Reliability Analysis for a Robust M-Estimator
Publication: Journal of Surveying Engineering
Volume 137, Issue 1
Abstract
The least-squares estimation exhibits a poor performance in the presence of gross errors. One of the typical approaches to control the influence of outliers is to use robust estimation techniques. The well-established geodetic reliability theory is comprised of two main components: internal and external reliability. Both reliability measures are important diagnostic tools for inferring the strength of the model validation. To gain further insight into robust M-estimation performance, the variation characteristics of internal and external reliability measures are addressed for a particular robust estimator. Theoretical analyses show that, during the iterative reweighting procedure for uncorrelated observations, the internal reliability measures as represented by minimal detectable bias become larger and larger. For purpose of illustration, a numerical example associated with a simulated geodetic leveling network is provided. As expected, for the outlying observations, their corresponding external reliability measures get smaller and smaller when the iteratively reweighted least-squares method is implemented.
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Acknowledgments
The project was sponsored by the China National Funds for Distinguished Young Scientists (Grant No. UNSPECIFIED40625013) and the Natural Science Foundation of China (Grant Nos. UNSPECIFIED40874007 and UNSPECIFIED40874009). The writers would like to thank the anonymous reviewers for their critical comments on the early version of this paper.
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Information
Published In
Journal of Surveying Engineering
Volume 137 • Issue 1 • February 2011
Pages: 9 - 13
Copyright
© 2011 ASCE.
History
Received: Nov 23, 2009
Accepted: Apr 23, 2010
Published online: May 1, 2010
Published in print: Feb 2011
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