基于信息扩散函数定权的抗差估计及其应用

Robust Estimation Based on Weighting of Information Spreading Model and Its Application

摘要: 利用最小二乘估计的观测向量标准化残差计算信息扩散函数值并构造权阵进行抗差估计。该方法由于事先根据标准化残差估计了残差的实际分布，从而无需任何迭代过程即可获得包含粗差信息的观测值的可靠权阵。试验结果表明：当观测向量中包含粗差时，利用信息扩散函数计算的相应观测量的权值相对较小，从而抑制了粗差的影响。与IGG方案以及拟准检定法相比，新方法仍能取得较好抗差估计结果。

Abstract: A robust estimation method based on weighting with the information diffusion function value being calculated by the standardized residuals of the observation vectors of least squares estimation is proposed. Compared with the classical robust estimation methods based on mean shift model or variance expansion model, the new method estimates the actual distribution of the residual in advance according to the standardized residual, so that the reliable weight matrix of the observed value containing gross error information can be obtained without any iteration process. The experimental results show that when gross errors are included in the observation vectors, the weights of the corresponding observations calculated by the information diffusion function are relatively smaller than those of others; thus the effect of gross errors is weakened. Compared with IGG schemes and quasi-accurate detection method, the new method can still achieve better robust results.