大角度三维基准转换的解析封闭解

doi:10.11947/j.AGCS.2016.20150108

测绘学报 ›› 2016, Vol. 45 ›› Issue (3): 267-273.doi: 10.11947/j.AGCS.2016.20150108

大角度三维基准转换的解析封闭解

李博峰, 黄善琪

同济大学测绘与地理信息学院, 上海 200092

收稿日期:2015-03-02 修回日期:2015-05-25 出版日期:2016-03-20 发布日期:2016-03-25
作者简介:李博峰(1983-),男,博士,教授,研究方向为多频多模GNSS数据处理理论及应用新技术。
基金资助:
国家自然科学基金(41374031;41574023);地理信息工程国家重点试验室开放研究基金(SKLGIE2013-M-2-2);测绘地理信息公益性行业科研专项经费(HY14122136)

Analytical Close-form Solutions for Three-dimensional Datum Transformation with Big Rotation Angles

LI Bofeng, HUANG Shanqi

College of Surveying and Geo-informatics, Tongji University, Shanghai 200092, China

Received:2015-03-02 Revised:2015-05-25 Online:2016-03-20 Published:2016-03-25
Supported by:
The National Natural Science Foundation of China(Nos.41374031;41574023);Open Research Fund of the State Key Laboratory of Geo-information Engineering(No.SKLGIE2013-M-2-2);China Special Fund for Surveying, Mapping and Geo-information Research in the Public Interest(No.HY14122136)

摘要/Abstract

摘要： 传统大地测量应用中的基准转换往往涉及小角度旋转,可只考虑旋转角的一阶量采用线性化方法求解。现代空间测量技术成果应用的基准转换涉及大角度旋转,通过将旋转矩阵所有元素作为未知数并利用旋转矩阵正交条件采用附约束条件平差法迭代求解。本文以空间三维基准转换为例,采用多元模型的矩阵形式将多点坐标组成矩阵处理,并利用旋转矩阵的正交条件导出了大角度三维基准转换的解析分步解。同时引入两套公共点坐标误差对传统三维基准转换模型扩展,导出了同时顾及两套公共点坐标误差的大角度三维基准转换模型的解析解。试验表明:给出的大角度三维基准转换解析解能在实现与传统迭代解等效转换结果的同时,有效避免复杂耗时的迭代计算,提高计算效果。

关键词: 三维基准变换, 大旋转角, 布尔沙模型, EIV模型

Abstract: The small rotation angles are typically involved in the traditional geodetic datum transformation, for which one can iteratively solve for its linearized model with ignoring its second-smaller terms. However, the big rotation angles are introduced to transform the outcomes from the advanced space surveying techniques. For this transformation model with big rotation angles, all elements of rotation matrix are usually parameterized as unknown parameters and then solved with the constrained adjustment theory by using the orthogonal condition of rotation matrix. With three-dimensional datum transformation with big rotation angles as example, this paper derives the analytical close-form solutions by formularizing the coordinates of multi-points as a matrix and using the orthogonal condition of rotation matrix. Expanding the transformation model with introducing the errors to common points of both datum, we derive out its analytical solutions as well. The results of simulation computations show that the presented three-dimensional datum transformation can realize the comparable transformation result while the new method can outcome the complicated and time-consuming iterations, therefore improving the computation efficiency.

Key words: three-dimension datum transformation, big rotation angle, Bursa model, error-in-variables(EIV) model

中图分类号:

P223

李博峰, 黄善琪. 大角度三维基准转换的解析封闭解[J]. 测绘学报, 2016, 45(3): 267-273.

LI Bofeng, HUANG Shanqi. Analytical Close-form Solutions for Three-dimensional Datum Transformation with Big Rotation Angles[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(3): 267-273.

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大角度三维基准转换的解析封闭解

Analytical Close-form Solutions for Three-dimensional Datum Transformation with Big Rotation Angles

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