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

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 alter-B Hu Youjian 123 Math Geosci native 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.

2d Coordinate Transformation Using Artificial Neural Networks

“…The back propagation artificial neural network (BPANN) is the most commonly used one in Geodesy (Zaletnyik, 2004;Maria, 2012;Lei, Qi, 2010;Tierra and Romero, 2014;Ziggah et al, 2016). This network consists of three types of layers: the input layer, one or more hidden layers and output layer (see Figure 1).…”

“…In recent years, artificial neural networks (ANNs) have gained popularity in geodetic sciences community. ANNs have been used for coordinate transformation (Zaletnyik, 2004;Maria, 2012;Tierra, et al, 2008;Gullu, 2010;Weiwei and Xiudong, 2010;Gullu et al, 2011;Tierra and Romero, 2014;Ziggah et al, 2016), geoid determination (Kavzoglu and Saka, 2005;Pikridas, et al, 2011;Memarian Sorkhabi, 2015), geodetic deformation modelling (Bao et al, 2011;Chen and Zeng, 2013;Du et al, 2014;Gao et al, 2014), image and signal processing (Ibrahim, 2010;ALAllaf, 2012;Hai and Thuy, 2012) and determination of earth orientation parameters (Schuh, 2002;Liao, 2012). In this study, the feed forward back propagation (FFBP), cascade forward back propagation (CFBP) and radial basis function neural network (RBFNN) were used as alternative coordinate transformation methods to conduct 2D transformation between the ED50 and ITRF96 systems.…”

Performance Evaluation of Multivariate Adaptive Regression Splines (MARS) and Multiple Linear Regression (MLR) for Forward Conversion of Geodetic Coordinates (ϕ, λ, h) to Cartesian Coordinates (X, Y, Z)

“…Global Navigation Satellite System (GNSS) such as the Global Positioning System (GPS) in capturing locations of stationary and non-stationary objects on, above, and beneath the Earth's surface has increased the possibility of obtaining coordinate positions with improved high accuracy and precision [1]. These satellite positioning technologies provide numerous amounts of spatiotemporal datums in either curvilinear geodetic coordinates (ϕ , λ, h) or Cartesian coordinate (X, Y, Z) system.…”

“…The process of converting geodetic coordinates to Cartesian coordinates is known as the forward conversion [1].…”

“…This is because before the invention of the GPS, local geodetic datums were established based on traditional surveying techniques such as triangulation, trilateration, traversing, astronomical observation and among others [8,9]. Hence, the local geodetic datum involved data in only geodetic coordinates without the existence of Cartesian coordinates [1]. This prevalent situation has been problematic over the years to utilize GPS coordinates based on the global datum of world geodetic system 1984 (WGS84) into a local geodetic system.…”