<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We compared the method of least squares (LS), Pope’s iterative data snooping (IDS) and Huber’s M-estimator (HU) in realistic leveling networks, for which the heights or the vertical displacements of points are known. The study was conducted using the Monte Carlo simulation, in which one repeatedly generates sets of observations related to the measurement data, then calculates values of the estimators and, finally, assesses it with respect to the real coordinates. To simulate outliers we used popular mixture models with two or more normal distributions. It is shown that for small, strong networks robust methods IDS and HU are more accurate than LS, but for large, weak networks occurring in practice there is no significant difference between the considered methods in the accuracy of the solution.</p></abstract>

We compared the method of least squares (LS), Pope’s iterative data snooping (IDS) and Huber’s M-estimator (HU) in realistic leveling networks, for which the heights or the vertical displacements of points are known. The study was conducted using the Monte Carlo simulation, in which one repeatedly generates sets of observations related to the measurement data, then calculates values of the estimators and, finally, assesses it with respect to the real coordinates. To simulate outliers we used popular mixture models with two or more normal distributions. It is shown that for small, strong networks robust methods IDS and HU are more accurate than LS, but for large, weak networks occurring in practice there is no significant difference between the considered methods in the accuracy of the solution.

Comparison of robust estimators for leveling networks in Monte Carlo simulations

Chair of Engineering Geodesy and Control-Measuring Systems, Faculty of Geodesy and Cartography, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland

Reports on Geodesy and Geoinformatics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Comparison of robust estimators for leveling networks in Monte Carlo simulations"}

We compared the method of least squares (LS), Pope’s iterative data snooping (IDS) and Huber’s M-estimator (HU) in realistic leveling networks, for which the...

Comparison of robust estimators for leveling networks in Monte Carlo simulations

Published Online: Jul 14, 2016

Page range: 70 - 81

DOI: https://doi.org/10.1515/rgg-2016-0023

Keywords
leveling network, robust estimation, outliers, gross errors, internal reliability index

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Comparison of robust estimators for leveling networks in Monte Carlo simulations

Published Online: Jul 14, 2016

Page range: 70 - 81

DOI: https://doi.org/10.1515/rgg-2016-0023

Keywordsleveling network, robust estimation, outliers, gross errors, internal reliability index

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
leveling network, robust estimation, outliers, gross errors, internal reliability index