| 以相对偏差平方和为指标函数的最小二乘法 |
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| 引用本文： | 付景峰,陈海军.以相对偏差平方和为指标函数的最小二乘法[J].宇航计测技术,1991(3):66-72. |
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| 作者姓名： | 付景峰 陈海军 |
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| 作者单位： | 哈尔滨工业大学，哈尔滨工业大学，哈尔滨工业大学 |
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| 摘 要： | 就测量中最小二乘法用于静态模型估计的问题,分析了传统最小二乘法在某些实验条件下应用的不合理现象,提出以相对偏差平方和为指标函数的最小二乘法。简记LSR法。给出了该方法的实用公式,分析了数学特征并证明在所给实验条件下具有无偏性、一致性,有效性.给出了用该方法拟合电位差计静态特性方程的例子。证明该方法在测量工作中是有实际意义的。
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| 关 键 词： | 最小二乘法 数据处理 误差理论 Least square method Data processing Error theory Mathematical model |
The Least Square Method Based upon Minimizing the Sum of Squared Relative Deviation |
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| Fu Jingfeng Chen Haijun Lan Kangmeng.The Least Square Method Based upon Minimizing the Sum of Squared Relative Deviation[J].Journal of Astronautic Metrology and Measurement,1991(3):66-72. |
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| Authors: | Fu Jingfeng Chen Haijun Lan Kangmeng |
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| Institution: | Fu Jingfeng Chen Haijun Lan Kangmeng |
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| Abstract: | In this paper,the least square method based upon minimizing the sum of squared relative diviation (LSR) is proposed.The authors analyze the problems of classical least square (LS) in fitting static characteristic equation of system and point out the short- comings of LS method in some experimental conditions.The proposed method could over-come these shortcomings.The mathematical formulas of LSR are given and the mathematical characteristics of LSR are analyzed in this paper.The method has the proper- ties of unbiased,concordance and effective in the given conditions.It is a significant meth- od in measurement.The examples are given for fitting static characteristic equation of potentiometer by using this method. |
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| Keywords: | Least square method Data processing Error theory Mathematical model |
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