| 王骈臻,林鹏.附加约束条件的坐标转换参数求解方法[J].安徽建筑大学学报,2022,30(4):27-34 |
| 附加约束条件的坐标转换参数求解方法 |
| Method for Solving Coordinate Transformation Parameters with Additional Constraints WA |
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| DOI： |
| 中文关键词: 坐标转换 高斯—马尔柯夫模型 最小二乘 |
| 英文关键词: coordinate transformation Gauss-Markov model least squares |
| 基金项目:安徽省自然科学基金青年基金项目（2008085QD179） |
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| 中文摘要: |
| 针对坐标转换问题，基于最小二乘原理以及高斯—马尔柯夫模型，研究了约束解法与非约束解法对坐标转换参数求解的影响。以三维坐标转换模型为研究对象，通过仿真实验分别探讨其约束解法与非约束解法在大、小旋转角情况下求解参数的精度情况，并以求得参数的均方差为精度评定的指标。实验结果显示：小旋转角情况下，坐标转换模型的约束解法与非约束解法精度一致，布尔莎模型运算速率最快；大旋转角情况下，线性模型误差较大，非线性模型的约束解法与非约束解法精度一致，非线性十三参数（虚拟观测值法）运算速率最快。实验结果表明：线性模型仅适用于小旋转角情况下的坐标转换参数求解，非线性十三参数模型（虚拟观测值法）适用于大旋转角情况下的坐标转换参数求解。 |
| 英文摘要: |
| Based on the least squares principle and Gauss-Markov model，the effects of constrained and unconstrained solutions on the solution of coordinate transformation parameters are investigated. The accuracy of the constrained and unconstrained solutions for large and small rotation angles is investigated by simulation experiments with three-dimensional coordinate transformation models，and the standard deviation of the obtained parameters is used as the index for accuracy evaluation. The experimental results show that in the case of small rotation angle，the accuracy of the constrained and unconstrained solutions of the coordinate transformation model is the same and the rate of the Bursa model is the fastest；in the case of large rotation angle，the error of the linear model is larger，the accuracy of the constrained and unconstrained solutions of the nonlinear model is the same，and the rate of the nonlinear thirteen parameters （with virtual observation method） is the fastest. Therefore，the linear Bursa model is only applicable for solving the coordinate transformation parameters in the case of small rotation angle，and the nonlinear thirteen-parameter model （virtual observation method） is applicable for solving the coordinate transformation parameters in the case of large rotation angle. |
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