The Use of Second-Generation Wavelets to Combine a Gravimetric Quasigeoid Model with GPS-Levelling Data
The merging of a gravimetric quasigeoid model with GPS-levelling data using second-generation wavelets is considered so as to provide better transformation of GPS ellipsoidal heights to normal heights. Since GPS-levelling data are irregular in the space domain and the classical wavelet transform rel...
| Main Authors: | , , |
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| Format: | Journal Article |
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Springer - Verlag
2006
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| Online Access: | http://hdl.handle.net/20.500.11937/39267 |
| _version_ | 1848755545011388416 |
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| author | Soltanpour, A. Nahavandchi, H. Featherstone, Will |
| author_facet | Soltanpour, A. Nahavandchi, H. Featherstone, Will |
| author_sort | Soltanpour, A. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The merging of a gravimetric quasigeoid model with GPS-levelling data using second-generation wavelets is considered so as to provide better transformation of GPS ellipsoidal heights to normal heights. Since GPS-levelling data are irregular in the space domain and the classical wavelet transform relies on Fourier theory, which is unable to deal with irregular data sets without prior gridding, the classical wavelet transform is not directly applicable to this problem. Instead, second-generation wavelets and their associated lifting scheme, which do not require regularly spaced data, are used to combine gravimetric quasigeoid models and GPS-levelling data over Norway and Australia, and the results are cross-validated. Cross-validation means that GPS-levelling points not used in the merging are used to assess the results, where one point is omitted from the merging and used to test the merged surface, which is repeated for all points in the dataset. The wavelet-based results are also compared to those from least squares collocation (LSC) merging. This comparison shows that the second-generation wavelet method can be used instead of LSC with similar results, but the assumption of stationarity for LSC is not required in the wavelet method. Specifically, it is not necessary to (somewhat arbitrarily) remove trends from the data before applying the wavelet method, as is the case for LSC. It is also shown that the wavelet method is better at decreasing the maximum and minimum differences between the merged geoid and the cross-validating GPS-levelling data. |
| first_indexed | 2025-11-14T08:58:00Z |
| format | Journal Article |
| id | curtin-20.500.11937-39267 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:58:00Z |
| publishDate | 2006 |
| publisher | Springer - Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-392672019-02-19T05:35:17Z The Use of Second-Generation Wavelets to Combine a Gravimetric Quasigeoid Model with GPS-Levelling Data Soltanpour, A. Nahavandchi, H. Featherstone, Will Second generation wavelets Quasigeoid Lifting scheme GPS-levelling Geoid Least squares collocation (LSC) Cross-validation The merging of a gravimetric quasigeoid model with GPS-levelling data using second-generation wavelets is considered so as to provide better transformation of GPS ellipsoidal heights to normal heights. Since GPS-levelling data are irregular in the space domain and the classical wavelet transform relies on Fourier theory, which is unable to deal with irregular data sets without prior gridding, the classical wavelet transform is not directly applicable to this problem. Instead, second-generation wavelets and their associated lifting scheme, which do not require regularly spaced data, are used to combine gravimetric quasigeoid models and GPS-levelling data over Norway and Australia, and the results are cross-validated. Cross-validation means that GPS-levelling points not used in the merging are used to assess the results, where one point is omitted from the merging and used to test the merged surface, which is repeated for all points in the dataset. The wavelet-based results are also compared to those from least squares collocation (LSC) merging. This comparison shows that the second-generation wavelet method can be used instead of LSC with similar results, but the assumption of stationarity for LSC is not required in the wavelet method. Specifically, it is not necessary to (somewhat arbitrarily) remove trends from the data before applying the wavelet method, as is the case for LSC. It is also shown that the wavelet method is better at decreasing the maximum and minimum differences between the merged geoid and the cross-validating GPS-levelling data. 2006 Journal Article http://hdl.handle.net/20.500.11937/39267 10.1007/s00190-006-0033-0 Springer - Verlag fulltext |
| spellingShingle | Second generation wavelets Quasigeoid Lifting scheme GPS-levelling Geoid Least squares collocation (LSC) Cross-validation Soltanpour, A. Nahavandchi, H. Featherstone, Will The Use of Second-Generation Wavelets to Combine a Gravimetric Quasigeoid Model with GPS-Levelling Data |
| title | The Use of Second-Generation Wavelets to Combine a Gravimetric Quasigeoid Model with GPS-Levelling Data |
| title_full | The Use of Second-Generation Wavelets to Combine a Gravimetric Quasigeoid Model with GPS-Levelling Data |
| title_fullStr | The Use of Second-Generation Wavelets to Combine a Gravimetric Quasigeoid Model with GPS-Levelling Data |
| title_full_unstemmed | The Use of Second-Generation Wavelets to Combine a Gravimetric Quasigeoid Model with GPS-Levelling Data |
| title_short | The Use of Second-Generation Wavelets to Combine a Gravimetric Quasigeoid Model with GPS-Levelling Data |
| title_sort | use of second-generation wavelets to combine a gravimetric quasigeoid model with gps-levelling data |
| topic | Second generation wavelets Quasigeoid Lifting scheme GPS-levelling Geoid Least squares collocation (LSC) Cross-validation |
| url | http://hdl.handle.net/20.500.11937/39267 |