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

摘要

In Ghana’s local Geodetic Reference Network, the standard forward transformation equation has played a major role in coordinate transformation between World Geodetic System 1984 (WGS84) and local geodetic datum. Thus, it is an initial step in forward conversion of geodetic coordinates (?, λ, h) to Cartesian coordinates (X, Y, Z) in transformation from global to local datum and vice versa. Several studies in the recent decades have been conducted on converting Cartesian coordinates to geodetic coordinates (reverse procedure) through the utilisation of iterative, approximate, closed form, vector-based and computational intelligence algorithms. However, based on the existing literature covered pertaining to this present study, it was found that the existing knowledge do not fully adhere to the issue of evaluating alternative techniques in the case of the forward conversion. Hence, the aim of this present study was to explore the coordinate conversion performance of the Multivariate Adaptive Regression Splines (MARS) and Multiple Linear Regression (MLR). The performance of each model was assessed based on statistical indicators of Mean Square Error (MSE), Root Mean Square Error (RMSE), Mean Bias Error (MBE), Mean Absolute Error (MAE), Standard Deviation (SD), Noise to Signal Ratio (NSR), Correlation Coefficient (R), and Correlation of Determination (R2). The statistical findings revealed that the MARS and MLR offered satisfactory prediction of Cartesian coordinates. However, the MLR compared to MARS showed better stability and more accurate prediction results. From the results of this present study, the main conclusion drawn is that, MLR provides a promising alternative in the forward conversion of geodetic coordinates into Cartesian coordinates. Therefore, the capability of MLR as a powerful tool for solving majority of function approximation problems in mathematical geodesy has been demonstrated in this present study.