Estimation of Height Anomalies from Gradients of the Gravitational Potential Using a Spectral Combination Method Article Swipe
Martin Pitoňák
,
Michal Šprlák
,
Pavel Novák
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1007/1345_2023_194
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1007/1345_2023_194
In this study, we apply a spectral combination method for estimation of height anomalies from gradients of the gravitational potential measured by satellites. The spectral combination method is used for solving over-determined problems within gravity field modelling when multiple types of gravity data are collected and used for recovery of unobservable quantities (typically the gravitational potential). The method applies solutions to geodetic boundary-value problems formulated in spherical approximation for gradients of the gravitational potential of up to the third order. Spectral forms of the solutions are combined using spectral weights defined under the condition of minimizing the global mean-square error of the estimators. Mathematical models are implemented and tested using gradients synthesized from a global geopotential model which allows for closed-loop testing of the estimators. The tests reveal among others that horizontal derivatives of the gravitational potential influence recovered values more than their vertical counterparts.
Related Topics
Concepts
Metadata
- Type
- book-chapter
- Language
- en
- Landing Page
- https://doi.org/10.1007/1345_2023_194
- https://link.springer.com/content/pdf/10.1007/1345_2023_194.pdf
- OA Status
- hybrid
- References
- 9
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4381303451
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W4381303451Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.1007/1345_2023_194Digital Object Identifier
- Title
-
Estimation of Height Anomalies from Gradients of the Gravitational Potential Using a Spectral Combination MethodWork title
- Type
-
book-chapterOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-01-01Full publication date if available
- Authors
-
Martin Pitoňák, Michal Šprlák, Pavel NovákList of authors in order
- Landing page
-
https://doi.org/10.1007/1345_2023_194Publisher landing page
- PDF URL
-
https://link.springer.com/content/pdf/10.1007/1345_2023_194.pdfDirect link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
hybridOpen access status per OpenAlex
- OA URL
-
https://link.springer.com/content/pdf/10.1007/1345_2023_194.pdfDirect OA link when available
- Concepts
-
Geopotential, Gravitational field, Estimator, Gravitation, Spectral method, Geodetic datum, Gravitational potential, Geodesy, Unobservable, Mathematics, Boundary value problem, Applied mathematics, Mathematical analysis, Physics, Geology, Statistics, Classical mechanics, EconometricsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- References (count)
-
9Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W4381303451 |
|---|---|
| doi | https://doi.org/10.1007/1345_2023_194 |
| ids.doi | https://doi.org/10.1007/1345_2023_194 |
| ids.openalex | https://openalex.org/W4381303451 |
| fwci | 0.0 |
| type | book-chapter |
| title | Estimation of Height Anomalies from Gradients of the Gravitational Potential Using a Spectral Combination Method |
| biblio.issue | |
| biblio.volume | |
| biblio.last_page | 45 |
| biblio.first_page | 37 |
| topics[0].id | https://openalex.org/T11405 |
| topics[0].field.id | https://openalex.org/fields/19 |
| topics[0].field.display_name | Earth and Planetary Sciences |
| topics[0].score | 0.9998999834060669 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/1910 |
| topics[0].subfield.display_name | Oceanography |
| topics[0].display_name | Geophysics and Gravity Measurements |
| topics[1].id | https://openalex.org/T10655 |
| topics[1].field.id | https://openalex.org/fields/22 |
| topics[1].field.display_name | Engineering |
| topics[1].score | 0.995199978351593 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/2202 |
| topics[1].subfield.display_name | Aerospace Engineering |
| topics[1].display_name | GNSS positioning and interference |
| topics[2].id | https://openalex.org/T13487 |
| topics[2].field.id | https://openalex.org/fields/26 |
| topics[2].field.display_name | Mathematics |
| topics[2].score | 0.9905999898910522 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2604 |
| topics[2].subfield.display_name | Applied Mathematics |
| topics[2].display_name | Statistical and numerical algorithms |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C160121416 |
| concepts[0].level | 2 |
| concepts[0].score | 0.7957529425621033 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q1423347 |
| concepts[0].display_name | Geopotential |
| concepts[1].id | https://openalex.org/C14257148 |
| concepts[1].level | 2 |
| concepts[1].score | 0.7532727718353271 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q558066 |
| concepts[1].display_name | Gravitational field |
| concepts[2].id | https://openalex.org/C185429906 |
| concepts[2].level | 2 |
| concepts[2].score | 0.6598659157752991 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q1130160 |
| concepts[2].display_name | Estimator |
| concepts[3].id | https://openalex.org/C124017977 |
| concepts[3].level | 2 |
| concepts[3].score | 0.6054926514625549 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q11412 |
| concepts[3].display_name | Gravitation |
| concepts[4].id | https://openalex.org/C23463724 |
| concepts[4].level | 2 |
| concepts[4].score | 0.5712437033653259 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q2308831 |
| concepts[4].display_name | Spectral method |
| concepts[5].id | https://openalex.org/C58754882 |
| concepts[5].level | 2 |
| concepts[5].score | 0.53690505027771 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q1502887 |
| concepts[5].display_name | Geodetic datum |
| concepts[6].id | https://openalex.org/C127090403 |
| concepts[6].level | 3 |
| concepts[6].score | 0.5225674510002136 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q1544012 |
| concepts[6].display_name | Gravitational potential |
| concepts[7].id | https://openalex.org/C13280743 |
| concepts[7].level | 1 |
| concepts[7].score | 0.5138218998908997 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q131089 |
| concepts[7].display_name | Geodesy |
| concepts[8].id | https://openalex.org/C2780695315 |
| concepts[8].level | 2 |
| concepts[8].score | 0.4766564965248108 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q3799040 |
| concepts[8].display_name | Unobservable |
| concepts[9].id | https://openalex.org/C33923547 |
| concepts[9].level | 0 |
| concepts[9].score | 0.4591268002986908 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[9].display_name | Mathematics |
| concepts[10].id | https://openalex.org/C182310444 |
| concepts[10].level | 2 |
| concepts[10].score | 0.417459100484848 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q1332643 |
| concepts[10].display_name | Boundary value problem |
| concepts[11].id | https://openalex.org/C28826006 |
| concepts[11].level | 1 |
| concepts[11].score | 0.3532307744026184 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q33521 |
| concepts[11].display_name | Applied mathematics |
| concepts[12].id | https://openalex.org/C134306372 |
| concepts[12].level | 1 |
| concepts[12].score | 0.2753538489341736 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q7754 |
| concepts[12].display_name | Mathematical analysis |
| concepts[13].id | https://openalex.org/C121332964 |
| concepts[13].level | 0 |
| concepts[13].score | 0.27035754919052124 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[13].display_name | Physics |
| concepts[14].id | https://openalex.org/C127313418 |
| concepts[14].level | 0 |
| concepts[14].score | 0.2252112329006195 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q1069 |
| concepts[14].display_name | Geology |
| concepts[15].id | https://openalex.org/C105795698 |
| concepts[15].level | 1 |
| concepts[15].score | 0.1642673909664154 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q12483 |
| concepts[15].display_name | Statistics |
| concepts[16].id | https://openalex.org/C74650414 |
| concepts[16].level | 1 |
| concepts[16].score | 0.12905213236808777 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q11397 |
| concepts[16].display_name | Classical mechanics |
| concepts[17].id | https://openalex.org/C149782125 |
| concepts[17].level | 1 |
| concepts[17].score | 0.0 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q160039 |
| concepts[17].display_name | Econometrics |
| keywords[0].id | https://openalex.org/keywords/geopotential |
| keywords[0].score | 0.7957529425621033 |
| keywords[0].display_name | Geopotential |
| keywords[1].id | https://openalex.org/keywords/gravitational-field |
| keywords[1].score | 0.7532727718353271 |
| keywords[1].display_name | Gravitational field |
| keywords[2].id | https://openalex.org/keywords/estimator |
| keywords[2].score | 0.6598659157752991 |
| keywords[2].display_name | Estimator |
| keywords[3].id | https://openalex.org/keywords/gravitation |
| keywords[3].score | 0.6054926514625549 |
| keywords[3].display_name | Gravitation |
| keywords[4].id | https://openalex.org/keywords/spectral-method |
| keywords[4].score | 0.5712437033653259 |
| keywords[4].display_name | Spectral method |
| keywords[5].id | https://openalex.org/keywords/geodetic-datum |
| keywords[5].score | 0.53690505027771 |
| keywords[5].display_name | Geodetic datum |
| keywords[6].id | https://openalex.org/keywords/gravitational-potential |
| keywords[6].score | 0.5225674510002136 |
| keywords[6].display_name | Gravitational potential |
| keywords[7].id | https://openalex.org/keywords/geodesy |
| keywords[7].score | 0.5138218998908997 |
| keywords[7].display_name | Geodesy |
| keywords[8].id | https://openalex.org/keywords/unobservable |
| keywords[8].score | 0.4766564965248108 |
| keywords[8].display_name | Unobservable |
| keywords[9].id | https://openalex.org/keywords/mathematics |
| keywords[9].score | 0.4591268002986908 |
| keywords[9].display_name | Mathematics |
| keywords[10].id | https://openalex.org/keywords/boundary-value-problem |
| keywords[10].score | 0.417459100484848 |
| keywords[10].display_name | Boundary value problem |
| keywords[11].id | https://openalex.org/keywords/applied-mathematics |
| keywords[11].score | 0.3532307744026184 |
| keywords[11].display_name | Applied mathematics |
| keywords[12].id | https://openalex.org/keywords/mathematical-analysis |
| keywords[12].score | 0.2753538489341736 |
| keywords[12].display_name | Mathematical analysis |
| keywords[13].id | https://openalex.org/keywords/physics |
| keywords[13].score | 0.27035754919052124 |
| keywords[13].display_name | Physics |
| keywords[14].id | https://openalex.org/keywords/geology |
| keywords[14].score | 0.2252112329006195 |
| keywords[14].display_name | Geology |
| keywords[15].id | https://openalex.org/keywords/statistics |
| keywords[15].score | 0.1642673909664154 |
| keywords[15].display_name | Statistics |
| keywords[16].id | https://openalex.org/keywords/classical-mechanics |
| keywords[16].score | 0.12905213236808777 |
| keywords[16].display_name | Classical mechanics |
| language | en |
| locations[0].id | doi:10.1007/1345_2023_194 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S4210233367 |
| locations[0].source.issn | 0939-9585, 2197-9359 |
| locations[0].source.type | book series |
| locations[0].source.is_oa | False |
| locations[0].source.issn_l | 0939-9585 |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | International Association of Geodesy symposia |
| locations[0].source.host_organization | https://openalex.org/P4310319965 |
| locations[0].source.host_organization_name | Springer Nature |
| locations[0].source.host_organization_lineage | https://openalex.org/P4310319965 |
| locations[0].source.host_organization_lineage_names | Springer Nature |
| locations[0].license | cc-by |
| locations[0].pdf_url | https://link.springer.com/content/pdf/10.1007/1345_2023_194.pdf |
| locations[0].version | publishedVersion |
| locations[0].raw_type | book-chapter |
| locations[0].license_id | https://openalex.org/licenses/cc-by |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | International Association of Geodesy Symposia |
| locations[0].landing_page_url | https://doi.org/10.1007/1345_2023_194 |
| indexed_in | crossref |
| authorships[0].author.id | https://openalex.org/A5040743378 |
| authorships[0].author.orcid | https://orcid.org/0000-0003-4730-7758 |
| authorships[0].author.display_name | Martin Pitoňák |
| authorships[0].countries | CZ |
| authorships[0].affiliations[0].institution_ids | https://openalex.org/I92715842 |
| authorships[0].affiliations[0].raw_affiliation_string | NTIS—New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Plzeň, Czech Republic |
| authorships[0].institutions[0].id | https://openalex.org/I92715842 |
| authorships[0].institutions[0].ror | https://ror.org/040t43x18 |
| authorships[0].institutions[0].type | education |
| authorships[0].institutions[0].lineage | https://openalex.org/I92715842 |
| authorships[0].institutions[0].country_code | CZ |
| authorships[0].institutions[0].display_name | University of West Bohemia |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Martin Pitoňák |
| authorships[0].is_corresponding | True |
| authorships[0].raw_affiliation_strings | NTIS—New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Plzeň, Czech Republic |
| authorships[1].author.id | https://openalex.org/A5032034926 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-3861-7001 |
| authorships[1].author.display_name | Michal Šprlák |
| authorships[1].countries | CZ |
| authorships[1].affiliations[0].institution_ids | https://openalex.org/I92715842 |
| authorships[1].affiliations[0].raw_affiliation_string | NTIS—New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Plzeň, Czech Republic |
| authorships[1].institutions[0].id | https://openalex.org/I92715842 |
| authorships[1].institutions[0].ror | https://ror.org/040t43x18 |
| authorships[1].institutions[0].type | education |
| authorships[1].institutions[0].lineage | https://openalex.org/I92715842 |
| authorships[1].institutions[0].country_code | CZ |
| authorships[1].institutions[0].display_name | University of West Bohemia |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Michal Šprlák |
| authorships[1].is_corresponding | False |
| authorships[1].raw_affiliation_strings | NTIS—New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Plzeň, Czech Republic |
| authorships[2].author.id | https://openalex.org/A5086343521 |
| authorships[2].author.orcid | https://orcid.org/0000-0001-7173-7905 |
| authorships[2].author.display_name | Pavel Novák |
| authorships[2].countries | CZ |
| authorships[2].affiliations[0].institution_ids | https://openalex.org/I92715842 |
| authorships[2].affiliations[0].raw_affiliation_string | NTIS—New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Plzeň, Czech Republic |
| authorships[2].institutions[0].id | https://openalex.org/I92715842 |
| authorships[2].institutions[0].ror | https://ror.org/040t43x18 |
| authorships[2].institutions[0].type | education |
| authorships[2].institutions[0].lineage | https://openalex.org/I92715842 |
| authorships[2].institutions[0].country_code | CZ |
| authorships[2].institutions[0].display_name | University of West Bohemia |
| authorships[2].author_position | last |
| authorships[2].raw_author_name | Pavel Novák |
| authorships[2].is_corresponding | False |
| authorships[2].raw_affiliation_strings | NTIS—New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Plzeň, Czech Republic |
| has_content.pdf | True |
| has_content.grobid_xml | True |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | https://link.springer.com/content/pdf/10.1007/1345_2023_194.pdf |
| open_access.oa_status | hybrid |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Estimation of Height Anomalies from Gradients of the Gravitational Potential Using a Spectral Combination Method |
| has_fulltext | True |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T11405 |
| primary_topic.field.id | https://openalex.org/fields/19 |
| primary_topic.field.display_name | Earth and Planetary Sciences |
| primary_topic.score | 0.9998999834060669 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/1910 |
| primary_topic.subfield.display_name | Oceanography |
| primary_topic.display_name | Geophysics and Gravity Measurements |
| related_works | https://openalex.org/W2379479698, https://openalex.org/W2935839918, https://openalex.org/W1650184276, https://openalex.org/W4308145589, https://openalex.org/W137900219, https://openalex.org/W1985055893, https://openalex.org/W2076095156, https://openalex.org/W2359413702, https://openalex.org/W1996285030, https://openalex.org/W2360831354 |
| cited_by_count | 0 |
| locations_count | 1 |
| best_oa_location.id | doi:10.1007/1345_2023_194 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S4210233367 |
| best_oa_location.source.issn | 0939-9585, 2197-9359 |
| best_oa_location.source.type | book series |
| best_oa_location.source.is_oa | False |
| best_oa_location.source.issn_l | 0939-9585 |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | International Association of Geodesy symposia |
| best_oa_location.source.host_organization | https://openalex.org/P4310319965 |
| best_oa_location.source.host_organization_name | Springer Nature |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4310319965 |
| best_oa_location.source.host_organization_lineage_names | Springer Nature |
| best_oa_location.license | cc-by |
| best_oa_location.pdf_url | https://link.springer.com/content/pdf/10.1007/1345_2023_194.pdf |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | book-chapter |
| best_oa_location.license_id | https://openalex.org/licenses/cc-by |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | International Association of Geodesy Symposia |
| best_oa_location.landing_page_url | https://doi.org/10.1007/1345_2023_194 |
| primary_location.id | doi:10.1007/1345_2023_194 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S4210233367 |
| primary_location.source.issn | 0939-9585, 2197-9359 |
| primary_location.source.type | book series |
| primary_location.source.is_oa | False |
| primary_location.source.issn_l | 0939-9585 |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | International Association of Geodesy symposia |
| primary_location.source.host_organization | https://openalex.org/P4310319965 |
| primary_location.source.host_organization_name | Springer Nature |
| primary_location.source.host_organization_lineage | https://openalex.org/P4310319965 |
| primary_location.source.host_organization_lineage_names | Springer Nature |
| primary_location.license | cc-by |
| primary_location.pdf_url | https://link.springer.com/content/pdf/10.1007/1345_2023_194.pdf |
| primary_location.version | publishedVersion |
| primary_location.raw_type | book-chapter |
| primary_location.license_id | https://openalex.org/licenses/cc-by |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | International Association of Geodesy Symposia |
| primary_location.landing_page_url | https://doi.org/10.1007/1345_2023_194 |
| publication_date | 2023-01-01 |
| publication_year | 2023 |
| referenced_works | https://openalex.org/W2033728250, https://openalex.org/W2026200200, https://openalex.org/W2006769884, https://openalex.org/W4232368692, https://openalex.org/W2796827384, https://openalex.org/W3041582022, https://openalex.org/W1985971419, https://openalex.org/W2354035757, https://openalex.org/W6936793897 |
| referenced_works_count | 9 |
| abstract_inverted_index.a | 6, 114 |
| abstract_inverted_index.In | 1 |
| abstract_inverted_index.by | 22 |
| abstract_inverted_index.in | 66 |
| abstract_inverted_index.is | 28 |
| abstract_inverted_index.of | 12, 17, 41, 50, 71, 75, 83, 95, 101, 123, 134 |
| abstract_inverted_index.to | 61, 77 |
| abstract_inverted_index.up | 76 |
| abstract_inverted_index.we | 4 |
| abstract_inverted_index.The | 24, 57, 126 |
| abstract_inverted_index.and | 46, 108 |
| abstract_inverted_index.are | 44, 86, 106 |
| abstract_inverted_index.for | 10, 30, 48, 69, 120 |
| abstract_inverted_index.the | 18, 54, 72, 78, 84, 93, 97, 102, 124, 135 |
| abstract_inverted_index.data | 43 |
| abstract_inverted_index.from | 15, 113 |
| abstract_inverted_index.more | 141 |
| abstract_inverted_index.than | 142 |
| abstract_inverted_index.that | 131 |
| abstract_inverted_index.this | 2 |
| abstract_inverted_index.used | 29, 47 |
| abstract_inverted_index.when | 38 |
| abstract_inverted_index.among | 129 |
| abstract_inverted_index.apply | 5 |
| abstract_inverted_index.error | 100 |
| abstract_inverted_index.field | 36 |
| abstract_inverted_index.forms | 82 |
| abstract_inverted_index.model | 117 |
| abstract_inverted_index.tests | 127 |
| abstract_inverted_index.their | 143 |
| abstract_inverted_index.third | 79 |
| abstract_inverted_index.types | 40 |
| abstract_inverted_index.under | 92 |
| abstract_inverted_index.using | 88, 110 |
| abstract_inverted_index.which | 118 |
| abstract_inverted_index.allows | 119 |
| abstract_inverted_index.global | 98, 115 |
| abstract_inverted_index.height | 13 |
| abstract_inverted_index.method | 9, 27, 58 |
| abstract_inverted_index.models | 105 |
| abstract_inverted_index.order. | 80 |
| abstract_inverted_index.others | 130 |
| abstract_inverted_index.reveal | 128 |
| abstract_inverted_index.study, | 3 |
| abstract_inverted_index.tested | 109 |
| abstract_inverted_index.values | 140 |
| abstract_inverted_index.within | 34 |
| abstract_inverted_index.applies | 59 |
| abstract_inverted_index.defined | 91 |
| abstract_inverted_index.gravity | 35, 42 |
| abstract_inverted_index.solving | 31 |
| abstract_inverted_index.testing | 122 |
| abstract_inverted_index.weights | 90 |
| abstract_inverted_index.Abstract | 0 |
| abstract_inverted_index.Spectral | 81 |
| abstract_inverted_index.combined | 87 |
| abstract_inverted_index.geodetic | 62 |
| abstract_inverted_index.measured | 21 |
| abstract_inverted_index.multiple | 39 |
| abstract_inverted_index.problems | 33, 64 |
| abstract_inverted_index.recovery | 49 |
| abstract_inverted_index.spectral | 7, 25, 89 |
| abstract_inverted_index.vertical | 144 |
| abstract_inverted_index.anomalies | 14 |
| abstract_inverted_index.collected | 45 |
| abstract_inverted_index.condition | 94 |
| abstract_inverted_index.gradients | 16, 70, 111 |
| abstract_inverted_index.influence | 138 |
| abstract_inverted_index.modelling | 37 |
| abstract_inverted_index.potential | 20, 74, 137 |
| abstract_inverted_index.recovered | 139 |
| abstract_inverted_index.solutions | 60, 85 |
| abstract_inverted_index.spherical | 67 |
| abstract_inverted_index.(typically | 53 |
| abstract_inverted_index.estimation | 11 |
| abstract_inverted_index.formulated | 65 |
| abstract_inverted_index.horizontal | 132 |
| abstract_inverted_index.minimizing | 96 |
| abstract_inverted_index.quantities | 52 |
| abstract_inverted_index.closed-loop | 121 |
| abstract_inverted_index.combination | 8, 26 |
| abstract_inverted_index.derivatives | 133 |
| abstract_inverted_index.estimators. | 103, 125 |
| abstract_inverted_index.implemented | 107 |
| abstract_inverted_index.mean-square | 99 |
| abstract_inverted_index.potential). | 56 |
| abstract_inverted_index.satellites. | 23 |
| abstract_inverted_index.synthesized | 112 |
| abstract_inverted_index.Mathematical | 104 |
| abstract_inverted_index.geopotential | 116 |
| abstract_inverted_index.unobservable | 51 |
| abstract_inverted_index.approximation | 68 |
| abstract_inverted_index.counterparts. | 145 |
| abstract_inverted_index.gravitational | 19, 55, 73, 136 |
| abstract_inverted_index.boundary-value | 63 |
| abstract_inverted_index.over-determined | 32 |
| cited_by_percentile_year | |
| corresponding_author_ids | https://openalex.org/A5040743378 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 3 |
| corresponding_institution_ids | https://openalex.org/I92715842 |
| citation_normalized_percentile.value | 0.19145803 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |