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平面直角坐标正形变换简易解算方法

A simple solution method for orthomorphic transformation of plane rectangular coordinates

Geomatics Observation / 2021,3(4): 187-199 / 2021-10-29 1149 1067

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• Authors: 刘大海¹ ² 陈永红² 张 萧² 曾鄂春¹ ² 李春云² 曾庆桂²
• Information:

  1．深圳市地质局，深圳；
  2．深圳地质建设工程公司，深圳

• Keywords:
  Beijing 54 coordinates, independent coordinates; CGCS2000 coordinates; nonlinear fitting; optimization; regression analysis; Excel; 1stOpt
  北京54 坐标; CGCS2000 坐标; 回归分析; 非线性拟合; 1stOpt
• Abstract: After the full use of CGCS2000 coordinate system, it is often necessary to batch convert plane rectangular coordinates such as Beijing 54 coordinates and local independent coordinates into CGCS2000 coordinates. Coordinate transformation is divided into indirect method and direct method. The indirect method takes geodetic coordinates (B, l) as indirect parameters and converts them according to the ellipsoidal projection principle. The theory is rigorous and the conversion is accurate. The direct method is to establish the coordinate transformation equations or numerical approximation model based on the least square method according to the regional common point coordinates. Orthomorphic transformation is one of the direct methods. It has the advantages of equiangular transformation and can be used in rectangular coordinate transformation of Gaussian projection plane of the same sphere and different spheres. In this paper, a simple nonlinear fitting global optimization method and multiple linear regression analysis method are used to solve the parameters of orthomorphic transformation, and the results are the same. The method of multiple linear regression analysis is simple, the calculation is fast, and the conversion accuracy is enough to meet the needs of engineering. 在全面启用CGCS2000 坐标系后，常常需要将北京54 坐标及地方独立坐标等平面直角坐标批量转换为CGCS2000 坐标。坐标变换分间接法及直接法。间接法是以大地坐标（B，L）作为间接参数，根据椭球投影原理进行转换，理论严密，转换精准。直接法是直接根据区域公共点坐标，以最小二乘法为基础建立坐标 变换方程组或数值逼近模型，转换近似。正形变换是直接法之一，它具有等角变换的优点，可通用于同球及异球的高斯投影平面直角坐标变换。本文对正形变换的参数求解采用了简易的非线性拟合全局最优化方法以及多元线性回归分析方法，两者解算结果完全相同。多元线性回归分析，方法简单，计算快捷，转换精度足以满足工程需要。
• DOI: https://doi.org/10.35534/go.0304019
• Cite: 刘大海，陈永红，张萧平，等．平面直角坐标正形变换简易解算方法［J］．测绘观察，2021，3（4）：187-199．