顾及框架点坐标误差的三维基准转换严密模型

曾安敏; 明锋

doi:10.11947/j.AGCS.2017.20160295

测绘学报 >

2017 , Vol. 46 >Issue 1: 16 - 25

DOI: https://doi.org/10.11947/j.AGCS.2017.20160295

大地测量学与导航

顾及框架点坐标误差的三维基准转换严密模型

曾安敏 ,
明锋

展开

1. 地理信息工程国家重点实验室, 陕西西安 710054;
2. 信息工程大学地理空间信息学院, 河南郑州 450001

曾安敏(1972-),男,博士生,副研究员,主要从事动态大地测量数据处理。E-mail:Zeng_anmin@163.com

收稿日期: 2016-06-14

修回日期: 2016-11-30

网络出版日期: 2017-02-06

基金资助

国家重点研发计划（2016YFB0501701）；国家863计划（2013AA122501）；国家自然科学基金（41474015；41604013；41574003；41374019；41374003；41274040）

收起

The Rigorous Model for Similarity Transformation under Intra-frame and Inter-frame Covariance

ZENG Anmin ,
MING Feng

Expand

1. State Key Laboratory of Geo-information Engineering, Xi'an 710054, China;
2. Institute of Geospatial Information, Information Engineering University, Zhengzhou 450001, China

Received date: 2016-06-14

Revised date: 2016-11-30

Online published: 2017-02-06

Supported by

The National Key Research and Development Program of China (No.2016YFB0501701);The National High-tech Research and Development Program of China (863 Program) (No. 2013AA122501);The National Natural Science Foundation of China (Nos.41474015;41604013;41574003;41374019;41374003;41274040)

Fold

摘要

框架点坐标是由观测数据通过平差得到的，不可避免地受到观测误差的影响。针对原框架和目标框架坐标均存在误差、非公共点与公共点间存在相关性，以及转换系数矩阵中仅部分元素存在误差的实际情况，提出了同时考虑框架内误差以及转换点间相关性的基准转换严密模型，该模型将公共点和非公共点联合处理，同时计算坐标转换参数和所有点的坐标转换值，推导出了新的严格坐标转换公式，该公式为传统坐标转换公式基础上增加一改正量的形式；进一步，推导了原框架和目标框架坐标的方差不一致情况下的坐标转换模型的自适应解法；最后，利用“陆态网络工程”2000个区域站的实测坐标进行坐标转换验证，结果表明，这种严密模型较传统坐标转换模型具有更高的坐标转换精度。

关键词： 坐标转换; 相似变换; 自适应估计; 联合统一模型; 框架协方差

本文引用格式

曾安敏 , 明锋 . 顾及框架点坐标误差的三维基准转换严密模型[J]. 测绘学报, 2017 , 46(1) : 16 -25 . DOI: 10.11947/j.AGCS.2017.20160295

Abstract

The coordinates are obtained from observations by using least-squares method, so their precision should be contaminated by observation errors and the covariance also exists between common points and non-common points. The coordinate errors don't only exist in the initial frame but also in the target frame. But the classical stepwise approach for coordinate frame transformation usually takes the coordinate errors of the initial frame into account and overlooks the stochastic correlation between common points and non-common points. A new rigorous unified model is proposed for coordinate frame transformation that takes into account both the errors of all coordinates in both fame and inter-frame coordinate covariance between common points and non-common points, and the corresponding estimator for the transformed coordinates are derived and involve appropriate corrections to the standard approach, in which the transformation parameters and the transformed coordinates for all points are computed in a single-step least squares approach. The inter frame coordinate covariance should be consistent to their uncertainties, but in practice their uncertainties are not consistent. To balance the covariance matrices of both frames, a new adaptive estimator for the unified model is thus derived in which the corresponding adaptive factor is constructed by the ratio computed by Helmert covariance component estimation, reasonable and consistent covariance matrices are arrived through the adjustment of the adaptive factor. Finally, an actual experiments with 2000 points from the crustal movement observation network of China (abbreviated CMONOC) is carried out to verify the implement of the new model, the results show that the proposed model can significantly improve the precision of the coordinate transformation.

Key words： coordinate transformation; similarity transformation; adaptive estimation; unified rigorous model; intra-frame and inter-frame covariance

参考文献

[1] 朱华统,杨元喜,吕志平.GPS坐标系统的变换[M].北京:测绘出版社,1994. ZHU Huatong,YANG Yuanxi,LV Zhiping.Transformation of GPS Datum[M].Beijing:Press of Surveying and Mapping,1994.
[2] YANG Y,SONG L,XU T.Robust Estimator for Correlated Observations Based on Bifactor Equivalent Weights[J].Journal of Geodesy,2002,76(6-7):353-358.
[3] YANG Y.Robust Estimation of Geodetic Datum Transformation[J].Journal of Geodesy,1999,73(5):268-274.
[4] 沈云中,胡雷鸣,李博峰.Bursa模型用于局部区域坐标变换的病态问题及其解法[J].测绘学报,2006,35(2):95-98. SHEN Yunzhong,HU Leiming,LI Bofeng.Ill-posed Problem in Determination of Coordinate Transformation Parameters with Small Area's Data Based on Bursa Model[J].Acta Geodaetica et Cartographica Sinica,2006,35(2):95-98.
[5] 陈义,沈云中,刘大杰.适用于大旋转角的三维基准转换的一种简便模型[J].武汉大学学报(信息科学版),2004,29(2):1101-1105. CHEN Yi,SHEN Yunzhong,LIU Dajie.A Simplified Model of Three Dimensional-datum Transformation Adapted to Big Rotation Angle[J].Geomatics and Information Science of Wuhan University,2004,29(2):1101-1105.
[6] ABOU-BEIH O M,AL-GARNI A M.Precise Geodetic Positioning Based on the Concept of Variable Datum Transformation Parameters[J].Australian Surveyor,1996,41(3):214-220.
[7] 熊介,杨元喜.三维大地网的转换与变形[J].测绘学报,1988,17(1):1-8. XIONG Jie,YANG Yuanxi.On the Transformation and Deformation of Three-dimensional Geodetic Network[J].Acta Geodaetica et Cartographica Sinica,1988,17(1):1-8.
[8] 杨元喜,徐天河.不同坐标系综合变换法[J].武汉大学学报(信息科学版),2001,26(6):509-513. YANG Yuanxi,XU Tianhe.The Combined Method of Datum Transformation between Different Coordinate Systems[J].Geomatics and Information Science of Wuhan University,2001,26(6):509-513.
[9] 曾安敏,张丽萍.顾及随机误差和局部变形误差的坐标组合转换法[J].大地测量与地球动力学,2012,32(2):120-123,127. ZENG Anmin,ZHANG Liping.Combined Method for Datum Transformation Considering Stochastic Error and Local Deformation[J].Journal of Geodesy and Geodynamics,2012,32(2):120-123,127.
[10] YOU R J,HWANG H W.Coordinate Transformation Between Two Geodetic Datums of Taiwan by Least-squares Collocation[J].Journal of Surveying Engineering,2006,132(2):64-70.
[11] 曾安敏.基于拟合推估的1980西安坐标系到2000国家坐标系的变换[J].大地测量与地球动力学,2008,28(5):157-160. ZENG Anmin.Transformation from 1980 Xi'an Coordinate System to 2000 Chinese Coordinate System Based on Collocation[J].Journal of Geodesy and Geodynamics,2008,28(5):157-160.
[12] 周江文.拟合推估新解之一——两步解法[J].测绘学报,2002,31(3):189-191. ZHOU Jiangwen.A Two Steps Solution of Collocation[J].Acta Geodaetica et Cartographica Sinica,2002,31(3):189-191.
[13] 杨元喜,刘念.拟合推估两步极小解法[J].测绘学报,2002,31(3):192-195. YANG Yuanxi,LIU Nian.A New Resolution of Collocation by Two Minimization Steps[J].Acta Geodaetica et Cartographica Sinica,2002,31(3):192-195.
[14] 杨元喜,张菊清,张亮.基于方差分量估计的拟合推估及其在GIS误差纠正的应用[J].测绘学报,2008,37(2):152-157. YANG Yuanxi,ZHANG Juqing,ZHANG Liang.Variance Component Estimation Based Collocation and Its Application in GIS Error Fitting[J].Acta Geodaetica et Cartographica Sinica,2008,37(1):152-157.
[15] YANG Y,HE H,XU T.Adaptively Robust Filtering for Kinematic Geodetic Positioning[J].Journal of Geodesy,2001,75(2-3):109-116.
[16] YANG Yuanxi,XU Tianhe.An Adaptive Kalman Filter Based on Sage Windowing Weights and Variance Components[J].The Journal of Navigation, 2003,56(2):231-240.
[17] YANG Y,ZENG A,ZHANG J.Adaptive Collocation with Application in Height System Transformation[J].Journal of Geodesy,2009,83(5):403-410.
[18] 曾安敏,张丽萍,吴富梅,等.XAS80到CGCS2000坐标转换的自适应拟合推估算法[J].武汉大学学报(信息科学版),2012,37(12):1434-1437. ZENG Anmin,ZHANG Liping,WU Fumei,et al.Adaptive Collocation Method to Coordinate Transformation from XAS80 to CGCS2000[J].Geomatics and Information Science of Wuhan University,2012,37(12):1434-1437.
[19] 袁庆,楼立志,陈玮娴.加权总体最小二乘在三维基准转换中的应用[J].测绘学报,2011,40(S):115-119. YUAN Qing,LOU Lizhi,CHEN Weixian.The Application of the Weighted Total Least-squares to Three Dimensional-datum Transformation[J].Acta Geodaetica et Cartographica Sinica,2011,40(S):115-119.
[20] 方兴,曾文宪,刘经南,等.三维坐标转换的通用整体最小二乘算法[J].测绘学报,2014,43(11):1139-1143,DOI:10.13485/j.cnki.11-2089.2014.0193. FANG Xing,ZENG Wenxian,LIU Jingnan,et al.A General Total Least Squares Algorithm for Three Dimensional Coordinate Transformations[J].Acta Geodaetica et Cartographica Sinica,2014,43(11):1139-1143,DOI:10.13485/j.cnki.11-2089.2014.0193.
[21] 陈义,陆珏.以三维坐标转换为例解算稳健总体最小二乘方法[J].测绘学报,2012,41(5):715-722. CHEN Yi,LU Jue. Performing 3D Similarity Transformation by Robust Total Least Squares[J].Acta Geodaetica et Cartographica Sinica,2012,41(5):715-722.
[22] 姚宜斌,孔建.顾及设计矩阵随机误差的最小二乘组合新解法[J].武汉大学学报(信息科学版),2014,39(9):1028-1032. YAO Yibin,KONG Jian.A New Combined LS Method Considering Random Errors of Design Matrix[J].Geomatics and Information Science of Wuhan University,2014,39(9):1028-1032.
[23] 姚宜斌,黄书华,张良,等.求解三维坐标转换参数的整体最小二乘新方法[J].武汉大学学报(信息科学版),2015,40(7):853-857. YAO Yibin,HUANG Shuhua,ZHANG Liang, et al.A New Method of TLS for Solving the Parameters of Three-dimensional Coordinate transformation[J].Geomatics and Information Science of Wuhan University,2015,40(7):853-857.
[24] 孔建,姚宜斌,吴寒.整体最小二乘的迭代解法[J].武汉大学学报(信息科学版),2010,35(6):711-714. KONG Jian,YAO Yibin,WU Han.Iterative Method for Total Least-squares[J].Geomatics and Information Science of Wuhan University,2010,35(6):711-714.
[25] SHEN Yunzhong,LI Bofeng,CHEN Yi.An Iterative Solution of Weighted Total Least-squares Adjustment[J].Journal of Geodesy,2011,85(4):229-238.
[26] SHEN Y Z,CHEN Y,ZHANG D H.A Quaternion-based Geodetic Datum Transformation Algorithm[J].Journal of Geodesy,2006,80(5):233-239.
[27] KOTSAKIS C,VATALIS A,SANSò F.On the Importance of Intra-frame and Inter-frame Covariances in Frame Transformation Theory[J].Journal of Geodesy,2014,88(12):1187-1201.
[28] 李微晓,沈云中,李博峰.顾及2套坐标误差的三维坐标变换方法[J].同济大学学报(自然科学版),2011,39(8):1243-1246. LI Weixiao,SHEN Yunzhong,LI Bofeng.Three-dimensional Coordinate Transformation with Consideration of Coordinate Errors in Two Coordinate Systems[J].Journal of Tongji University (Natural Science),2011,39(8):1243-1246.
[29] 李博峰,沈云中,李微晓.无缝三维基准转换模型[J].中国科学:地球科学,2012,42(7):1047-1054. LI Bofeng,SHEN Yunzhong,LI Weixiao.The Seamless Model for Three-dimensional Datum Transformation[J].Science China Earth Science,2012,55(12):2099-2108.
[30] 李博峰.无缝仿射基准转换模型的方差分量估计[J].测绘学报,2016,45(1):30-35,DOI:10.11947/j.AGCS.2016.20140676. LI Bofeng.Variance Component Estimation in the Seamless Affine Transformation Model[J].Acta Geodaetica et Cartographica Sinica,2016,45(1):30-35,DOI:10.11947/j.AGCS.2016.20140676.
[31] BLEWITT G.GPS Data Processing Methodology[C]//TEUNISSEN P J G,KLEUSBERG A.GPS for Geodesy.2nd ed.Berlin:Springer,1998:231-270.

Options

文章导航

模态框（Modal）标题

摘要

本文引用格式

Abstract

参考文献