关于平差残差和单位权中误差的统计分析

Statistical Analysis of Residual Error and Mean Square of Weight

从残差的定量关系出发评述了检测粗差的数据探测法和抗差估计的选权迭代法 ,指出了其中用残差代替真误差所产生的问题及解决办法 ,并且导出了单位权方差估值、单位权中误差估值的概率分布 ,给出了后者的数字特征 ,对平差问题的精度体系作了统计分析。

As an important statistic,the residual error of adjustment is the estimation of the true error of observation in nature,but quantitatively it is a linear function of a group of true errors,whose values reflect the corporate effects of many true errors.By considering the quantitative relation between the residual error and the true error,this paper focuses on the data snooping and the iterative methods of weight defining for the robust estimation which are used to detect gross error.We point out the problems that will be met during the course of substituting the true error for residual error and how to resolve them.The statistical feature of mean square of weight is also discussed in this paper,so we deduce the estimation of the variance of weight and the statistical distribution of the estimation of mean square of weight,and also prompt the mathematical features of the latter.The statistical analysis of adjustment precise system is discussed.