Scholarly record

A COMPARISON BETWEEN SOME ROBUST ADJUSTMENTS OF PRECISE LEVELLING NETWORKS

Vasil Cvetkov

Abstract

The reliability of adjustment results in geodetic networks is of critical importance for the investigation of geodynamic processes such as deformation and tectonic movements, where vertical displacements represent a key monitoring component. Precise levelling remains the fundamental technique for such observations. Recent studies indicate that the adjustment of all possible combinations of measurements can yield more accurate and reliable results compared to the classical least squares adjustment of levelling networks. In this study, the analysis of optimal adjustment strategies for state levelling networks is extended through the application of robust statistical methods, specifically S-Estimation and MM-Estimation. The skeleton network of the Third Levelling of Finland is used as a test case. Adjustments are performed using four approaches: the classical method, the 3n combinations approach, MM-Estimation, and S-Estimation with varying breakdown points of 50%, 25%, and 10%. The results demonstrate that the smallest standard errors of the adjusted benchmark heights are achieved using the 3n combinations approach, followed closely by S-Estimation with a 50% breakdown point. In contrast, the classical adjustment yields the largest standard errors, with MM-Estimation and S-Estimation at a 10% breakdown point also showing comparatively weaker performance. Notably, S-Estimation with a 25% breakdown point produces results similar to both the 3n combinations method and S-Estimation with a 50% breakdown point, indicating its effectiveness in mitigating the impact of undetected or underestimated observational errors. A comparative analysis of adjusted benchmark heights reveals that S-Estimation with a 50% breakdown point provides results most consistent with the 3n combinations approach, with differences generally below 5 mgpu, except for a single benchmark where a larger deviation is observed. In contrast, MM-Estimation and S-Estimation with a 10% breakdown point produce discrepancies exceeding 20 mgpu for some benchmarks. These findings confirm that, in precise levelling networks where masked outliers are commonly present, robust estimation techniques offer a more reliable alternative to the classical least squares method, which is highly sensitive to contaminated observations.

Publication details

Back to publication list