Evaluating levelling adjustment methods in deformation analysis

The article evaluates the reliability of geometric levelling network adjustments used in deformation monitoring of buildings and infrastructure. It compares classical adjustment, adjustments using all combinations of measured height differences, and robust approaches such as M-, S-, and MM-Estimation. Simulated levelling data were generated so that forward and backward elevation observations shared the same expected value but had different variances. The results indicate that the classical method, which uses the mean of the two elevation measurements, is optimal only when both observation groups have identical variances, meaning that all data strictly follow a single Gaussian distribution. When variances differ, averaging the paired observations is no longer advisable. In such situations, adjusting all possible combinations of observations, including their mean, provides the most reliable results. The simulations show that this strategy offers higher empirical efficiency and greater robustness than commonly used robust estimators, including Huber, Tukey, Andrew, IGG III, L1-Norm, the Danish Method, S-Estimation, and MM-Estimation, even when variance differences are small.