多次组合测量数据处理的一般方法及其合理性的证明

The General Methed for Data Processing of Several Combination Measurements and its Proof of Validity

本文以最普遍的形式,给出了多次组合测量数据处理的一般方法,这方法适用于带有约束方程和不等准确度测量等情况。方法的处理结果以下列形式给出: Y_j=Y_(jB)±[ΔY_(jB)](K_oσ)(j=1～n) 方法给出了各Y_(jB)及其误差Δy_(jB)估计值[ΔY_(jB)]的计算方法。如果原始测量数据X_i的误差Δx_i的估计值[ΔX_i]与Δx_i均方值σ(Δx_i)之比K_i均为K_o值,则[ΔY_(jB)]值将为Δy_(jB)均方值σ(Δy_(jB))的K_o值。方法还给出了确定K_o值的计算公式。本文还在各原始数据X_i的误差Δx_i均为独立的偶然误差及各K_i=[Δx_i]/σ(Δx_i)均等于K_o的条件下,用一般的数学工具,简要而严格地证实了这样处理方法的合理性。

This paper gives general method for data processing of severalcombination measurements by commonent form. It can be used for measurementswith restrict equalities and unequal accuracy as well as other cases. The pro-cessing results of method are given by Y_j = Y_(jB)±[△Y_(jB)] (K_oσ) (j = 1～n)This paper gives method for calcutating each Y_(jB) and estimate value [△Y_(jB)] oferror △y_(jB). If the ratios K_i of [△X_i] (initial measurement data X_i's. error △x_iestimate value to root mean square value σ (△x_i) are all equal to K_o, [△Y_(jB)] mustbe equal to σ(△y_(jB)) (the root mean square value of error △y_(jB)) multiplied by K_o.The method also gives calculation formula to determine value K_o. Under the con-ditions that the errors of every data K_i are independent random errors and eachK_i= K_o, using common mathematical means, the paper proves the validity of thisprocessing method in a simple and strict way.