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Application of neural network technique to determine a corrector surface for global geopotential model using GPS/levelling measurements in Egypt

  • Hossam Talaat Elshambaky EMAIL logo
Published/Copyright: October 11, 2017
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Abstract

Owing to the appearance of many global geopotential models, it is necessary to determine the most appropriate model for use in Egyptian territory. In this study, we aim to investigate three global models, namely EGM2008, EIGEN-6c4, and GECO. We use five mathematical transformation techniques, i.e., polynomial expression, exponential regression, least-squares collocation, multilayer feed forward neural network, and radial basis neural networks to make the conversion from regional geometrical geoid to global geoid models and vice versa. From a statistical comparison study based on quality indexes between previous transformation techniques, we confirm that the multilayer feed forward neural network with two neurons is the most accurate of the examined transformation technique, and based on the mean tide condition, EGM2008 represents the most suitable global geopotential model for use in Egyptian territory to date. The final product gained from this study was the corrector surface that was used to facilitate the transformation process between regional geometrical geoid model and the global geoid model.

References

[1] Abd-Elmotaal, H., (1994), “Comparison of polynomial and similarity transformation based datum-shifts for Egypt”, Bulletin Geodesique 68:168–172.10.1007/BF00808290Search in Google Scholar

[2] Abd-Elmotaal, H. A., (2008a), “Gravimetric Geoid for Egypt Using High-Degree Tailored Reference Geopotential Model”, NRIAG Journal of Geophysics Special Issue, 507–531.Search in Google Scholar

[3] Abd-Elmotaal, H., (2008b), “Evaluation of PGM2007A Geopotential Model in Egypt”, Presented at the IAG International Symposium on Gravity, Geoid and Earth Observation “GGEO 2008”, Chania, Greece, June 23–27, 2008.Search in Google Scholar

[4] Abd-Elmotaal, H. A., (2009), “Evaluation of the EGM2008 Geopotential Model for Egypt”, Newton’s Bulletin Issue no. 4, April 2009, ISSN 1810-8555, Publication of the International Association of Geodesy and International Gravity Field Service.Search in Google Scholar

[5] Abd-Elmotaal, H. A., (2011), “FFT Versus Least-Squares Collocation Techniques for Gravimetric Geoid Determination in EGYPT”, Journal of Applied Geophysics, 10(1):121–133.Search in Google Scholar

[6] Acar, M., Ozludemir, M. T., Celik, R. N., (2006), “Local geoid surface approximation by Fuzzy inference systems: case studies in Turkey”, Proceeding of the 1st international symposium of the international gravity fields service: “Gravity Field of the Earth”, 28 August–1 September, 2006.Search in Google Scholar

[7] Akcin, H., and Celik, C. T., (2013), “Performance of artificial neural networks on Kriging method in modeling local geoid”, J. Bulletin of Geodetic Science, 19(1):84–97, Jan-mar, 2013.10.1590/S1982-21702013000100006Search in Google Scholar

[8] Akyilmaz, O., Özlüdemir, M. T., Ayan, T., and Çelik, R. N., (2009), “Soft computing methods for geoidal height transformation”, Earth Planets and Space, 61(7):825–833. July 2009.10.1186/BF03353193Search in Google Scholar

[9] Ali, M. H., Abustan, I., (2014), “A new novel index for evaluating model performance”, Journal of Natural Resources and Development, 04:1–9, doi:10.5027/jnrd.v4i0.01.Search in Google Scholar

[10] Al-Krargy, E. M., Doma, M. I., Dawod, G. M., (2014), “Towards an Accurate Definition of the Local Geoid Model in Egypt using GPS/Leveling Data: A Case Study at Rosetta Zone”, International Journal of Innovative Science and Modern Engineering (IJISME), 2(11), ISSN: 2319-6386, October 2014.Search in Google Scholar

[11] Al-Krargy, E., Hosny, M., and Dawod, G., (2015), “Investigating the Precision of Recent Global Geoid Models and Global Digital Elevation Models for Geoid Modelling in Egypt”, Regional Conference on Surveying & Development, Sharm El-Sheikh, Egypt, 3–6 October 2015.Search in Google Scholar

[12] Alnaggar, D., (1986), “Determination of the geoid in Egypt using heterogeneous geodetic data”, Ph.D. Dissertation, Cairo University, Cairo, Egypt.Search in Google Scholar

[13] Amin, M. M., (2002), “Evaluation of Some Recent High Degree Geopotential Harmonic Models in Egypt”, Port-Said Engineering Research Journal PSERJ, 6(2), Published by Faculty of Engineering, Suez Canal University, Port-Said, Egypt.Search in Google Scholar

[14] Amin, M., El-Fatairy, S., and Hassouna, R., (2005), “A precise geoidal map of the southern part of Egypt by collocation: Toshka geoid.” FIG Working Week 2005 and GSDI-8 Conf., International Federation of Surveyors, Cairo, Egypt.Search in Google Scholar

[15] Amin, M. M., Zaky, K. M., El Fatairy, S. M. and Habib, M. A., (2013), “Fetching the Most Appropriate Global Geopotential Model for Egypt”, Civil Engineering Research Magazine CERM, 35(3), Published by Faculty of Engineering, Al-Azhar University, Cairo, Egypt.Search in Google Scholar

[16] Banarjee, T., Singh, S. B. and Srivastava, R. K., (2011), “Development and performance evaluation of statistical models correlating air pollution and metrological variables at Pantangar, India”, Atmospheric Research, 99(2011):505–517, doi:10.1016/j.atmosres.2010.12.003.Search in Google Scholar

[17] Barthelmes, F., Kohler, W., (2012) International Centre for Global Earth Models (ICGEM). Journal of Geodesy, The Geodesists Handbook 2012, 86(10):932–934, doi:10.1007/s00190-012-0584-1, URL http://dx.doi.org/10.1007/s00190-012-0584-1.Search in Google Scholar

[18] Barthelmes, F., (2014) Global Models. In: Grafarend, E.. Encyclopedia of Geodesy, Springer International Publishing, 1–9, doi:10.1007/978-3-319-02370-0_43-1, URL http://dx.doi.org/10.1007/978-3-319-02370-0_43-1.Search in Google Scholar

[19] Beale, M. H., Hagan, M. T., Demuth, H. B. (2015). Neural Network Toolbox User’s Guide, The Math Works Inc..Search in Google Scholar

[20] Cakir, L., Yilmaz, N., (2014), “Polynomial, radial basis functions and multilayer perceptron neural network methods in local geoid determination with GPS/levelling”, J. Measurements, 57(2014):48–153.10.1016/j.measurement.2014.08.003Search in Google Scholar

[21] Cross, P. A., (1983), “Advanced least squares applied to position fixing”, North east London polytechnic department of land Surveying.Search in Google Scholar

[22] Dawod G. M., (1998), “A National Gravity Standardization Network for Egypt”, Ph.D. Thesis, Shoubra Faculty of Engineering, Zagazig University, Egypt.Search in Google Scholar

[23] Dawod G. M. and Ismail, S. S., (2005), “Enhancing the integrity of the national geodetic data bases in Egypt”. In: Proceeding of FIG Working Week 2005 and GSDI-8 Cairo, Egypt, 16–21 April 2005.Search in Google Scholar

[24] Dawod, G. (2008), “Towards the redefinition of the Egyptian geoid: Performance analysis of recent global geoid models and digital terrain models.” Journal of Spatial Science, 53(1), 31–42.10.1080/14498596.2008.9635133Search in Google Scholar

[25] Dawod, G. M., and Mohamed, H. F., (2009), “Fitting Gravimetric Local and Global Quasi-Geoids to GPS/Levelling Data: The Role of Geoid/Quasi-Geoid Variations”, JKAU: Eng. Sci., 20(1), 47–59 (2009 A.D. / 1430 A.H.).10.4197/Eng.20-1.3Search in Google Scholar

[26] Dawod, G. M., Mohamed, H. F., Ismail, S. S., (2010), “Evaluation and Adaptation of the EGM2008 Geopotential Model along the Northern Nile Valley, Egypt: Case Study”, Journal of Surveying Engineering, 136(1), February 1, 2010. ©ASCE, ISSN 0733-9453/2010/1-36–40/$25.00. doi:10.1061/_ASCE_SU.1943-5428.0000002.Search in Google Scholar

[27] El Sagheer, A., (1995), “Development of digital terrain model for Egypt and its application for gravimetric geoid determination”, Ph.D. Thesis, Shoubra Faculty of Engineering, Zagazig University, Egypt.Search in Google Scholar

[28] El-Shazly, A. H., (2005), “GPS Levelling Without Geoid in Egypt Applied to Borg El-Arab City”, TS 33.2 – Vertical Reference Frame, From Pharaohs to Geoinformatics, FIG Working Week 2005 and GSDI-8, Cairo, Egypt, April 16–21, 2005.Search in Google Scholar

[29] El Tokhy, M., (1993), “Towards the redefinition of the Egyptian geodetic control networks: Geoid and best fitting reference ellipsoid by combination of heterogeneous data”, Ph.D. Thesis, Faculty of Engineering, Ain Shams University, Egypt.Search in Google Scholar

[30] Erol, B., and Erol, S., (2012). “GNSS in practical determination of regional heights”, Global navigation satellite systems: Signal, theory and applications, J. Shuanggen, ed., InTech, Croatia, 127–160.Search in Google Scholar

[31] Erol, B., and Erol, S., (2013). “Learning-based computing techniques in geoid modeling for precise height transformation.” Computer & Geosciences 52(2013). 95–107.10.1016/j.cageo.2012.09.010Search in Google Scholar

[32] European Space Agency, (2014), “GUT TUTORIAL”, Reference: ESA/XGCE-DTEX-EOPS-SW-07-0001, Version:7.2, Date: 19 December 2014, https://earth.esa.int/web/guest/software-tools/gut/about-gut/overview.Search in Google Scholar

[33] Förste C., Bruinsma S., Abrikosov O., Lemoine J. M., Marty J. C., Charles J., Flechtner F., Balmino G., Barthelmes F., Biancale R. (2015), EIGEN-6C4 The latest combined global gravity model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse. GFZ Data Services, doi:10.5880/icgem.2015.1, URL http://doi.org/10.5880/icgem.2015.1.Search in Google Scholar

[34] Fotopoulos, G., Featherstone, W. E., and Sideris, M. G., (2002), “Fitting a gravimetric geoid model to the Australian height datum via GPS data”, IAG Third Meeting of the International Gravity and Geoid Commission, Thessaloniki, Greece, Aug. 26–30, 2002.Search in Google Scholar

[35] Ghanem, E., (2001), “GPS-gravimetric geoid determination in Egypt”, Geo-spatial Information Science, 4(1), 19–23.10.1007/BF02826631Search in Google Scholar

[36] Gilardoni, M., Reguzzoni, M., and Sampiletro, D., (2016), “GECO: a global gravity model by locally combining GOCE data and EGM2008”, Stud. Geophys. Geod., 60(2016), 1–xxx, doi:10.1007/s11200-015-1114-4.Search in Google Scholar

[37] Gullu, M., (2010). “Coordinate Transformation by radial basis function neural network”, Scientific Research and Essays, 5(20), 3141–3146, 18 October, 2010, Available online at http://www.academicjournals.org/sre, ISSN 1992-2248 ©2010 Academic Journals.Search in Google Scholar

[38] Gullu, M., Yilmaz, M., Yilmaz, I., and Turgut, B. (2011a). “Datum Transformation by Artificial Neural Networks for Geographic Information Systems Applications”, International Symposium on Environmental Protection and Planning: Geographic Information Systems (GIS) and Remote Sensing (RS) Applications (ISEPP), 28–29 June 2011, Izmir-Turkey.10.5053/isepp.2011.1-6Search in Google Scholar

[39] Gullu, M., Yilmaz, M., Yilmaz, I., and Turgut, B. (2011b). “Application of Back Propagation Artificial Neural Network for Modeling Local GPS/Levelling Geoid Undulation: A Comparative Study”, Ts007C-Geoid and GNSS Heighting, 5239, FIG Working Week 2011, Bridging the Gap between Cultures, Marrakech, Morocco, 18–22 May 2011.Search in Google Scholar

[40] Hagan, M. T., Demuth, H. B., and Beale, M. H.. (1996). Neural Network Design, PWS PublishingBoston, MA.Search in Google Scholar

[41] Haykin, S. (2001). Neural Network: A Comprehensive Foundation, Second Edition. Hamilton, Ontario, Canada.Search in Google Scholar

[42] Hirt, C., Marti, U., Bürki, B., and Featherstone, W. E., (2010), “Assessment of EGM2008 in Europe using accurate astrogeodetic vertical deflections and omission error estimates from SRTM/DTM2006.0 residual terrain model data”, Journal of Geophysical Research, 115(B10404), doi:10.1029/2009JB007057.Search in Google Scholar

[43] Hornik, K. M., Stinchcombe, M., and White, H., (1989), “Multilayer Feedforward Networks are Universal Approximators”, Neural Networks, 2(5), 359–366.10.1016/0893-6080(89)90020-8Search in Google Scholar

[44] Hu, W., Sha, Y., and Kuang, S., (2004), “New method for transforming global positioning system height into normal height based on neural network”, J. Survy. Eng., 130(1), 36–39.10.1061/(ASCE)0733-9453(2004)130:1(36)Search in Google Scholar

[45] Kaloop, M., Rabah, M., El-shambaky, H., (2008), “High Accurate Local Geoid in Egypt”, Integrating Generations, FIG Working Week 2008, Stockholm, Sweden, 14–19 June 2008.Search in Google Scholar

[46] Kavazoglu, T., and Saka, M. H., (2005), “Modeling local GPS/Leveling geoid undulations using artificial neural networks”, J. Geodesy, Berlin, 78(9), 520–527.10.1007/s00190-004-0420-3Search in Google Scholar

[47] Kostelecký, J., Klokocník, J., Bucha, B., Bezdek, A., and Förste, C., (2015), “Evaluation of the gravity field model EIGEN-6C4 in comparison with EGM2008 by means of various functions of the gravity potential and by GNSS/levelling”, Geoinformatics FCE CTU, 14(1) doi:10.14311/gi.14.1.1.Search in Google Scholar

[48] Kotsakis, C., and Sideris, M. G., (1999), “On the adjustment of combined GPS/levelling/geoid networks”, Journal of Geodesy, 73, 412–421.10.1007/s001900050261Search in Google Scholar

[49] Lin, L. S., (2007), “Application of a back-propagation artificial neural network to regional grid-based geoid model generation using GPS and leveling data”, J. Survy. Eng., 133, 81–89.10.1061/(ASCE)0733-9453(2007)133:2(81)Search in Google Scholar

[50] Mikhail, E. M., (1976), “Observations and Least Squares”, Dun DonnellyNew York.Search in Google Scholar

[51] Milton, J. S., and Arnold, J. C., (1995), “Introduction to Probability and Statistics Principals and Applications for Engineering and the Computing Science.”, Third Edition, McGraw – Hill Book CompanyNew York, U.S.A.Search in Google Scholar

[52] Newton’s Bulletin (2009), Newton’s Bulletin Issue no. 4, April 2009, ISSN 1810-8555, Publication of the International Association of Geodesy and International Gravity Field Service.Search in Google Scholar

[53] Pavlis, N. K., Holmes,S. A., Kenyon, S. C., and Factor, J. K. (2008), An Earth Gravitational Model to Degree 2160: EGM2008, presented at the 2008 General Assembly of the European Geosciences Union, Vienna, Austria, April 13–18.Search in Google Scholar

[54] Pikaridas, C., and Fotiou, A., (2011), “Estimation and evaluation of GPS geoid heights using artificial neural network model”, Appl. Geomat., 3, 183–187, doi:10.1007/s12518-011-0052-2.Search in Google Scholar

[55] Powell, S. M. (1997). “Results of the Final Adjustment of the New National Geodetic Network”, Technical report, Egyptian Surveying Authority, Egypt.Search in Google Scholar

[56] Rabah, M., Kaloop, M., (2013), “The use of minimum curvature surface technique in geoid computation processing of Egypt”, Arab. J. Geosci. 6, 1263–1272, doi:10.1007/s12517-011-0418-0.Search in Google Scholar

[57] Saad, A., Dawod, G., (2002), “A precise Integrated GPS/Gravity Geoid Model for Egypt”, Civil Engineering Research Magazine (CERM), Al-Azhar University, 24(1), 291–405.Search in Google Scholar

[58] Shaker, A., Saad, A., and El Sagheer, A., (1997), “Enhancement of the Egyptian gravimetric geoid 1995 using GPS observations”, Proceeding of the International Symposium on GIS/GPS, Istanbul, Turkey, Sept. 15–19.Search in Google Scholar

[59] Shuanggen, J., (2012), “Global navigation satellite system: Signals, Theory, and Application”, ISBN 978-953-307-843-4, In Tech Europe, University Campus SteP Ri, Slavaka Krautzeka 83/A, 51000 Rijeka, Croatia, www.intechopen.com.Search in Google Scholar

[60] Soltanpour, A., Nahavandchi, H., Featherstone, W. E., (2006), “Geoid type surface determination using wavelet-based combination of gravimetric quasi/geoid and GPS/Levelling data”, Geophesical Research Abstract, 8, 04612.Search in Google Scholar

[61] Sorkhabi, O. M., (2015), “Geoid determination based on Log Sigmoid Function of artificial neural network: (A case study: Iran)”, J. of artificial intelligence in electrical engineering, 3(12).Search in Google Scholar

[62] Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., and Salakhutdinov, R. (2014). “A Simple Way to Prevent Neural Networks from Overfitting”, Journal of Machine Learning Research, 15(2014), 1929–1958.Search in Google Scholar

[63] Stopar, B., Ambrozic, T., Kuhar, M., and Turk, G., (2006), “GPS-derived geoid using artificial neural network and least squares collocation”, Survey Review, 38(300).10.1179/sre.2006.38.300.513Search in Google Scholar

[64] Szu, P. K., Chao, N. C., Hui, C. H., and Yu, T. S., (2014), “Using a least squares supportive vector machine to estimate a local geometric geoid model”, Bol. Ciênc. Geod., sec. Artigos, Curitiba, 20(2), 427–443.10.1590/S1982-21702014000200025Search in Google Scholar

[65] Tierra, A., Dalazoana, R., and De Freitas, S., (2008), “Using Artificial Neural Network To Improve The Transformation of Coordinates Between Classical Geodetic Reference Frames”, Computers & Geosciences, 181–189, doi:10.1016, Netherlands.Search in Google Scholar

[66] Tierra, A., Romero, R. (2014). “Planes coordinates transformation between PSAD56 to SIRGAS using a Multilayer Artificial Neural Network”, Geodesy and Cartography, Polish Academy of Sciences, 63(2), doi:10.2478/geocart-2014-0014, 199–209.Search in Google Scholar

[67] Tscherning, C. C., Radwan, A., Tealab, A. A., Mahmoud, S. M., Abd El-Monum, M., Hassan, R., El-Sayed, I., and, Saker, K., (2001), “Local Geoid determination combining gravity disturbances and GPS/Levelling: a case study in the Lake Nasser area, Aswan, Egypt”, Journal of Geodesy, 75, 343–348.10.1007/s001900100185Search in Google Scholar

[68] Tusat, E., (2011), “A comparison of geoid height obtained with adaptive neural fuzzy inference systems and polynomial coefficients methods”, International Journal of the Physical Sciences, 6(4), 789–795.Search in Google Scholar

[69] Veronez, M. R., De Suza, S. F., Matsuoka, M. T., Reinhart, A., and De Silva, R. M., (2011), “Regional mapping of the geoid using GNSS (GPS) measurements and an artificial neural network”, Remote Sens., 3, 668–683, doi:10.3390/rs3040668.Search in Google Scholar

[70] Veronez, M. R., Thum, A. B., and De Suza, G. C., (2006), “A new method for obtaining geoidal undulation through artificial neural networks”, 7th International Symposium on Spatial Accuracy Assessment in Neural Resources and Environmental Sciences. 306–316.Search in Google Scholar

[71] Yilmaz, M., (2010), “Adaptive network based on Fuzzy inference system estimated of geoid heights interpolation”, Scientific Research and essays, 5(16), 2148–2154, ISSN 1992-2248 ©2010 Academic Journals, Available online at http://www.academicjournals.org/sre.Search in Google Scholar

[72] Yilmaz, M., (2008), “Effect of the type of membership function on geoid height modeling with fuzzy logic”, Survey Review, 40(310), 379–391.10.1179/003962608X325439Search in Google Scholar

[73] Yilmaz, M., Acer, M., Ayan, T., and Arslan, E., (2006), “Application of Fuzzy logic theory to geoid height determination”, Advances in Soft Computing, 5, 383–388, ©Springer-Verlag Berlin Heidelbrg 2006, www.springerlink.com.10.1007/3-540-33521-8_41Search in Google Scholar

[74] Zaletnyik, P., Völguesi, L., Kirchner, I., and Paláncz, B., (2007), “Combination of GPS/Leveling and gravimetric geoid by using the thin plate spline interpolation technique via finite element method”, Journal of Applied Geodesy, 1(2007), 233–239 ©de Gruyter 2007. doi:10.1515/JAG.2007.025.Search in Google Scholar

[75] Zaletnyik, P., Völguesi, L., Kirchner, I., and Paláncz, B., (2008), “Modeling local GPS/Levelling geoid undulations using support vector machine”, Periodica Polytechnica, Civil Engineering, 52/1(2008), 39–43, web: http://www.pp.bme.hu/ci, © Periodica Polytechnica 2008.10.3311/pp.ci.2008-1.06Search in Google Scholar

[76] Ziggah, Y. Y., Youjian, H., Tierra, A., and Konaté, A. A., (2016a), “Performance evaluation of artificial neural networks for planimetric coordinate transformation – a case study, Ghana”, Arab. Geosci., 9, 698, doi:10.1007/s12517-016-2729-7.Search in Google Scholar

[77] Ziggah, Y. Y., Youjian, H., Yu, X., and Basommi, L. P., (2016b), “Capability of artificial neural network for forward conversion of geodetic coordinates (φ,λ,h) to Cartesian coordinates (x, y, z)”, Math. Geosci., doi:10.1007/s11004-016-9638-x.Search in Google Scholar

Received: 2016-9-29
Accepted: 2017-9-2
Published Online: 2017-10-11
Published in Print: 2018-1-26

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