隶属度函数改进的IGGIII抗差方案及其在测量数据处理中的应用

Improved IGGIII Robust Scheme with Membership Function and Its Application in Measurement Data Processing

摘要: 针对IGGIII抗差估计方法根据残差大小是否满足设定的界限阈值进行分段定权不能很好处理粗差模糊边界的问题，提出一种利用标准化残差属于粗差的模糊子集隶属度函数改进的IGGIII抗差估计方法(MF-IGGIII)，具体为：首先通过模糊统计的方法确定标准化残差最大程度受粗差污染的模糊集合的隶属函数，然后根据计算的隶属度函数值构建等价权函数并进行选权迭代过程。通一个实际测角网平差算例验证本文方法，即在角度观测值中分别模拟4个、5个和6个三种不同数目粗差后再分别进行平差处理。选取参数估值误差的范数作为精度指标，结果表明，与传统IGGIII抗差估计方法相比，新方法精度分别提升了35.9%、32.5%和32.7%。说明同等条件下，由于新方法考虑了粗差的模糊性质，故取得了更高的参数估计精度，且在粗差个数增加到观测值总数的1/3情况下，仍然获得了较好的结果，其抗差性能更稳定，结果更可靠。

Abstract: In response to the problem that the IGGIII robust estimation method cannot effectively handle rough fuzzy boundaries by segmenting and weighting based on whether the residual size meets the set threshold, a modified IGGIII robust estimation method (MF-IGGIII) is proposed, which utilizes the membership function of the fuzzy subset of standardized residuals belonging to rough errors. Specifically, the membership function of the fuzzy set that is most heavily contaminated by rough errors in the standardized residuals is first determined through fuzzy statistics, and then an equivalent weight function is constructed based on the calculated membership function values and subjected to a weight selection iteration process. Verify the method proposed in this paper through an actual angle measurement network adjustment example, which simulates four, five, and six different numbers of gross errors in the angle observation values, and then performs adjustment processing separately. The analysis results of the case study show that under the same conditions, even when the number of gross errors increased to one-third of the total number of observations, good results were still obtained, with more stable robustness and more reliable results.