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Capability of Artificial Neural Network for Forward Conversion of Geodetic Coordinates \((\phi ,\lambda ,h)\) to Cartesian Coordinates (X, Y, Z)

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Abstract

The standard forward transformation equation plays a major role in coordinate transformation between global and local datums. Thus, it is a prerequisite step in the forward conversion of geodetic coordinates into cartesian coordinates in coordinate transformation from global to local datum and vice versa. Numerous studies have been carried out on converting cartesian coordinates to geodetic coordinates (reverse procedure) through the application of iterative, approximate, closed form, vector-based and computational intelligence algorithms. However, based on literature covered pertaining to this study, it was realized that the existing researches do not fully address the issue of applying and testing alternative techniques in the case of the forward conversion. Hence, the purpose of this present study was to explore the coordinate conversion performance of two different artificial neural network approaches (backpropagation artificial neural network (BPANN) and radial basis function neural network (RBFNN)) and multiple linear regression (MLR). The statistical findings revealed that the BPANN, RBFNN and MLR offered satisfactory prediction of cartesian coordinates. However, the RBFNN compared to BPANN and MLR showed better stability and more accurate prediction results. Furthermore, in terms of maximum three-dimensional position error, the RBFNN attained 0.004 m while 0.011 and 0.627 m were achieved, respectively, by MLR and BPANN. By virtue of the success achieved in this study, the main conclusion drawn here is that RBFNN provides a promising alternative in the forward conversion of geodetic coordinates into cartesian coordinates. Therefore, the capability of artificial neural network as a powerful tool for solving majority of function approximation problems in geodesy has been demonstrated.

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Acknowledgments

The authors would like to express their profound gratitude to the anonymous reviewers for their helpful comments.

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Authors and Affiliations

  1. Department of Surveying and Mapping, Faculty of Information Engineering, China University of Geosciences, Wuhan, 430074, People’s Republic of China

    Yao Yevenyo Ziggah, Hu Youjian & Xianyu Yu

  2. Department of Geomatic Engineering, Faculty of Mineral Resource Technology, University of Mines and Technology, Tarkwa, Western Region, Ghana

    Yao Yevenyo Ziggah

  3. Department of Environment and Resource Studies, University of Development Studies, Wa, Ghana

    Laari Prosper Basommi

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  1. Yao Yevenyo Ziggah
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Correspondence to Hu Youjian.

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Ziggah, Y.Y., Youjian, H., Yu, X. et al. Capability of Artificial Neural Network for Forward Conversion of Geodetic Coordinates \((\phi ,\lambda ,h)\) to Cartesian Coordinates (X, Y, Z). Math Geosci 48, 687–721 (2016). https://doi.org/10.1007/s11004-016-9638-x

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