Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

An alternative method for estimating densification point velocity based on back propagation artificial neural networks

  • 105 Accesses

  • 7 Citations


The establishment of Turkish National Fundamental GPS Network (TNFGN) was completed in 2001 and Large Scale Map and Map Information Production Regulation (LSMMIPR) came into force in 2005 in parallel with the establishment of TNFGN and the increase in the use of GPS applications. TNFGN has been designed as first order GPS network and it comprises second-, third- and fourth-order GPS densification networks. LSMMIPR has required determining the positions of first-, second- and third-order GPS densification (C1, C2 and C3) points with the reference epoch besides the measurement epoch. Therefore, it is necessary to estimate the velocity vectors of the densification points. In practise, the velocity vectors of C1, C2 and C3 points are estimated from TNFGN points or higher-order densification points velocity vectors by interpolation methods but LSMMIPR did not specify the interpolation method for this procedure. The objective of this study is to use a back propagation artificial neural network (BPANN) that has been more widely applied in engineering among all other neural network models for estimating the velocity of the densification point as an alternative to the interpolation methods. BPANN and selected ten interpolation methods are evaluated over a test area, in terms of root mean square error (RMSE). The results showed that the employment of BPANN estimated the densification point velocity (VX,Y,Z) with a better accuracy (±5.0 mm, ±4.0 mm, ±3.9 mm, respectively) than the interpolation methods in the test area and indicated that BPANN can be a useful tool for estimating point velocity in the densification networks as a real alternative to the interpolation methods.

This is a preview of subscription content, log in to check access.


  1. Bishop C., 1995. Neural Networks for Pattern Recognition. Oxford University Press, New York.

  2. Burrough P.A. and Mcdonnell R.A., 1998. Principles of Geographical Information Systems. Oxford University Pres, New York.

  3. Chaplot V., Darboux F., Bourennane H., Leguedois S., Silvera N. and Phachomphon K., 2006. Accuracy of interpolation techniques for the derivation of digital elevation models in relation to landform types and data density. Geomorphology, 77, 126–141.

  4. Çağlar Y., 2006. National Report of Turkey — 2005. Mitteilungen des Bundesamtes fuer Kartographie und Geodaesie, 38, 299–306.

  5. Çelik R.N., Ayan T., Deniz R. and Özlüdemir M.T., 2004. Geodetic infrastructure of Turkey for GIS, GPS and remote sensing applications. XXth ISPRS Congress, Commission VI, WG VI/4, 12–23 July 2004, Istanbul, Turkey (http://www.isprs.org/proceedings/XXXV/congress/comm4/papers/363.pdf).

  6. D’Anastasio E., De Martini P.M., Selvaggi G., Pantosti D., Marchioni A. and Maseroli R., 2006. Short-term vertical velocity field in the Apennines (Italy) revealed by geodetic levelling data. Tectonophysics, 418, 219–234.

  7. Deniz I. and Ozener H., 2008. Determination of velocity field and strain accumulation of densification network in Marmara region. Integrating Generations, FIG Working Week, 14–19 June 2008, Stockholm, Sweden (http://www.fig.net/pub/fig2008/papers/ts04g/ts04g_01_deniz_ozener_2915.pdf).

  8. Fausett L., 1994. Fundamentals of Neural Networks. Prentice Hall, Upper Saddle River, New Jersey, USA.

  9. Ferland R., Altamimi Z., Bruyninx C., Craymer M., Habrich H. and Kouba J., 2002. Regional networks densification. IGS Workshop “Towards Real-Time”, 8–11 April 2002, Ottawa, Canada (ftp://geod.nrcan.gc.ca/pub/GSD/craymer/pubs/densification_igs2002.pdf).

  10. Haykin S., 1999. Neural Networks: A Comprehensive Foundation. Prentice Hall Upper Saddle River, New Jersey, USA.

  11. Hefty J., 2008. Densification of the central Europe velocity field using velocities from local and regional geokinematical projects. Geophys. Res. Abs., 10, EGU2008–A–01735

  12. Leandro R.F. and Santos M.C., 2007. A neural network approach for regional vertical total electron content modelling. Stud. Geophys. Geod., 51, 279–292.

  13. Moghtased-Azar K. and Zaletnyik P., 2009. Crustal velocity field modelling with neural network and polynomials. In: Sideris M.G. (Ed.), Observing our Changing Earth. International Association of Geodesy Symposia, 133, 809–816.

  14. Nikolova N. and Vassilev S., 2006. Mapping precipitation variability using different interpolation methods. Proceedings of the Conference on Water Observation and Information System for Decision Support (BALWOIS). 25–29 May 2006, Ohrid, Macedonia. (http://balwois.com/balwois/administration/full_paper/ffp-631.pdf).

  15. Nocquet J.M. and Calais E., 2003. Crustal velocity field of western Europe from permanent GPS array solutions, 1996–2001. Geophys. J. Int., 154, 72–88.

  16. Nørgaard M., 1997. Neural Network Based System Identification Toolbox. Tech. Report. 97-E-851, Department of Automation, Technical University of Denmark, Copenhagen, Denmark.

  17. Pandya A.S. and Macy R.B., 1995. Pattern Recognition with Neural Networks in C++. CRC Press, Boca Raton, Florida, USA.

  18. Perez J.A.S., Monico J.F.G. and Chaves J.C., 2003. Velocity field estimation using GPS precise point positioning: The south American plate case. J. Glob. Position. Syst., 2, 90–99.

  19. Ripley B.D., 1996. Pattern Recognition and Neural Networks. Cambridge University Press, Cambridge, U.K.

  20. Skumar N., Moran B., Semenov A.Y. and Belikov B.B., 2001. Natural neighbour Galerkin methods. Int. J. Num. Methods Eng., 50, 1–27.

  21. Smith M.J., Goodchild M.F. and Longley P.A., 2007. Geospatial Analysis: a Comprehensive Guide to Principles, Techniques and Software Tools.. The Winchelsea Press, Troubadour, Leicester, U.K.

  22. Turkish Chamber of Survey and Cadastre Engineers, 2008. Large Scale Map and Map Information Production Regulation. Iskur Press, Ankara, Turkey (in Turkish).

  23. Valach F., Hejda P. and Bochníček J., 2007. Geoeffectiveness of XRA events associated with RSP II and/or RSP IV estimated using the artificial neural network. Stud. Geophys. Geod., 51, 551–562.

  24. Wright T. and Wang H., 2010. Large-scale crustal velocity field of western Tibet from InSAR and GPS reveals internal deformation of the Tibetan plateau. Geophys. Res. Abs., 12, EGU2010–7092.

  25. Yang CS., Kao SP., Lee FB. and Hung PS., 2004. Twelve different interpolation methods: a case study of Surfer 8.0. XXth ISPRS Congress, 12–23 July 2004, Istanbul, Turkey, 778–785. (http://www.isprs.org/proceedings/XXXV/congress/comm2/papers/231.pdf)

  26. Yılmaz İ., 2009. A research on the accuracy of landform volumes determined using different interpolation methods. Scientific Research and Essay, 4(11), 1248–1259.

  27. Zhang G., Patuwo B.E. and Hu M.Y., 1998. Forecasting with artificial neural networks: The state of the art. Int. J. Forecast., 14, 35–62.

Download references

Author information

Correspondence to Mevlüt Güllü.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Güllü, M., Yilmaz, İ., Yilmaz, M. et al. An alternative method for estimating densification point velocity based on back propagation artificial neural networks. Stud Geophys Geod 55, 73–86 (2011). https://doi.org/10.1007/s11200-011-0005-6

Download citation


  • site velocity determination
  • artificial neural network
  • interpolation
  • densification network
  • back propagation