{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T01:08:45Z","timestamp":1772068125475,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2011,3,30]],"date-time":"2011-03-30T00:00:00Z","timestamp":1301443200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The determination of the orthometric height from geometric leveling has practical difficulties that, despite a number of scientific and technological advances, passed a century without substantial modifications or advances. Currently, the Global Navigation Satellite System (GNSS) has been used with reasonable success for orthometric height determination. With a sufficient number of benchmarks with known horizontal and vertical coordinates, it is often possible to adjust using the least squares method mathematical expressions that allow interpolation of geoid heights. The objective of this study is to present an alternative method to interpolate geoid heights based on the technique of Artificial Neural Networks (ANNs). The study area is the Brazilian state of S\u00e3o Paulo, and for training the ANN the authors have used geoid height information from the EGM08 gravity model with a grid spacing of 10 minutes of arc. The efficiency of the model was tested at 157 points with known geoid heights distributed across the study area. The results were also compared with the Brazilian Geoid Model (MAPGEO2004). Based on those 157 benchmarks it was possible to verify that the model generated by ANNs provided a mean absolute error of 0.24 m in obtaining a geoid height value. Statistical tests have shown that there was no difference between the means from known geoid heights and geoid heights provided by the neural model for a significance level of 5%. It was also found that ANNs provided an improvement of 2.7 times in geoid height estimates when compared with the MAPGEO2004 geoid model.<\/jats:p>","DOI":"10.3390\/rs3040668","type":"journal-article","created":{"date-parts":[[2011,4,4]],"date-time":"2011-04-04T10:07:21Z","timestamp":1301911641000},"page":"668-683","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Regional Mapping of the Geoid Using GNSS (GPS) Measurements and an Artificial Neural Network"],"prefix":"10.3390","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5914-3546","authenticated-orcid":false,"given":"Mauricio Roberto","family":"Veronez","sequence":"first","affiliation":[{"name":"Graduate Program in Geology, Remote Sensing and Digital Cartography Laboratory (LASERCA), Universidade do Vale do Rio dos Sinos (UNISINOS), Av. Unisinos, 950, CEP 93022-000 S\u00e3o Leopoldo, RS, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S\u00e9rgio","family":"Flor\u00eancio de Souza","sequence":"additional","affiliation":[{"name":"Laboratory of Geodetic Researches (LAGEO), Geosciences Institute, Geodetic Department, Universidade Federal do Rio Grande do Sul (UFRGS), Av. Bento Gon\u00e7alves, 9500, CEP 91501-970 Porto Alegre, RS, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcelo Tomio","family":"Matsuoka","sequence":"additional","affiliation":[{"name":"Laboratory of Geodetic Researches (LAGEO), Geosciences Institute, Geodetic Department, Universidade Federal do Rio Grande do Sul (UFRGS), Av. Bento Gon\u00e7alves, 9500, CEP 91501-970 Porto Alegre, RS, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alessandro","family":"Reinhardt","sequence":"additional","affiliation":[{"name":"Graduate Program in Geology, Remote Sensing and Digital Cartography Laboratory (LASERCA), Universidade do Vale do Rio dos Sinos (UNISINOS), Av. Unisinos, 950, CEP 93022-000 S\u00e3o Leopoldo, RS, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Reginaldo","family":"Maced\u00f4nio da Silva","sequence":"additional","affiliation":[{"name":"Graduate Program in Geology, Remote Sensing and Digital Cartography Laboratory (LASERCA), Universidade do Vale do Rio dos Sinos (UNISINOS), Av. Unisinos, 950, CEP 93022-000 S\u00e3o Leopoldo, RS, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2011,3,30]]},"reference":[{"key":"ref_1","unstructured":"M\u00fcller, M., and Fill, H.D. (2003, January 23\u201327). Redes Neurais aplicadas na programa\u00e7\u00e3o de vaz\u00f5es. Proceedings of Simp\u00f3sio Brasileiro de Recursos H\u00eddricos, Curitiba, Brazil."},{"key":"ref_2","unstructured":"Haykin, S. (2001). Redes Neurais: Princ\u00edpios e pr\u00e1tica, Bookman."},{"key":"ref_3","unstructured":"Galv\u00e3o, C.O., and Valen\u00e7a, M.J.S. (1999). Sistemas inteligentes: Aplica\u00e7\u00f5es a recursos h\u00eddricos e ci\u00eancias ambientais, UFRGS\/ABRH."},{"key":"ref_4","unstructured":"Atluri, V., Hung, C.C., and Coleman, T.L. (1999, January 25\u201328). An artificial neural network for classifying and predicting soil moisture and temperature using Levenberg-Marquat algorithm. Proceedings of IEEE Southeastcon \u201999, Lexington, KY, USA."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1737","DOI":"10.1016\/S0362-546X(01)00306-6","article-title":"Prediction of soil temperature by using artificial neural networks algorithms","volume":"47","author":"George","year":"2001","journal-title":"Nonlinear Analysis"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1061\/(ASCE)0733-9437(2002)128:4(224)","article-title":"Estimating evapotranspiration using artificial neural network","volume":"128","author":"Kumar","year":"2002","journal-title":"J. Irrig. Drainage Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1109\/TGRS.2007.907333","article-title":"Neural network technique for separating land surface emissivity and temperature from ASTER imagery","volume":"46","author":"Mao","year":"2008","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1590\/S0102-261X2009000400004","article-title":"Estimativa de alturas geoidais para o estado de S\u00e3o Paulo baseada em redes neurais artificiais","volume":"27","author":"Veronez","year":"2009","journal-title":"Revista Brasileira de Geof\u00edsica"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"649","DOI":"10.13031\/2013.21324","article-title":"Application of artificial neural networks for simulations of soil temperature","volume":"40","author":"Yang","year":"1997","journal-title":"Trans. ASAE"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1590\/S1415-43662008000200010","article-title":"Estima\u00e7\u00e3o da evapotranspira\u00e7\u00e3o de refer\u00eancia no Estado do Rio de Janeiro usando redes neurais artificiais","volume":"12","author":"Zanetti","year":"2008","journal-title":"Revista Brasileira de Engenharia Agr\u00edcola e Ambiental"},{"key":"ref_11","unstructured":"Andrade, A.J.N. (1997). Aplica\u00e7\u00e3o de redes neurais artificiais na interpreta\u00e7\u00e3o de perfis de po\u00e7o aberto. [Ph.D. Thesis, Curso de P\u00f3s-gradua\u00e7\u00e3o em Geof\u00edsica, Universidade Federal do Par\u00e1]."},{"key":"ref_12","unstructured":"Bhatt, A. (2002). Reservoir Properties from Well Logs Using Neural Networks. [Ph.D. Thesis, Department of Petroleum Engineering and Applied Geophysics, Norwegian University of Science and Technology]."},{"key":"ref_13","first-page":"1","article-title":"Investiga\u00e7\u00e3o do treinamento de uma rede neural para o conhecimento de litof\u00e1cies combinando dados de testemunhos e perfis de po\u00e7os de petr\u00f3leo","volume":"2","author":"Oliveira","year":"2003","journal-title":"Congresso Brasileiro de P&S em Petr\u00f3leo & Gas"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.cageo.2004.07.004","article-title":"Lithology of aquifers from geophysical well logs and fuzzy logic analysis: Shui-Lin Area, Taiwan","volume":"31","author":"Hsieh","year":"2005","journal-title":"Comput. Geosci."},{"key":"ref_15","unstructured":"da Silva, A.N.R., Ramos, R.A.R., de Souza, L.C.L., Rodrigues, D.S., and Mendes, J.F.G. (2004). SIG: Uma plataforma para introdu\u00e7\u00e3o de t\u00e9cnicas emergentes no planejamento urbano regional e de transportes, EESC\/USP."},{"key":"ref_16","unstructured":"Siripitayananon, P., Chen, H.C., and Hart, B.S. (2001, January 16\u201317). A new technique for lithofacies prediction: Back-propagation neural network. Proceedings of ACMSE: The 39th Association of Computing and Machinery South Eastern Conference, Atlanta, GA, USA."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1144\/1354-079302-566","article-title":"Quantitative assessment of mudstone lithology using geophysical wireline logs and artificial neural networks","volume":"10","author":"Yang","year":"2004","journal-title":"Petroleum Geosci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"868","DOI":"10.2136\/vzj2007.0055","article-title":"Multiscale pedotransfer functions for soil water retention","volume":"6","author":"Jana","year":"2007","journal-title":"Vadose Zone J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1676","DOI":"10.2136\/sssaj2006.0396","article-title":"Estimating saturated hydraulic conductivity using genetic programming","volume":"71","author":"Parasueaman","year":"2007","journal-title":"Soil Sci. Soc. Am. J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"43","DOI":"10.2136\/sssaj2006.0098","article-title":"Excluding organic matter content from pedotransfer predictors of soil water retention","volume":"71","author":"Zacharias","year":"2007","journal-title":"Soil Sci. Soc. Am. J."},{"key":"ref_21","unstructured":"Da Silva, C.A.U. (2003). Um m\u00e9todo para estimar observ\u00e1veis GPS usando redes neurais artificiais. [Ph.D. Thesis, Escola de Engenharia de S\u00e3o Carlos, Universidade de S\u00e3o Paulo]."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1029\/97RS00431","article-title":"Neural network modeling of ionospheric electron content at global scale using GPS data","volume":"32","year":"1997","journal-title":"Radio Science"},{"key":"ref_23","unstructured":"Gemael, C. (1999). Introdu\u00e7\u00e3o \u00e0 Geod\u00e9sia F\u00edsica, UFPR."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Heiskanen, W.A., and Moritz, H. (1967). Physical Geodesy, W.H. Freeman and Company.","DOI":"10.1007\/BF02525647"},{"key":"ref_25","first-page":"485","article-title":"The use of FFT techniques in physical geodesy","volume":"110","author":"Schwarz","year":"1989","journal-title":"Geophys. Int. J."},{"key":"ref_26","unstructured":"Maia, T.C.B. (2003). Utiliza\u00e7\u00e3o de redes neurais artificiais na determina\u00e7\u00e3o de modelos geoidais. [Ph.D. Thesis, Escola de Engenharia de S\u00e3o Carlos, Universidade de S\u00e3o Paulo]."},{"key":"ref_27","unstructured":"Miranda, F.A., De Freitas, S.R.C., and Fraggion, P.L. (2007, January 24\u201327). Integra\u00e7\u00e3o e interpola\u00e7\u00e3o de dados de anomalias ar livre utilizando-se a t\u00e9cnica de RNA e krigagem. Simp\u00f3sio Brasileiro de Geom\u00e1tica, Presidente Prudente, Brazil."},{"key":"ref_28","unstructured":"Seager, J., Collie, P., and Kirb, J. (1999, January 10\u201316). Modelling geoid undulations with an artificial neural network. Proceedings of 1999 International Joint Conference on Neural Networks, Washington, DC, USA."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Tierra, A., and De Freitas, S.R.C. (2001, January 20\u201323). Predicting free-air gravity anomaly using artificial neural network. Proceedings of International Association of Geodesy Symposia: Vertical Reference Systems, Cartagena, Colombia.","DOI":"10.1007\/978-3-662-04683-8_41"},{"key":"ref_30","unstructured":"Lemoine, F.G., Kenyon, S.C., Factor, J.K., Trimmer, R.G., Pavlis, N.K., Chinn, D.S., Cox, C.M., Klosko, S.M., Luthcke, S.B., and Torrence, M.H. (1998). The Development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96, NASA Goddard Space Flight Center. NASA\/TP-1998-206861."},{"key":"ref_31","first-page":"27","article-title":"Determina\u00e7\u00e3o da superf\u00edcie geoidal atrav\u00e9s de redes neurais artificiais","volume":"3","author":"Reinke","year":"2007","journal-title":"GAEA"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Pavlis, N.K., Holmes, S.A., Kenyon, S.C., and Factor, J.K. (2008). An earth gravitational model to degree 2160: EGM2008. Geophys. Res. Abs., 10, EGU2008-A-01891.","DOI":"10.1190\/1.3063757"},{"key":"ref_33","unstructured":"Souza, S.F. (2002). Contribui\u00e7\u00e3o do GPS pra Aprimoramento do Ge\u00f3ide no Estado de S\u00e3o Paulo. [Ph.D. Thesis, IAG, Universidade de S\u00e3o Paulo]."},{"key":"ref_34","unstructured":"IBGE. Instituto Brasileiro de Geografia e Estat\u00edstica Geosci\u00eancias, Available on line: http:\/\/www.ibge.gov.br\/home\/geociencias\/geodesia\/modelo_geoidal.shtm."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/3\/4\/668\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:55:42Z","timestamp":1760219742000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/3\/4\/668"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3,30]]},"references-count":34,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2011,4]]}},"alternative-id":["rs3040668"],"URL":"https:\/\/doi.org\/10.3390\/rs3040668","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3,30]]}}}