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A Bayesian unmasking method for locating multiple gross errors based on posterior probabilities of classification variables

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Abstract

This paper puts forward a Bayesian method for multiple gross errors location and estimation, and studies the masking and swamping problem in multiple gross errors detection from a new point of view, further proposes the corresponding feasible solution. First, the Bayesian method for gross error location is established based on the posterior probabilities of classification variables, each of which is used to determine whether each observation contains gross error or not. When some interactions exist among observations with multiple gross errors, the above-mentioned method may lead to the failure of detection due to masking and swamping. For that, on the basis of analyzing the character of masking and swamping, starting from the eigen structure of the sample correlation coefficient matrix of the classification vector, we give the Bayesian unmasking method to locate multiple gross errors, and design the corresponding algorithm, namely the adaptive Gibbs sampling algorithm. Finally, applying the mean shift model, we raise a Bayesian approach to estimate gross errors. Significant applications of the approach show the promising results on overcoming masking and swamping.

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Abbreviations

MCMC:

Markov chain Monte Carlo

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Authors and Affiliations

  1. Institute of Science, Information Engineering University, No. 62, Kexue Road, 450001, Zhengzhou, China

    Q. Gui, B. Li & G. Li

  2. Institute of Surveying and Mapping, Information Engineering University, No. 66, Middle Longhai Road, 450052, Zhengzhou, China

    Q. Gui, Y. Gong, B. Li & G. Li

  3. Institute of Science, National University of Defense Technology, No. 47, Zheng Street, Yanwachi Road, 410073, Changsha, China

    X. Li

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  1. Q. Gui
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  2. X. Li
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  3. Y. Gong
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  4. B. Li
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  5. G. Li
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Correspondence to Q. Gui.

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Gui, Q., Li, X., Gong, Y. et al. A Bayesian unmasking method for locating multiple gross errors based on posterior probabilities of classification variables. J Geod 85, 191–203 (2011). https://doi.org/10.1007/s00190-010-0429-8

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  • DOI: https://doi.org/10.1007/s00190-010-0429-8

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