A partition-enhanced least-squares collocation approach (PE-LSC)
<jats:title>Abstract</jats:title><jats:p>We present a partition-enhanced least-squares collocation (PE-LSC) which comprises several modifications to the classical LSC method. It is our goal to circumvent various problems of the practical application of LSC. While these investigatio...
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ftzbmed:oai:frl.publisso.de:frl:6451821 2023-11-12T04:08:42+01:00 A partition-enhanced least-squares collocation approach (PE-LSC) Zingerle, Philipp Pail, R. Willberg, M. Scheinert, M. 2021 https://repository.publisso.de/resource/frl:6451821 https://doi.org/10.1007/s00190-021-01540-6 eng eng https://repository.publisso.de/resource/frl:6451821 https://doi.org/10.1007/s00190-021-01540-6 https://creativecommons.org/licenses/by/4.0/ http://lobid.org/resources/99370678539506441#!, 95(8):94 Original Article Gravity field Antarctica Data combination Least squares collocation (LSC) Prediction Covariance function Zeitschriftenartikel 2021 ftzbmed https://doi.org/10.1007/s00190-021-01540-6 2023-10-29T23:06:41Z <jats:title>Abstract</jats:title><jats:p>We present a partition-enhanced least-squares collocation (PE-LSC) which comprises several modifications to the classical LSC method. It is our goal to circumvent various problems of the practical application of LSC. While these investigations are focused on the modeling of the exterior gravity field the elaborated methods can also be used in other applications. One of the main drawbacks and current limitations of LSC is its high computational cost which grows cubically with the number of observation points. A common way to mitigate this problem is to tile the target area into sub-regions and solve each tile individually. This procedure assumes a certain locality of the LSC kernel functions which is generally not given and, therefore, results in fringe effects. To avoid this, it is proposed to localize the LSC kernels such that locality is preserved, and the estimated variances are not notably increased in comparison with the classical LSC method. Using global covariance models involves the calculation of a large number of Legendre polynomials which is usually a time-consuming task. Hence, to accelerate the creation of the covariance matrices, as an intermediate step we pre-calculate the covariance function on a two-dimensional grid of isotropic coordinates. Based on this grid, and under the assumption that the covariances are sufficiently smooth, the final covariance matrices are then obtained by a simple and fast interpolation algorithm. Applying the generalized multi-variate chain rule, also cross-covariance matrices among arbitrary linear spherical harmonic functionals can be obtained by this technique. Together with some further minor alterations these modifications are implemented in the PE-LSC method. The new PE-LSC is tested using selected data sets in Antarctica where altogether more than 800,000 observations are available for processing. In this case, PE-LSC yields a speed-up of computation time by a factor of about 55 (i.e., the computation ... Article in Journal/Newspaper Antarc* Antarctica PUBLISSO Fachrepositorium Lebenswissenschaften (ZB MED) Journal of Geodesy 95 8 |
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Open Polar |
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PUBLISSO Fachrepositorium Lebenswissenschaften (ZB MED) |
op_collection_id |
ftzbmed |
language |
English |
topic |
Original Article Gravity field Antarctica Data combination Least squares collocation (LSC) Prediction Covariance function |
spellingShingle |
Original Article Gravity field Antarctica Data combination Least squares collocation (LSC) Prediction Covariance function Zingerle, Philipp Pail, R. Willberg, M. Scheinert, M. A partition-enhanced least-squares collocation approach (PE-LSC) |
topic_facet |
Original Article Gravity field Antarctica Data combination Least squares collocation (LSC) Prediction Covariance function |
description |
<jats:title>Abstract</jats:title><jats:p>We present a partition-enhanced least-squares collocation (PE-LSC) which comprises several modifications to the classical LSC method. It is our goal to circumvent various problems of the practical application of LSC. While these investigations are focused on the modeling of the exterior gravity field the elaborated methods can also be used in other applications. One of the main drawbacks and current limitations of LSC is its high computational cost which grows cubically with the number of observation points. A common way to mitigate this problem is to tile the target area into sub-regions and solve each tile individually. This procedure assumes a certain locality of the LSC kernel functions which is generally not given and, therefore, results in fringe effects. To avoid this, it is proposed to localize the LSC kernels such that locality is preserved, and the estimated variances are not notably increased in comparison with the classical LSC method. Using global covariance models involves the calculation of a large number of Legendre polynomials which is usually a time-consuming task. Hence, to accelerate the creation of the covariance matrices, as an intermediate step we pre-calculate the covariance function on a two-dimensional grid of isotropic coordinates. Based on this grid, and under the assumption that the covariances are sufficiently smooth, the final covariance matrices are then obtained by a simple and fast interpolation algorithm. Applying the generalized multi-variate chain rule, also cross-covariance matrices among arbitrary linear spherical harmonic functionals can be obtained by this technique. Together with some further minor alterations these modifications are implemented in the PE-LSC method. The new PE-LSC is tested using selected data sets in Antarctica where altogether more than 800,000 observations are available for processing. In this case, PE-LSC yields a speed-up of computation time by a factor of about 55 (i.e., the computation ... |
format |
Article in Journal/Newspaper |
author |
Zingerle, Philipp Pail, R. Willberg, M. Scheinert, M. |
author_facet |
Zingerle, Philipp Pail, R. Willberg, M. Scheinert, M. |
author_sort |
Zingerle, Philipp |
title |
A partition-enhanced least-squares collocation approach (PE-LSC) |
title_short |
A partition-enhanced least-squares collocation approach (PE-LSC) |
title_full |
A partition-enhanced least-squares collocation approach (PE-LSC) |
title_fullStr |
A partition-enhanced least-squares collocation approach (PE-LSC) |
title_full_unstemmed |
A partition-enhanced least-squares collocation approach (PE-LSC) |
title_sort |
partition-enhanced least-squares collocation approach (pe-lsc) |
publishDate |
2021 |
url |
https://repository.publisso.de/resource/frl:6451821 https://doi.org/10.1007/s00190-021-01540-6 |
genre |
Antarc* Antarctica |
genre_facet |
Antarc* Antarctica |
op_source |
http://lobid.org/resources/99370678539506441#!, 95(8):94 |
op_relation |
https://repository.publisso.de/resource/frl:6451821 https://doi.org/10.1007/s00190-021-01540-6 |
op_rights |
https://creativecommons.org/licenses/by/4.0/ |
op_doi |
https://doi.org/10.1007/s00190-021-01540-6 |
container_title |
Journal of Geodesy |
container_volume |
95 |
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8 |
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1782328925813211136 |