| 隐式标度因子的总体最小二乘估计方法 |
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| 引用本文： | 刘志平,李思达,张秋昭.隐式标度因子的总体最小二乘估计方法[J].测绘科学技术学报,2016(5):441-446. |
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| 作者姓名： | 刘志平 李思达 张秋昭 |
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| 作者单位： | 中国矿业大学 环境与测绘学院,江苏 徐州,221116 |
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| 基金项目： | 国家自然科学基金项目(41204011;41504032)，江苏高校优势学科建设工程项目(SZBF2011-6-B35) |
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| 摘 要： | 分析指出了标度总体最小二乘方法(STLS)存在的问题,提出了一种隐式标度因子的标度总体最小二乘方法(Im STLS)。区别于现有STLS方法在平差准则中引入标度因子,Im STLS方法在EIV函数模型中顾及标度因子,从而解决了现有STLS平差准则形式与标度因子实际表征的平差结果不一致的问题。此外,利用所建函数模型的重构表达式推导的Im STLS估计量及其方差-协方差阵,与经典最小二乘平差理论具有形式同构性。最后,验证了所提方法统一表达LS,DLS和TLS的正确性,并讨论给出了标度因子对平差结果的影响及确定方法。
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| 关 键 词： | 最小二乘法 EIV模型 隐式标度因子 标度总体最小二乘 平差准则 |
Scaled Total Least Squares Method with Implicit Scaled Factor |
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| LIU Zhiping,LI Sida,ZHANG Qiuzhao.Scaled Total Least Squares Method with Implicit Scaled Factor[J].Journal of Zhengzhou Institute of Surveying and Mapping,2016(5):441-446. |
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| Authors: | LIU Zhiping LI Sida ZHANG Qiuzhao |
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| Abstract: | The defect of the existing scaled total least squares ( STLS) method is investigated in detail, and then a scaled total least squares method with implicit scaled factor ( short for ImSTLS) is proposed. To solve the problem that adjustment criterion form with scaled factor employed by the existing STLS method is inconsistent with actual adjustment result at specific scaled factor, the ImSTLS method establishes the new EIV function model using im-plicit scaled factor which is a creative way to achieve that problem. Moreover, ImSTLS estimation and its variance-covariance matrix derived from a reconstruction form of the function model can be completely formulated by stand-ard least squares theory. Finally, experiment results show the validity of the proposed method for generalizing LS, DLS and TLS is verified, and both determination method and influence of the implicit scaled factor on the adjust-ment result are discussed in detail. |
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| Keywords: | least squares method errors-in-variables model implicit scaled factor scaled total least squares method adjustment criteria |
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