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Journal of Applied Geodesy

Editor-in-Chief: Kahmen, Heribert / Rizos, Chris

CiteScore 2018: 1.61

SCImago Journal Rank (SJR) 2018: 0.532
Source Normalized Impact per Paper (SNIP) 2018: 1.064

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Volume 7, Issue 2


Comparison of two robust estimations by expectation maximization algorithms with Huber’s method and outlier tests

Karl- Rudolf Koch
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  • Institute of Geodesy and Geoinformation, Theoretical Geodesy, University of Bonn, Nussallee 17, 53115 Bonn, Germany
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Published Online: 2013-05-18 | DOI: https://doi.org/10.1515/jag-2013-0050


The robust estimation by the expectation maximization (EM) algorithm is derived for the variance-inflation model in addition to the known estimation for the mean-shift model. To compare these methods with the τ - test, Huber’s robust M-estimation and the multiple outlier test, a random linear model and laser scans for fitting a plane are generated by Monte Carlo methods. It turns out that the results for detecting outliers by the EM algorithms for the mean-shift and variance-inflation model approximately agree although the numbers of convergences are different. The results are superior to the ones of the methods with which they are compared. In case of the generated laser scans, the maximum number of outliers, which can be detected, is approximately identified.

Keywords: EM algorithm; mean-shift model; variance-inflation model; τ -test; Huber’s M-estimation; multiple outlier test; Monte Carlo method

About the article

Published Online: 2013-05-18

Published in Print: 2013-05-01

Citation Information: Journal of Applied Geodesy, Volume 7, Issue 2, Pages 115–124, ISSN (Online) 1862-9024, ISSN (Print) 1862-9016, DOI: https://doi.org/10.1515/jag-2013-0050.

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