基于判断矩阵的观测量粗差发现和定位相关性分析

Abstract

用布尔矩阵分析、研究判断矩阵,得到观测量粗差发现和定位的相关数以及测量系统的最大可发现粗差和定位粗差数的计算公式。试验证明,当粗差发现和定位相互影响的观测量同时含有粗差时,现行的迭代数据探测法和选权迭代法不可能完全正确定位粗差。通过算例验证了使用布尔矩阵和判断矩阵分析多维粗差发现和定位相关性的有效性和优越性。 The Boolean matrix is used to analyze the judgement matrix in this paper. The number of interaction observations in detecting and locating gross errors, the maximum number of detectable gross errors in the observations, and the maximum number of locatable gross errors in the observations in a surveying system are formulated. The test indicates that the current methods of detecting gross errors, i.e. iteration data snooping and iteration method with variable weights, can’t wholly correctly locate the gross errors if the gross errors arise simultaneously and observations are interaction for locating gross errors. The solutions of the experiments verify the effectiveness and superiority of which the judgement matrix and the Boolean matrix are used to analyze the correlation of multiple detectable and locatable gross errors.