101. Revisiting Baarda's concept of minimal detectable bias with regard to outlier identifiability.
- Author
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Prószyński, W.
- Subjects
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MINIMUM detectable activity , *GAUSSIAN distribution , *ERRORS , *GEODESY , *VECTORS (Calculus) - Abstract
The concept of minimal detectable bias (MDB) as initiated by Baarda (Publ Geod New Ser 2(5), ) and later developed by Wang and Chen (Acta Geodaet et Cartograph Sin Engl Edn 42-51, ), Schaffrin (J Eng Surv 123:126-137, ), Teunissen (IEEE Aerosp Electron Syst Mag 5(7):35-41, , J Geod 72:236-244 , Testing theory: an introduction. Delft University Press, Delft, ) and others, refers to the issue of outlier detectability. A supplementation of the concept is proposed for the case of correlated observations contaminated with a single gross error. The supplementation consists mainly of an outlier identifiability index assigned to each individual observation in a network and a mis-identifiability index being the maximum probability of identifying a wrong observation. To those indices there can also be added the MDB multiplying factor to increase the identifiability index to a satisfactory level. As auxiliary measures there are indices of partial identifiability concerning pairs of observations. The indices were derived assuming the generalized outlier identification procedure as in Knight et al. (J Geod. doi:, ), which with one outlier case being assumed is similar to Baarda's w-test (Baarda in Publ Geod New Ser 2(5), ). The following two options of identifiability indices and partial identifiability indices are distinguished: I. the indices related to identification of a contaminated observation within a set of observations suspected of containing a gross error (identifiability), II. the indices related to identification of a contaminated observation within a whole set of observations (pseudo-identifiability). To characterize the proposed approach in the context of the existing solutions of similar topic being the separability testing, the properties of both types of identifiability indices are discussed with reference to the concept of Minimal Separable Bias (Wang and Knight in J Glob Position Syst 11(1):46-57, ) and a general approach in Yang et al. (J Geod 87(6):591-604, ). Numerical examples are provided to verify the proposed approach. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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