A partition-enhanced least-squares collocation approach (PE-LSC)
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 fiel...
Published in: | Journal of Geodesy |
---|---|
Main Authors: | , , , , , |
Format: | Article in Journal/Newspaper |
Language: | English |
Published: |
Springer Berlin Heidelberg
2021
|
Subjects: | |
Online Access: | https://doi.org/10.1007/s00190-021-01540-6 http://resolver.sub.uni-goettingen.de/purl?gldocs-11858/10790 |
id |
ftsubggeo:oai:e-docs.geo-leo.de:11858/10790 |
---|---|
record_format |
openpolar |
spelling |
ftsubggeo:oai:e-docs.geo-leo.de:11858/10790 2023-07-16T03:52:14+02:00 A partition-enhanced least-squares collocation approach (PE-LSC) Zingerle, P. Pail, R. Willberg, M. Scheinert, M. Institute of Astronomical and Physical Geodesy, Technical University of Munich, Munich, Germany Institut Für Planetare Geodäsie, Technische Universität Dresden, Dresden, Germany 2021-07-31 https://doi.org/10.1007/s00190-021-01540-6 http://resolver.sub.uni-goettingen.de/purl?gldocs-11858/10790 eng eng Springer Berlin Heidelberg doi:10.1007/s00190-021-01540-6 http://resolver.sub.uni-goettingen.de/purl?gldocs-11858/10790 https://creativecommons.org/licenses/by/4.0/ ddc:526 Gravity field Least squares collocation (LSC) Covariance function Data combination Prediction Antarctica doc-type:article 2021 ftsubggeo https://doi.org/10.1007/s00190-021-01540-6 2023-06-25T22:12:18Z 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 needs only hours instead of weeks) in comparison with the ... Article in Journal/Newspaper Antarc* Antarctica GEO-LEOe-docs (FID GEO) Journal of Geodesy 95 8 |
institution |
Open Polar |
collection |
GEO-LEOe-docs (FID GEO) |
op_collection_id |
ftsubggeo |
language |
English |
topic |
ddc:526 Gravity field Least squares collocation (LSC) Covariance function Data combination Prediction Antarctica |
spellingShingle |
ddc:526 Gravity field Least squares collocation (LSC) Covariance function Data combination Prediction Antarctica Zingerle, P. Pail, R. Willberg, M. Scheinert, M. Institute of Astronomical and Physical Geodesy, Technical University of Munich, Munich, Germany Institut Für Planetare Geodäsie, Technische Universität Dresden, Dresden, Germany A partition-enhanced least-squares collocation approach (PE-LSC) |
topic_facet |
ddc:526 Gravity field Least squares collocation (LSC) Covariance function Data combination Prediction Antarctica |
description |
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 needs only hours instead of weeks) in comparison with the ... |
format |
Article in Journal/Newspaper |
author |
Zingerle, P. Pail, R. Willberg, M. Scheinert, M. Institute of Astronomical and Physical Geodesy, Technical University of Munich, Munich, Germany Institut Für Planetare Geodäsie, Technische Universität Dresden, Dresden, Germany |
author_facet |
Zingerle, P. Pail, R. Willberg, M. Scheinert, M. Institute of Astronomical and Physical Geodesy, Technical University of Munich, Munich, Germany Institut Für Planetare Geodäsie, Technische Universität Dresden, Dresden, Germany |
author_sort |
Zingerle, P. |
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) |
publisher |
Springer Berlin Heidelberg |
publishDate |
2021 |
url |
https://doi.org/10.1007/s00190-021-01540-6 http://resolver.sub.uni-goettingen.de/purl?gldocs-11858/10790 |
genre |
Antarc* Antarctica |
genre_facet |
Antarc* Antarctica |
op_relation |
doi:10.1007/s00190-021-01540-6 http://resolver.sub.uni-goettingen.de/purl?gldocs-11858/10790 |
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 |
container_issue |
8 |
_version_ |
1771544937329852416 |