| 应用设计矩阵求解不同坐标系统转换下的参数问题 |
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| 引用本文： | 韩笑,蒲英霞.应用设计矩阵求解不同坐标系统转换下的参数问题[J].地理信息世界,2017,24(1). |
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| 作者姓名： | 韩笑 蒲英霞 |
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| 作者单位： | 1. 南京大学地理与海洋科学学院,江苏南京,210023;2. 江苏省地理信息技术重点实验室,江苏南京,210023 |
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| 摘 要： | 不同坐标系统和空间基准的转换已经被广泛研究,为了将不同的坐标变换方法联系起来,引用设计矩阵的概念,基于最小二乘法推导了坐标变换统一的参数估计表达式,给出了二维和三维空间坐标系统下常用变换方法的设计矩阵。随后通过北京1954和西安1980、西安1980和CGCS 2000的坐标转换实例,计算了相似变换、仿射变换和七参数相似变换的参数值,并将这些参数应用于其他控制点,比较计算值与真实值的均方根误差,有效验证了引用设计矩阵的合理性,简化了计算过程。
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| 关 键 词： | 坐标转换 最小二乘法 设计矩阵 变换参数 |
Application of Design Matrix to Solve the Parametric Problems under Different Coordinate Transformations |
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| HAN Xiao,PU Yingxia.Application of Design Matrix to Solve the Parametric Problems under Different Coordinate Transformations[J].Geomatics World,2017,24(1). |
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| Authors: | HAN Xiao PU Yingxia |
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| Abstract: | Transformations under different coordinate systems and spatial references have been studied extensively.In order to make the connection between different coordinate transformation methods,this paper introduces the concept of the design matrix,and derives the uniform expression of parameter estimation of coordinate transformation based on the least square method.The design matrices of common transformation methods in 2D and 3D coordinate system are set forth.Taking the transformation between Beijing 54 and Xi'an 80,CGCS2000 and Xi'an 80 as an example,parameters of similarity transformation,affine transformation and seven-parameter similarity transformation are calculated.By applying these parameters into other control points and comparing the computing results to real values,the rationality of introducing design matrix is verified and the calculation process of coordinate transformation is simplified. |
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| Keywords: | coordinate transformation least square method design matrix transformation parameters |
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