Subjective Breakdown Points of R-estimators Applied in Deformation Analysis

Abstract

This paper presents practical aspect of the breakdown point theory in deformation analysis by applying R-estimators. The main aim of the paper is to determine impact of the probability of positive (or negative) gross errors and the number of such errors on the value of breakdown point of the estimates applied. Authors consider two types of networks: a levelling network and a horizontal one. Calculations are made for two cases, namely when observations are affected by gross errors in both measurement epochs or only in the second epoch. The main results are based on the Monte Carlo method, which is a very useful tool to solve such a geodetic problem. The simulations show that the breakdown point depends on the probability of positive gross errors but also on the number of epochs in which the gross errors occur. This is especially vivid in the case of levelling networks. Another interesting finding is that even if the number of gross errors exceeds the breakdown point, we can still get reasonable results; however, not always. Thus, the paper shows the probabilities that the method breaks down for several different cases. The paper includes some numerical tests, which provided practical information about the subjective breakdown points and their importance for R-estimates applied in deformation analysis.