利用L1范数和中位数选取拟准观测值

A Method for Selecting the Quasi-Accurate Observations Based on L1 Norm and Median

粗差探测拟准检定法的核心是拟准观测的选取。提出了L_1范数和中位数相结合的方法选取拟准观测值,并设计了相应的准则。首先利用L1范数方法得到稳健的残差,将其中残差接近于零时对应的观测值直接确定为拟准观测值,然后将余下残差形成新的残差向量,并计算其绝对值的中位数,拟准观测值即为那些余下残差绝对值小于中位数所对应的观测值。GPS网平差和GPS单点定位计算结果表明本文提出的选取拟准观测值的方法有效可行。

The outlier problem is always the hot topic in surveying data processing.Due to the complexity of detecting multiple outliers simultaneously,the more efficient method may be highly desirable.The quasi-accurate detection of outliers is a method to identify and position outliers through the estimates of real errors,which is relatively complete in principle,computing and applications.The key part for this method is just to select the quasi-accurate observations.Taking above into consideration,a new method to choose quasi-accurate observation for two parts by combining L1 norm minimization method with median is proposed.The criterion for determining quasi-accurate observations is built.Firstly,the L1 norm minimization method is developed to obtain the robustified residuals,and the observations whose residuals are approximately zeros will be treated directly as the first part of quasi-accurate observations.Then,a new vector would be formed by computing the absolute values of the remaining residuals.By obtaining the median of the new vector of residuals,the second part of quasi-accurate observations are the observations whose residuals are less than the given median.The detailed analysis of GPS network adjustment and GNSS single point positioning example has been conducted to assess the performance of the proposed method.The results show that the proposed method for selecting quasi-accurate observations is effective and feasible.