Testing the compatibility of constraints for parameters of a geodetic adjustment model.
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| Title: | Testing the compatibility of constraints for parameters of a geodetic adjustment model. |
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| Authors: | Lehmann, Rüdiger1 r.lehmann@htw-dresden.de, Neitzel, Frank2 frank.neitzel@tu-berlin.de |
| Source: | Journal of Geodesy. Jun2013, Vol. 87 Issue 6, p555-566. 12p. |
| Subjects: | Geodesy, Astronomy, Gauss's law (Electric fields), Electrostatics, Electricity |
| Abstract: | Geodetic adjustment models are often set up in a way that the model parameters need to fulfil certain constraints. The normalized Lagrange multipliers have been used as a measure of the strength of constraint in such a way that if one of them exceeds in magnitude a certain threshold then the corresponding constraint is likely to be incompatible with the observations and the rest of the constraints. We show that these and similar measures can be deduced as test statistics of a likelihood ratio test of the statistical hypothesis that some constraints are incompatible in the same sense. This has been done before only for special constraints (Teunissen in Optimization and Design of Geodetic Networks, pp. 526-547, ). We start from the simplest case, that the full set of constraints is to be tested, and arrive at the advanced case, that each constraint is to be tested individually. Every test is worked out both for a known as well as for an unknown prior variance factor. The corresponding distributions under null and alternative hypotheses are derived. The theory is illustrated by the example of a double levelled line. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Geodesy is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 87563579 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Testing the compatibility of constraints for parameters of a geodetic adjustment model. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Lehmann%2C+Rüdiger%22">Lehmann, Rüdiger</searchLink><relatesTo>1</relatesTo><i> r.lehmann@htw-dresden.de</i><br /><searchLink fieldCode="AR" term="%22Neitzel%2C+Frank%22">Neitzel, Frank</searchLink><relatesTo>2</relatesTo><i> frank.neitzel@tu-berlin.de</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Geodesy%22">Journal of Geodesy</searchLink>. Jun2013, Vol. 87 Issue 6, p555-566. 12p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Geodesy%22">Geodesy</searchLink><br /><searchLink fieldCode="DE" term="%22Astronomy%22">Astronomy</searchLink><br /><searchLink fieldCode="DE" term="%22Gauss's+law+%28Electric+fields%29%22">Gauss's law (Electric fields)</searchLink><br /><searchLink fieldCode="DE" term="%22Electrostatics%22">Electrostatics</searchLink><br /><searchLink fieldCode="DE" term="%22Electricity%22">Electricity</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Geodetic adjustment models are often set up in a way that the model parameters need to fulfil certain constraints. The normalized Lagrange multipliers have been used as a measure of the strength of constraint in such a way that if one of them exceeds in magnitude a certain threshold then the corresponding constraint is likely to be incompatible with the observations and the rest of the constraints. We show that these and similar measures can be deduced as test statistics of a likelihood ratio test of the statistical hypothesis that some constraints are incompatible in the same sense. This has been done before only for special constraints (Teunissen in Optimization and Design of Geodetic Networks, pp. 526-547, ). We start from the simplest case, that the full set of constraints is to be tested, and arrive at the advanced case, that each constraint is to be tested individually. Every test is worked out both for a known as well as for an unknown prior variance factor. The corresponding distributions under null and alternative hypotheses are derived. The theory is illustrated by the example of a double levelled line. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Geodesy is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00190-013-0627-2 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 555 Subjects: – SubjectFull: Geodesy Type: general – SubjectFull: Astronomy Type: general – SubjectFull: Gauss's law (Electric fields) Type: general – SubjectFull: Electrostatics Type: general – SubjectFull: Electricity Type: general Titles: – TitleFull: Testing the compatibility of constraints for parameters of a geodetic adjustment model. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Lehmann, Rüdiger – PersonEntity: Name: NameFull: Neitzel, Frank IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2013 Type: published Y: 2013 Identifiers: – Type: issn-print Value: 09497714 Numbering: – Type: volume Value: 87 – Type: issue Value: 6 Titles: – TitleFull: Journal of Geodesy Type: main |
| ResultId | 1 |
