Optimal Minimum L1-Norm Criteria for Outlier Identification in GNSS and Leveling Networks

The goal of this paper was to perform an exhaustive search regarding which combination of minimum L1-norm (MinL1) criteria is a better option for outlier identification. By means of Monte Carlo simulations (MCS), we compared the mean success rate (MSR) of combinations of three approaches for weight matrix × two approaches for test statistics × and two approaches for method of solution = 12 combinations of criteria for outlier identification with MinL1, in six geodetic network configurations. Six of them had never been evaluated via MCS, and four had never been tested in the literature. In general, the optimal combination was the adjustment with the same weights for the observations, normalized residual as the test statistic, and simplex method of solution (MinL1S - wi - simplex). In each case, we also computed the MSR of the iterative data-snooping (IDS) for reference. IDS presented MSR higher than all 12 MinL1 combinations in the four geodetic networks with mean redundancy numbers greater than or equal to 0.5. However, the MSR of the MinL1 optimal combination were 1.62 and 2.65 times higher than those of the IDS for the leveling and the global navigation satellite system (GNSS) networks with mean redundancy numbers less than 0.5, respectively. These results provide strong evidence that MinL1 with such criteria combinations has the potential to be the new state-of-the-art method for outlier identification in low redundancy GNSS and leveling networks.