Outlier Detection for the Nonlinear Gauss Helmert Model With Variance Components by the Expectation Maximization Algorithm
-
Karl-Rudolf Koch
Abstract
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.
© 2014 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Masthead
- Biased and Unbiased Estimates Based on Laser Scans of Surfaces with Unknown Deformations
- Outlier Detection for the Nonlinear Gauss Helmert Model With Variance Components by the Expectation Maximization Algorithm
- Absolute Performance of AUSGeoid09 in Mountainous Regions
- Challenges in Assessing PPP Performance
- Long-Range Geo-Monitoring Using Image Assisted Total Stations
Articles in the same Issue
- Masthead
- Biased and Unbiased Estimates Based on Laser Scans of Surfaces with Unknown Deformations
- Outlier Detection for the Nonlinear Gauss Helmert Model With Variance Components by the Expectation Maximization Algorithm
- Absolute Performance of AUSGeoid09 in Mountainous Regions
- Challenges in Assessing PPP Performance
- Long-Range Geo-Monitoring Using Image Assisted Total Stations
