) 2016 COSPAR. Published by Elsevier Ltd. All rights reserved.

作者关键词:3D similarity transformation; Errors-in-variables model; Total least squares prediction; Gauss-Newton approach

KeyWords Plus:IN-VARIABLES MODELS; 3-DIMENSIONAL DATUM TRANSFORMATION; INEQUALITY CONSTRAINTS; PARAMETERS; EQUALITY;BIAS

通讯作者地址: Wang, B (通讯作者)

地址:

电子邮件地址:[email protected]

基金资助机构授权号

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ELSEVIER SCI LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, OXON, ENGLAND

研究方向:Astronomy & Astrophysics; Geology; Meteorology & Atmospheric Sciences

Web of Science 类别:Astronomy & Astrophysics; Geosciences, Multidisciplinary; Meteorology & Atmospheric Sciences

文献类型:Article; Proceedings Paper

语种:English

入藏号: WOS:000392683400008

ISSN: 0273-1177

eISSN: 1879-1948

Impact Factor (影响因子): 1.409