多维平差问题粗差的局部分析法

用一个水准网说明了依据改正数进行粗差处理可能导致错误，而且粗差能够被正确处理与其所处的位置有关。为了解决这个问题，本文提出了局部分析法。局部分析法从多维平差问题的函数模型出发，根据设计矩阵得到一个被观测量的多个独立观测，包括被观测量的观测值和其他观测值的函数，并且给出了根据平差问题的设计矩阵搜索这些函数的方法。根据独立观测的数目即可判断被观测量的观测值能否容忍粗差。在此基础上提出了一种根据真误差判断被观测量的独立观测所涉及到的观测值是否含有粗差的方法。最后用一个测角网说明局部分析法和粗差探测方法的过程。

Local Analysis Method on Gross Error of Multidimensional Adjustment Problem

As demonstrated by an example of a leveling network,existing methods of correcting gross errors based on residuals have a few shortcomings including the dependence on the location of gross errors within the leveling network.To address these problems,local analysis method(LAM) is proposed.In multidimensional adjustment problem,an observed quantity usually can be expressed as function of other observed quantities.Then it can be obtained a group of indepen-dent observed values of the observed quantity,which includes observed value corresponding to the observed quantity and functions of other observed values.And an approach to search functions based on the design matrix is given.So it can be determined according to number of independent observed values whether the observed value can tolerate gross error.A method based on LAM is also developed to detect gross errors.Finally,the detection method and LAM are detailed in an example of a goniometric network.