| 三原则整体最小二乘用于平面自由网平差计算 |
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| 引用本文： | 郭绍禹.三原则整体最小二乘用于平面自由网平差计算[J].测绘工程,2022,31(1):30-34. |
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| 作者姓名： | 郭绍禹 |
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| 作者单位： | 江西理工大学,江西 赣州 341000 |
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| 摘 要： | 文中在平面网平差中应用整体最小二乘理念。在最小二乘模型中,为了消除观测方程系数误差和未知参数系统误差,加入系数改正数和参数改正数,并提出三原则整体最小二乘模型。研究平差两大步骤,用最小二乘多次改用"参考点组"而选出w个稳定点;用最小二乘多次改用"近似坐标"而消除系数误差和参数系统误差。三原则整体最小二乘适用于平面自由网平差,且得到的"各种平差值"符合实际的无偏估计。
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| 关 键 词： | 平面自由网平差 最小二乘 三原则整体最小二乘 消除 系数误差 参数系统误差 |
Three-principle total least squares applied to flat free net adjustment |
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| GUO Shaoyu.Three-principle total least squares applied to flat free net adjustment[J].Engineering of Surveying and Mapping,2022,31(1):30-34. |
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| Authors: | GUO Shaoyu |
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| Institution: | (Jiangxi University of Science and Technology, Ganzhou 341000, China) |
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| Abstract: | The application of total least squares(TLS)to the flat free net adjustment is still lack of achievements.In this paper,the TLS methodology is applied to the flat net adjustment.In the least squares model,to eliminate the observed equation coefficient errors and the unknown parameter systematic errors,the corrections of coefficient matrix and parameters are added,and the three-principle total least squares(TPTLS)model is proposed.To study the two main steps of its adjustment:the LS method is used to change“reference point group”several times to select w stable points;the LS method is used to change“approximate coordinates”several times to eliminate coefficient errors and the parameter systematic errors.The proposed TPTLS method is applied to the flat free net adjustment by obtaining various adjustment values which are consistent with the actual unbiased estimator. |
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| Keywords: | flat free net adjustment least squares three-principle total least squares eliminate coefficient errors parameter systematic error |
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