A Bayesian approach to the detection of gross errors based on posterior probability |
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Authors: | Q Gui Y Gong G Li B Li |
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Institution: | (1) Institute of Science, Information Engineering University, No.62, Kexue Road, 450001 Zhengzhou, China;(2) Institute of Surveying and Mapping, Information Engineering University, No. 66, Middle Longhai Road, 450052 Zhengzhou, China |
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Abstract: | Existing methods for gross error detection, based on the mean shift model or the variance inflation model, have hardly considered
or taken advantage of the potential prior information on the unknown parameters. This paper puts forward a Bayesian approach
for gross error detection when prior information on the unknown parameters is available. Firstly, based on the basic principle
of Bayesian statistical inference, the Bayesian method—posterior probability method—for the detection of gross errors is established.
Secondly, considering either non-informative priors or normal-gamma priors on the unknown parameters, the computational formula
of the posterior probability is given for both the mean shift model and the variance inflation model, respectively, under
the condition of unequal weight and independent observations. Finally, as an example, a triangulation network is computed
and analyzed, which shows that the method given here is feasible. |
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Keywords: | Gross error detection Posterior probability Mean shift model Variance inflation model |
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