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

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.