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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 8, Issue 3


Outlier Detection for the Nonlinear Gauss Helmert Model With Variance Components by the Expectation Maximization Algorithm

Karl-Rudolf Koch
Published Online: 2014-10-02 | DOI: https://doi.org/10.1515/jag-2014-0004


Best invariant quadratic unbiased estimates (BIQUE) of the variance and covariance components for a nonlinear Gauss Helmert (GH) model are derived. To detect outliers, the expectation maximization (EM) algorithm based on the variance-inflation model and the mean-shift model is applied, which results in an iterative reweighting least squares. Each step of the iterations for the EM algorithm therefore includes first the iterations for linearizing the GH model and then the iterations for estimating the variance components. The method is applied to fit a surface in three-dimensional space to the three coordinates of points measured, for instance, by a laser scanner. The surface is represented by a polynomial of second degree and the variance components of the three coordinates are estimated. Outliers are detected by the EM algorithm based on the variance-inflation model and identified by the EM algorithm for the mean-shift model.

Keywords: EM algorithm; variance-inflation model; meanshift model; variance and covariance components; nonlinear Gauss Helmert model; laser scanner

About the article

Published Online: 2014-10-02

Published in Print: 2014-09-01

Citation Information: Journal of Applied Geodesy, Volume 8, Issue 3, Pages 185–194, ISSN (Online) 1862-9024, ISSN (Print) 1862-9016, DOI: https://doi.org/10.1515/jag-2014-0004.

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