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Transformation of Geodetic Ellipsoidal Coordinates (φ, λ, h) to 3 Dimensional Global Cartesian Coordinates (X, Y, Z) with Multi-layer Perceptron Artificial Neural Network

Year 2020, Volume: 10 Issue: 3, 702 - 710, 15.07.2020
https://doi.org/10.17714/gumusfenbil.712100

Abstract

The problem of transformation between geodetic
ellipsoidal coordinates (φ, λ, h) and three-dimensional (3D) global Cartesian
coordinates (X, Y, Z) is a common one. Only one method for solving this
transformation problem has been found. An examination of the current studies
reveals that the application and testing of possible alternative techniques for
transforming geodetic ellipsoidal coordinates to 3D global Cartesian coordinates
have not been fully addressed. The aim of this study was to investigate the
performance of a method of transforming geodetic ellipsoidal coordinates to 3D
global Cartesian coordinates using a multilayer perceptron artificial neural
network (MLP-ANN). For the prediction, 594-point datasets of the Turkish
National Fundamental GPS Network (TNPGN) were used. As a result of many trials,
the Bayesian Regulation was determined as the training algorithm and the number
of hidden layers was 2. The mean squared error (MSE), mean absolute error
(MAE), and coefficient of determination (R2) were used for the
performance evaluation of the MLP-ANN model. According to the test results, the
MSE value for the components of the MLP-ANN and the 3D global Cartesian
coordinates varied between 0.4536 cm and 0.9411 cm, the MAE value ranged
between 0.3883 cm and 0.8165 cm, and the R2 value was calculated as
0.9999 for all models. To examine the results in more detail, the difference
between the estimated values and the calculated values was determined.
Accordingly, it was found that the difference in the values was quite close to
zero except for a few number of data. According to these statistical criteria,
it was concluded that the MLP-ANN used in this study could be used as an alternative
to the classical coordinate transformation method.

References

  • Cakir, L. ve Konakoglu, B., 2019. The Impact of Data Normalization on 2D Coordinate Transformation Using GRNN. Geodetski Vestnik, 63(4), 541-553. doi: 10.15292/geodetski-vestnik.2019.04.541-553
  • Elshambaky, H. T., Kaloop, M. R. ve Hu, J. W., 2018. A Novel Three-direction Datum Transformation of Geodetic Coordinates for Egypt Using Artificial Neural Network Approach. Arabian Journal of Geosciences, 11(6), 110. doi: 10.1007/s12517-018-3441-6.
  • Gullu, M., 2010. Coordinate Transformation by Radial Basis Function Neural Network. Scientific Research and Essays, 5, 3141-3146.
  • Haykin, S., 2009. Neural Networks and Learning Machines. NJ: Pearson Education Inc.
  • Heiskanen, W. A. ve Moritz, H., 1967. Physical geodesy. W. H. Freeman and Company, San Fransisco, USA, 364p.
  • Hornik, K., Stinchcombe, M. ve White, H., 1989. Multilayer Feedforward Networks Are Universal Approximators. Neural Networks, 2(5), 359-366. doi: 10.1016/0893-6080(89)90020-8.
  • Kisi, O. ve Alizamir, M., 2018. Modelling Reference Evapotranspiration Using a New Wavelet Conjunction Heuristic Method: Wavelet Extreme Learning Machine vs Wavelet Neural Networks. Agricultural and Forest Meteorology 263: 41-48. doi: 10.1016/j.agrformet.2018.08.007.
  • Kisi, O., Alizamir, M. ve Zounemat-Kermani, M., 2017. Modeling Groundwater Fluctuations by Three Different Evolutionary Neural Network Techniques Using Hydroclimatic Data. Natural Hazards, 87(1), 367-381. doi: 10.1007/s11069-017-2767-9.
  • Konakoglu, B., Cakır, L. ve Gökalp, E., 2016. 2D Coordinate Transformation Using Artificial Neural Networks. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. 42, 183-186. doi: 10.5194/ isprs-archives-XLII-2-W1-183-2016.
  • Konakoğlu, B. ve Gökalp, E., 2016. A Study on 2D Similarity Transformation Using Multilayer Perceptron Neural Networks and a Performance Comparison with Conventional and Robust Outlier Detection Methods. Acta Montanistica Slovaca, 21, 4, 324-332.
  • Lin, L. S. ve Wang, Y. J., 2006. A Study on Cadastral Coordinate Transformation Using Artificial Neural Network, 27th Asian conference on remote sensing, Ekim 2006, Ulaanbaatar, Mongolia.
  • MacKay, D. J., 1992. Bayesian Interpolation. Neural computation, 4(3), 415-447.
  • Tierra, A. ve Romero, R., 2014. Planes Coordinates Transformation Between PSAD56 to SIRGAS Using a Multilayer Artificial Neural Network. Geodesy and Cartography, 63(2), 199-209. doi: 10.2478/geocart-2014-0014.
  • Tierra, A., Dalazoana, R. ve De Freitas, S., 2008. Using An Artificial Neural Network to Improve The Transformation of Coordinates Between Classical Geodetic Reference Frames. Computers and Geosciences, 34(3), 181-189. doi: 10.1016/j.cageo.2007.03.011.
  • Turgut, B., 2010. A Back-propagation Artificial Neural Network Approach for Three Dimensional Coordinate Transformation. Scientific Research and Essays, 5 (21), 3330-3335.
  • Üstün, A., 1996. Datum Dönüşümleri, Yüksek Lisans Tezi, Yıldız Teknik Üniversitesi Fen Bilimleri Enstitüsü, İstanbul, 85s.
  • Yıldırım, F., Kaya, A. ve Kaplan, Y. (2011). Jeodezik Dik ve Coğrafi Koordinat Dönüşüm Yöntemlerinin Karşılaştırılması. Harita Dergisi, 146, 1-7.
  • Zaletnyik, P., 2004. Coordinate Transformation with Neural Networks and with Polynomials in Hungary. International symposium on modern technologies, education and professional practice in geodesy and related fields, Sofia, Bulgaria, s.471-479.
  • Ziggah, Y. Y., Youjian, H., Tierra, A. R. ve Laari, P. B., 2019. Coordinate Transformation Between Global and Local Data Based on Artificial Neural Network with K-Fold Cross-Validation in Ghana. Earth Sciences Research Journal, 23(1), 67-77. doi: 10.15446/esrj.v23n1.63860.
  • Ziggah, Y. Y., Youjian, H., Tierra, A., Konaté, A. A. ve Hui, Z., 2016a. Performance Evaluation of Artificial Neural Networks for Planimetric Coordinate Transformation—a Case Study, Ghana. Arabian Journal of Geosciences, 9(17), 698. doi: 10.1007/s12517-016-2729-7.
  • Ziggah, Y. Y., Youjian, H., Yu, X. ve Basommi, L. P., 2016b. Capability of Artificial Neural Network for Forward Conversion of Geodetic Coordinates (φ, λ, h) to Cartesian Coordinates (X, Y, Z). Mathematical Geosciences, 48(6), 687-721. doi: 10.1007/s11004-016-9638-x.

Çok Katmanlı Algılayıcı Yapay Sinir Ağı ile Jeodezik Elipsoidal Koordinatların (φ, λ, h) 3 Boyutlu Global Kartezyen Koordinatlara (X, Y, Z) Dönüşümü

Year 2020, Volume: 10 Issue: 3, 702 - 710, 15.07.2020
https://doi.org/10.17714/gumusfenbil.712100

Abstract

Jeodezik elipsoidal koordinatlar (φ, λ, h) ile
üç boyutlu (3B) global kartezyen koordinatlar (X, Y, Z) arasındaki dönüşüm işlemi
sıklıkla karşılaşılan bir problemdir.
 Bu dönüşüm problemini çözmek için sadece bir
yöntem bulunmuştur. Mevcut araştırmalar incelendiğinde jeodezik elipsoidal
koordinatlardan 3B global kartezyen koordinatlara
dönüşüm yöntemine alternatif olabilecek tekniklerin uygulanması ve test
edilmesi konusunda tam olarak değinilmediği belirlenmiştir. Bu çalışmanın amacı
çok katmanlı algılayıcı yapay sinir ağı (ÇKAYSA) kullanarak jeodezik elipsoidal
koordinatlardan 3B global kartez
yen
koordinatlara dönüşüm yönteminin
performansını araştırmaktır. Tahmin için Türkiye Ulusal Temel GPS Ağı’na
(TUTGA) ait 594 noktalı veri seti kullanılmıştır. Yapılan çok sayıda denemeler
sonucu eğitim algoritması olarak Bayesian Regulation ve gizli katman sayısı 2
olarak belirlenmiştir. ÇKAYSA modellerinin performans değerlendirmesi için
karesel ortalama hata (KOH), ortalama mutlak hata (OMH) ve belirlilik katsayısı
(R2) kriterleri kullanılmıştır.
Test sonuçlarına göre ÇKAYSA ile 3B global kartezyen koordinatların bileşenleri
için KOH değeri 0.4536 cm ile 0.9411 cm arasında, OMH değeri 0.3883 cm ile
0.8165 cm arasında değişim göstermiş, tüm modeller için R2 değeri
0.9999 olarak hesaplanmıştır. Sonuçları daha detaylı incelemek için tahmin
edilen değerler ile hesaplanan değerler arasındaki
fark değerleri hesaplanmıştır. Buna göre, fark değerlerinin az sayıda
veri hariç sıfır değerine oldukça yakın olduğu görülmüştür.
Söz konusu istatistiksel
kriterlere göre, bu çalışmada kullanılan ÇKAYSA’nın klasik koordinat dönüşüm
yöntemine alternatif olarak kullanılabilir bir yöntem olduğunu sonucuna
varılmıştır.

References

  • Cakir, L. ve Konakoglu, B., 2019. The Impact of Data Normalization on 2D Coordinate Transformation Using GRNN. Geodetski Vestnik, 63(4), 541-553. doi: 10.15292/geodetski-vestnik.2019.04.541-553
  • Elshambaky, H. T., Kaloop, M. R. ve Hu, J. W., 2018. A Novel Three-direction Datum Transformation of Geodetic Coordinates for Egypt Using Artificial Neural Network Approach. Arabian Journal of Geosciences, 11(6), 110. doi: 10.1007/s12517-018-3441-6.
  • Gullu, M., 2010. Coordinate Transformation by Radial Basis Function Neural Network. Scientific Research and Essays, 5, 3141-3146.
  • Haykin, S., 2009. Neural Networks and Learning Machines. NJ: Pearson Education Inc.
  • Heiskanen, W. A. ve Moritz, H., 1967. Physical geodesy. W. H. Freeman and Company, San Fransisco, USA, 364p.
  • Hornik, K., Stinchcombe, M. ve White, H., 1989. Multilayer Feedforward Networks Are Universal Approximators. Neural Networks, 2(5), 359-366. doi: 10.1016/0893-6080(89)90020-8.
  • Kisi, O. ve Alizamir, M., 2018. Modelling Reference Evapotranspiration Using a New Wavelet Conjunction Heuristic Method: Wavelet Extreme Learning Machine vs Wavelet Neural Networks. Agricultural and Forest Meteorology 263: 41-48. doi: 10.1016/j.agrformet.2018.08.007.
  • Kisi, O., Alizamir, M. ve Zounemat-Kermani, M., 2017. Modeling Groundwater Fluctuations by Three Different Evolutionary Neural Network Techniques Using Hydroclimatic Data. Natural Hazards, 87(1), 367-381. doi: 10.1007/s11069-017-2767-9.
  • Konakoglu, B., Cakır, L. ve Gökalp, E., 2016. 2D Coordinate Transformation Using Artificial Neural Networks. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. 42, 183-186. doi: 10.5194/ isprs-archives-XLII-2-W1-183-2016.
  • Konakoğlu, B. ve Gökalp, E., 2016. A Study on 2D Similarity Transformation Using Multilayer Perceptron Neural Networks and a Performance Comparison with Conventional and Robust Outlier Detection Methods. Acta Montanistica Slovaca, 21, 4, 324-332.
  • Lin, L. S. ve Wang, Y. J., 2006. A Study on Cadastral Coordinate Transformation Using Artificial Neural Network, 27th Asian conference on remote sensing, Ekim 2006, Ulaanbaatar, Mongolia.
  • MacKay, D. J., 1992. Bayesian Interpolation. Neural computation, 4(3), 415-447.
  • Tierra, A. ve Romero, R., 2014. Planes Coordinates Transformation Between PSAD56 to SIRGAS Using a Multilayer Artificial Neural Network. Geodesy and Cartography, 63(2), 199-209. doi: 10.2478/geocart-2014-0014.
  • Tierra, A., Dalazoana, R. ve De Freitas, S., 2008. Using An Artificial Neural Network to Improve The Transformation of Coordinates Between Classical Geodetic Reference Frames. Computers and Geosciences, 34(3), 181-189. doi: 10.1016/j.cageo.2007.03.011.
  • Turgut, B., 2010. A Back-propagation Artificial Neural Network Approach for Three Dimensional Coordinate Transformation. Scientific Research and Essays, 5 (21), 3330-3335.
  • Üstün, A., 1996. Datum Dönüşümleri, Yüksek Lisans Tezi, Yıldız Teknik Üniversitesi Fen Bilimleri Enstitüsü, İstanbul, 85s.
  • Yıldırım, F., Kaya, A. ve Kaplan, Y. (2011). Jeodezik Dik ve Coğrafi Koordinat Dönüşüm Yöntemlerinin Karşılaştırılması. Harita Dergisi, 146, 1-7.
  • Zaletnyik, P., 2004. Coordinate Transformation with Neural Networks and with Polynomials in Hungary. International symposium on modern technologies, education and professional practice in geodesy and related fields, Sofia, Bulgaria, s.471-479.
  • Ziggah, Y. Y., Youjian, H., Tierra, A. R. ve Laari, P. B., 2019. Coordinate Transformation Between Global and Local Data Based on Artificial Neural Network with K-Fold Cross-Validation in Ghana. Earth Sciences Research Journal, 23(1), 67-77. doi: 10.15446/esrj.v23n1.63860.
  • Ziggah, Y. Y., Youjian, H., Tierra, A., Konaté, A. A. ve Hui, Z., 2016a. Performance Evaluation of Artificial Neural Networks for Planimetric Coordinate Transformation—a Case Study, Ghana. Arabian Journal of Geosciences, 9(17), 698. doi: 10.1007/s12517-016-2729-7.
  • Ziggah, Y. Y., Youjian, H., Yu, X. ve Basommi, L. P., 2016b. Capability of Artificial Neural Network for Forward Conversion of Geodetic Coordinates (φ, λ, h) to Cartesian Coordinates (X, Y, Z). Mathematical Geosciences, 48(6), 687-721. doi: 10.1007/s11004-016-9638-x.
There are 21 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Berkant Konakoglu 0000-0002-8276-587X

Publication Date July 15, 2020
Submission Date March 31, 2020
Acceptance Date June 2, 2020
Published in Issue Year 2020 Volume: 10 Issue: 3

Cite

APA Konakoglu, B. (2020). Çok Katmanlı Algılayıcı Yapay Sinir Ağı ile Jeodezik Elipsoidal Koordinatların (φ, λ, h) 3 Boyutlu Global Kartezyen Koordinatlara (X, Y, Z) Dönüşümü. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 10(3), 702-710. https://doi.org/10.17714/gumusfenbil.712100