Increasing Reliability of Basic R-Estimates in Deformation Analysis

The paper concerns the Hodges-Lehmann weighted estimates which are one of the basic R-estimates applied in deformation analysis. We are interested how increasing reliability of the Hodges-Lehmann weighted estimate of the shift influences the distribution and the accuracy of the estimated point displacements. We examine a simulated levelling network and assume that the outliers may occur in both measurement epochs. We consider two variants of the Hodges-Lehmann weighted estimates and the classical non-robust approach, i.e., the least squares estimates. The results show that a new variant of the Hodges-Lehmann weighted estimates with "strengthening" some height differences (where it is possible) and applying the weighted mean results in better accuracy and smaller excess kurtosis in relation to the basic variant of the Hodges-Lehmann weighted estimates. The new estimate variant has superior reliability, so it may be advisable and helpful in some problems in deformation analysis.