| 三维坐标转换的非线性Gauss-Helmert模型及其解法 |
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| 引用本文： | 刘春阳,刘超.三维坐标转换的非线性Gauss-Helmert模型及其解法[J].测绘科学,2017,42(5). |
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| 作者姓名： | 刘春阳 刘超 |
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| 作者单位： | 安徽理工大学 测绘学院,安徽 淮南,232001 |
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| 基金项目： | 国家自然科学基金项目，中国博士后科学基金项目，安徽理工大学科研启动基金项目 |
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| 摘 要： | 针对传统的三维坐标转换模型局限于求解小旋转角的三维坐标转换参数的缺点,以及没有同时顾及观测向量和系数矩阵的随机误差,该文提出了一种新的三维坐标转换参数求解模型。基于非线性Gauss-Helmert模型,建立了三维坐标转换的Bursa-Wolf模型,采用Newton-Gauss迭代算法,构建了加权整体最小二乘问题的拉格朗日函数,并给出了该算法的具体推导过程及其精度评定公式。实测数据和仿真数据结果表明:新算法在无须假设条件的前提下,可以获得任意旋转角下的坐标转换参数,且待估参数数目大大降低,易于程序实现。
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| 关 键 词： | 三维坐标转换 Gauss-Helmert模型 整体最小二乘 Bursa-Wolf模型 |
Nonlinear Gauss-Helment model and its solution for 3D coordinate transformation |
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| LIU Chunyang,LIU Chao.Nonlinear Gauss-Helment model and its solution for 3D coordinate transformation[J].Science of Surveying and Mapping,2017,42(5). |
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| Authors: | LIU Chunyang LIU Chao |
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| Abstract: | In view of the traditional three dimensional coordinate transformation model limited to solve the small rotation angle of the three dimensional coordinate conversion parameters without considering the random errors and gross errors in the observation vector and the coefficient matrix.A three dimensional coordinate transformation method of Bursa-Wolf model on the nonlinear Gauss Helmert model was proposed in the paper.Then,a Lagrange function of weight total least squares by using Newton-Gauss iterative algorithm was constructed,the detailed derivation process and its precision evaluation formula were put forward for the proposed method simultaneously.Experiment results showed that the proposed method can obtain the coordinate transformation parameters on any rotation angles without any assumed conditions.Meanwhile,the number of the estimated parameters reduced significantly,and the new method can be programmed easily. |
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| Keywords: | 3D coordinate transformation Gauss-Helmert model total least squares Bursa-Wolf model |
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