Univariate Approach for Detecting Outliers in Geodetic Networks

Abstract

In geodetic networks, observations are measured repetitively, and the mean values of these observations are used for network adjustment, outlier detection, deformation analysis, etc. These repetitive observations are independent, and if one of them has outlier, the effect of the outlier decreases depending on the computed mean value. Also, the mean operator—a kind of least-squares estimation—smears the effects of the outlier over other observations. In this case, the detectability and reliability rates of the outlier detection method decrease. Moreover, the undetectable outliers spoil both of the estimated parameters and their standard deviations, causing incorrect results. To form a univariate sample, the same quantity must be measured at least twice for geodetic networks. The univariate case is simpler than the multivariate case, and if the repetitive observations may be analyzed as a univariate case, more reliable results can be obtained for outlier detection. In this study, the univariate analysis method was proposed for repetitive geodetic observations. The reliability of the univariate method was measured based on its mean success rate compared with the mean success rates of classical methods. The leveling network was simulated, and analyses were carried out. The results obtained from the univariate case are more reliable than those obtained from classical ones.