Estimating Canadian vertical datum offsets using GNSS/levelling benchmark information and GOCE global geopotential models
The performance of GOCE-based geopotential models is assessed for the estimation of offsets for three regional vertical datums in Canada with respect to a global equipotential surface using the GNSS benchmarks from the first-order vertical control network. Factors that affect the computed value of t...
Ausführliche Beschreibung
Autor*in: |
Hayden T. [verfasserIn] Amjadiparvar B. [verfasserIn] Rangelova E. [verfasserIn] Sideris M.G. [verfasserIn] |
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E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2012 |
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Übergeordnetes Werk: |
In: Journal of Geodetic Science - De Gruyter, 2015, 2(2012), 4, Seite 257-269 |
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Übergeordnetes Werk: |
volume:2 ; year:2012 ; number:4 ; pages:257-269 |
Links: |
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DOI / URN: |
10.2478/v10156-012-0008-4 |
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Katalog-ID: |
DOAJ030292492 |
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10.2478/v10156-012-0008-4 doi (DE-627)DOAJ030292492 (DE-599)DOAJ24685e1b8e854bf9bd09fe89e8602941 DE-627 ger DE-627 rakwb eng QB275-343 Hayden T. verfasserin aut Estimating Canadian vertical datum offsets using GNSS/levelling benchmark information and GOCE global geopotential models 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The performance of GOCE-based geopotential models is assessed for the estimation of offsets for three regional vertical datums in Canada with respect to a global equipotential surface using the GNSS benchmarks from the first-order vertical control network. Factors that affect the computed value of the local vertical datum offset include the GOCE commission and omission errors, measurement errors, the configuration of the network of GNSS/levelling benchmarks, and systematic levelling errors and distortions propagated through the vertical control network. Among these various factors, the effect of the GOCE omission error on the datum offsets is investigated by extending the models with the high resolution gravity field model EGM2008 and by means of Canada’s official high resolution geoid model CGG2010. The effect of the GOCE commission error in combination with errors from the GNSS/levelling data is also examined, in addition to the effect of systematic levelling errors. In Canada, the effect of the GOCE omission error is at the dm-level when computing local vertical datum offsets. The effect of including accuracy information for the GNSS/levelling data and the GOCE geoid heights can be up to 4 cm over the Canadian mainland and at the dm-level for island regions. Lastly, the spatial tilts found in the levelling network can be modelled with a 2-parameter bias corrector model, which reduces the RMS of the adjusted geoid height differences by 4 cm when compared to the RMS of adjusted geoid height differences computed without the use of a bias corrector model. Thus, when computing local vertical datum offsets in Canada, it is imperative to account for GOCE commission and omission errors, ellipsoidal and levelling height errors, as well as the systematic levelling errors of the vertical control network. height system unification cgvd28 goce global geopotential model goce omission error navd88 vertical datum Geodesy Amjadiparvar B. verfasserin aut Rangelova E. verfasserin aut Sideris M.G. verfasserin aut In Journal of Geodetic Science De Gruyter, 2015 2(2012), 4, Seite 257-269 (DE-627)645088358 (DE-600)2591739-0 20819943 nnns volume:2 year:2012 number:4 pages:257-269 https://doi.org/10.2478/v10156-012-0008-4 kostenfrei https://doaj.org/article/24685e1b8e854bf9bd09fe89e8602941 kostenfrei https://doi.org/10.2478/v10156-012-0008-4 kostenfrei https://doaj.org/toc/2081-9943 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4700 AR 2 2012 4 257-269 |
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10.2478/v10156-012-0008-4 doi (DE-627)DOAJ030292492 (DE-599)DOAJ24685e1b8e854bf9bd09fe89e8602941 DE-627 ger DE-627 rakwb eng QB275-343 Hayden T. verfasserin aut Estimating Canadian vertical datum offsets using GNSS/levelling benchmark information and GOCE global geopotential models 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The performance of GOCE-based geopotential models is assessed for the estimation of offsets for three regional vertical datums in Canada with respect to a global equipotential surface using the GNSS benchmarks from the first-order vertical control network. Factors that affect the computed value of the local vertical datum offset include the GOCE commission and omission errors, measurement errors, the configuration of the network of GNSS/levelling benchmarks, and systematic levelling errors and distortions propagated through the vertical control network. Among these various factors, the effect of the GOCE omission error on the datum offsets is investigated by extending the models with the high resolution gravity field model EGM2008 and by means of Canada’s official high resolution geoid model CGG2010. The effect of the GOCE commission error in combination with errors from the GNSS/levelling data is also examined, in addition to the effect of systematic levelling errors. In Canada, the effect of the GOCE omission error is at the dm-level when computing local vertical datum offsets. The effect of including accuracy information for the GNSS/levelling data and the GOCE geoid heights can be up to 4 cm over the Canadian mainland and at the dm-level for island regions. Lastly, the spatial tilts found in the levelling network can be modelled with a 2-parameter bias corrector model, which reduces the RMS of the adjusted geoid height differences by 4 cm when compared to the RMS of adjusted geoid height differences computed without the use of a bias corrector model. Thus, when computing local vertical datum offsets in Canada, it is imperative to account for GOCE commission and omission errors, ellipsoidal and levelling height errors, as well as the systematic levelling errors of the vertical control network. height system unification cgvd28 goce global geopotential model goce omission error navd88 vertical datum Geodesy Amjadiparvar B. verfasserin aut Rangelova E. verfasserin aut Sideris M.G. verfasserin aut In Journal of Geodetic Science De Gruyter, 2015 2(2012), 4, Seite 257-269 (DE-627)645088358 (DE-600)2591739-0 20819943 nnns volume:2 year:2012 number:4 pages:257-269 https://doi.org/10.2478/v10156-012-0008-4 kostenfrei https://doaj.org/article/24685e1b8e854bf9bd09fe89e8602941 kostenfrei https://doi.org/10.2478/v10156-012-0008-4 kostenfrei https://doaj.org/toc/2081-9943 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4700 AR 2 2012 4 257-269 |
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10.2478/v10156-012-0008-4 doi (DE-627)DOAJ030292492 (DE-599)DOAJ24685e1b8e854bf9bd09fe89e8602941 DE-627 ger DE-627 rakwb eng QB275-343 Hayden T. verfasserin aut Estimating Canadian vertical datum offsets using GNSS/levelling benchmark information and GOCE global geopotential models 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The performance of GOCE-based geopotential models is assessed for the estimation of offsets for three regional vertical datums in Canada with respect to a global equipotential surface using the GNSS benchmarks from the first-order vertical control network. Factors that affect the computed value of the local vertical datum offset include the GOCE commission and omission errors, measurement errors, the configuration of the network of GNSS/levelling benchmarks, and systematic levelling errors and distortions propagated through the vertical control network. Among these various factors, the effect of the GOCE omission error on the datum offsets is investigated by extending the models with the high resolution gravity field model EGM2008 and by means of Canada’s official high resolution geoid model CGG2010. The effect of the GOCE commission error in combination with errors from the GNSS/levelling data is also examined, in addition to the effect of systematic levelling errors. In Canada, the effect of the GOCE omission error is at the dm-level when computing local vertical datum offsets. The effect of including accuracy information for the GNSS/levelling data and the GOCE geoid heights can be up to 4 cm over the Canadian mainland and at the dm-level for island regions. Lastly, the spatial tilts found in the levelling network can be modelled with a 2-parameter bias corrector model, which reduces the RMS of the adjusted geoid height differences by 4 cm when compared to the RMS of adjusted geoid height differences computed without the use of a bias corrector model. Thus, when computing local vertical datum offsets in Canada, it is imperative to account for GOCE commission and omission errors, ellipsoidal and levelling height errors, as well as the systematic levelling errors of the vertical control network. height system unification cgvd28 goce global geopotential model goce omission error navd88 vertical datum Geodesy Amjadiparvar B. verfasserin aut Rangelova E. verfasserin aut Sideris M.G. verfasserin aut In Journal of Geodetic Science De Gruyter, 2015 2(2012), 4, Seite 257-269 (DE-627)645088358 (DE-600)2591739-0 20819943 nnns volume:2 year:2012 number:4 pages:257-269 https://doi.org/10.2478/v10156-012-0008-4 kostenfrei https://doaj.org/article/24685e1b8e854bf9bd09fe89e8602941 kostenfrei https://doi.org/10.2478/v10156-012-0008-4 kostenfrei https://doaj.org/toc/2081-9943 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4700 AR 2 2012 4 257-269 |
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10.2478/v10156-012-0008-4 doi (DE-627)DOAJ030292492 (DE-599)DOAJ24685e1b8e854bf9bd09fe89e8602941 DE-627 ger DE-627 rakwb eng QB275-343 Hayden T. verfasserin aut Estimating Canadian vertical datum offsets using GNSS/levelling benchmark information and GOCE global geopotential models 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The performance of GOCE-based geopotential models is assessed for the estimation of offsets for three regional vertical datums in Canada with respect to a global equipotential surface using the GNSS benchmarks from the first-order vertical control network. Factors that affect the computed value of the local vertical datum offset include the GOCE commission and omission errors, measurement errors, the configuration of the network of GNSS/levelling benchmarks, and systematic levelling errors and distortions propagated through the vertical control network. Among these various factors, the effect of the GOCE omission error on the datum offsets is investigated by extending the models with the high resolution gravity field model EGM2008 and by means of Canada’s official high resolution geoid model CGG2010. The effect of the GOCE commission error in combination with errors from the GNSS/levelling data is also examined, in addition to the effect of systematic levelling errors. In Canada, the effect of the GOCE omission error is at the dm-level when computing local vertical datum offsets. The effect of including accuracy information for the GNSS/levelling data and the GOCE geoid heights can be up to 4 cm over the Canadian mainland and at the dm-level for island regions. Lastly, the spatial tilts found in the levelling network can be modelled with a 2-parameter bias corrector model, which reduces the RMS of the adjusted geoid height differences by 4 cm when compared to the RMS of adjusted geoid height differences computed without the use of a bias corrector model. Thus, when computing local vertical datum offsets in Canada, it is imperative to account for GOCE commission and omission errors, ellipsoidal and levelling height errors, as well as the systematic levelling errors of the vertical control network. height system unification cgvd28 goce global geopotential model goce omission error navd88 vertical datum Geodesy Amjadiparvar B. verfasserin aut Rangelova E. verfasserin aut Sideris M.G. verfasserin aut In Journal of Geodetic Science De Gruyter, 2015 2(2012), 4, Seite 257-269 (DE-627)645088358 (DE-600)2591739-0 20819943 nnns volume:2 year:2012 number:4 pages:257-269 https://doi.org/10.2478/v10156-012-0008-4 kostenfrei https://doaj.org/article/24685e1b8e854bf9bd09fe89e8602941 kostenfrei https://doi.org/10.2478/v10156-012-0008-4 kostenfrei https://doaj.org/toc/2081-9943 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4700 AR 2 2012 4 257-269 |
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10.2478/v10156-012-0008-4 doi (DE-627)DOAJ030292492 (DE-599)DOAJ24685e1b8e854bf9bd09fe89e8602941 DE-627 ger DE-627 rakwb eng QB275-343 Hayden T. verfasserin aut Estimating Canadian vertical datum offsets using GNSS/levelling benchmark information and GOCE global geopotential models 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The performance of GOCE-based geopotential models is assessed for the estimation of offsets for three regional vertical datums in Canada with respect to a global equipotential surface using the GNSS benchmarks from the first-order vertical control network. Factors that affect the computed value of the local vertical datum offset include the GOCE commission and omission errors, measurement errors, the configuration of the network of GNSS/levelling benchmarks, and systematic levelling errors and distortions propagated through the vertical control network. Among these various factors, the effect of the GOCE omission error on the datum offsets is investigated by extending the models with the high resolution gravity field model EGM2008 and by means of Canada’s official high resolution geoid model CGG2010. The effect of the GOCE commission error in combination with errors from the GNSS/levelling data is also examined, in addition to the effect of systematic levelling errors. In Canada, the effect of the GOCE omission error is at the dm-level when computing local vertical datum offsets. The effect of including accuracy information for the GNSS/levelling data and the GOCE geoid heights can be up to 4 cm over the Canadian mainland and at the dm-level for island regions. Lastly, the spatial tilts found in the levelling network can be modelled with a 2-parameter bias corrector model, which reduces the RMS of the adjusted geoid height differences by 4 cm when compared to the RMS of adjusted geoid height differences computed without the use of a bias corrector model. Thus, when computing local vertical datum offsets in Canada, it is imperative to account for GOCE commission and omission errors, ellipsoidal and levelling height errors, as well as the systematic levelling errors of the vertical control network. height system unification cgvd28 goce global geopotential model goce omission error navd88 vertical datum Geodesy Amjadiparvar B. verfasserin aut Rangelova E. verfasserin aut Sideris M.G. verfasserin aut In Journal of Geodetic Science De Gruyter, 2015 2(2012), 4, Seite 257-269 (DE-627)645088358 (DE-600)2591739-0 20819943 nnns volume:2 year:2012 number:4 pages:257-269 https://doi.org/10.2478/v10156-012-0008-4 kostenfrei https://doaj.org/article/24685e1b8e854bf9bd09fe89e8602941 kostenfrei https://doi.org/10.2478/v10156-012-0008-4 kostenfrei https://doaj.org/toc/2081-9943 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4392 GBV_ILN_4700 AR 2 2012 4 257-269 |
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Estimating Canadian vertical datum offsets using GNSS/levelling benchmark information and GOCE global geopotential models |
abstract |
The performance of GOCE-based geopotential models is assessed for the estimation of offsets for three regional vertical datums in Canada with respect to a global equipotential surface using the GNSS benchmarks from the first-order vertical control network. Factors that affect the computed value of the local vertical datum offset include the GOCE commission and omission errors, measurement errors, the configuration of the network of GNSS/levelling benchmarks, and systematic levelling errors and distortions propagated through the vertical control network. Among these various factors, the effect of the GOCE omission error on the datum offsets is investigated by extending the models with the high resolution gravity field model EGM2008 and by means of Canada’s official high resolution geoid model CGG2010. The effect of the GOCE commission error in combination with errors from the GNSS/levelling data is also examined, in addition to the effect of systematic levelling errors. In Canada, the effect of the GOCE omission error is at the dm-level when computing local vertical datum offsets. The effect of including accuracy information for the GNSS/levelling data and the GOCE geoid heights can be up to 4 cm over the Canadian mainland and at the dm-level for island regions. Lastly, the spatial tilts found in the levelling network can be modelled with a 2-parameter bias corrector model, which reduces the RMS of the adjusted geoid height differences by 4 cm when compared to the RMS of adjusted geoid height differences computed without the use of a bias corrector model. Thus, when computing local vertical datum offsets in Canada, it is imperative to account for GOCE commission and omission errors, ellipsoidal and levelling height errors, as well as the systematic levelling errors of the vertical control network. |
abstractGer |
The performance of GOCE-based geopotential models is assessed for the estimation of offsets for three regional vertical datums in Canada with respect to a global equipotential surface using the GNSS benchmarks from the first-order vertical control network. Factors that affect the computed value of the local vertical datum offset include the GOCE commission and omission errors, measurement errors, the configuration of the network of GNSS/levelling benchmarks, and systematic levelling errors and distortions propagated through the vertical control network. Among these various factors, the effect of the GOCE omission error on the datum offsets is investigated by extending the models with the high resolution gravity field model EGM2008 and by means of Canada’s official high resolution geoid model CGG2010. The effect of the GOCE commission error in combination with errors from the GNSS/levelling data is also examined, in addition to the effect of systematic levelling errors. In Canada, the effect of the GOCE omission error is at the dm-level when computing local vertical datum offsets. The effect of including accuracy information for the GNSS/levelling data and the GOCE geoid heights can be up to 4 cm over the Canadian mainland and at the dm-level for island regions. Lastly, the spatial tilts found in the levelling network can be modelled with a 2-parameter bias corrector model, which reduces the RMS of the adjusted geoid height differences by 4 cm when compared to the RMS of adjusted geoid height differences computed without the use of a bias corrector model. Thus, when computing local vertical datum offsets in Canada, it is imperative to account for GOCE commission and omission errors, ellipsoidal and levelling height errors, as well as the systematic levelling errors of the vertical control network. |
abstract_unstemmed |
The performance of GOCE-based geopotential models is assessed for the estimation of offsets for three regional vertical datums in Canada with respect to a global equipotential surface using the GNSS benchmarks from the first-order vertical control network. Factors that affect the computed value of the local vertical datum offset include the GOCE commission and omission errors, measurement errors, the configuration of the network of GNSS/levelling benchmarks, and systematic levelling errors and distortions propagated through the vertical control network. Among these various factors, the effect of the GOCE omission error on the datum offsets is investigated by extending the models with the high resolution gravity field model EGM2008 and by means of Canada’s official high resolution geoid model CGG2010. The effect of the GOCE commission error in combination with errors from the GNSS/levelling data is also examined, in addition to the effect of systematic levelling errors. In Canada, the effect of the GOCE omission error is at the dm-level when computing local vertical datum offsets. The effect of including accuracy information for the GNSS/levelling data and the GOCE geoid heights can be up to 4 cm over the Canadian mainland and at the dm-level for island regions. Lastly, the spatial tilts found in the levelling network can be modelled with a 2-parameter bias corrector model, which reduces the RMS of the adjusted geoid height differences by 4 cm when compared to the RMS of adjusted geoid height differences computed without the use of a bias corrector model. Thus, when computing local vertical datum offsets in Canada, it is imperative to account for GOCE commission and omission errors, ellipsoidal and levelling height errors, as well as the systematic levelling errors of the vertical control network. |
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Estimating Canadian vertical datum offsets using GNSS/levelling benchmark information and GOCE global geopotential models |
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The effect of including accuracy information for the GNSS/levelling data and the GOCE geoid heights can be up to 4 cm over the Canadian mainland and at the dm-level for island regions. Lastly, the spatial tilts found in the levelling network can be modelled with a 2-parameter bias corrector model, which reduces the RMS of the adjusted geoid height differences by 4 cm when compared to the RMS of adjusted geoid height differences computed without the use of a bias corrector model. 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