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)

Abstract

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 (ϕ , 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 ( ). 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.

Statistical Assessment of the Difference between the Height Differences Obtained by Spirit and Trigonometric Leveling Techniques

“…Solutions with either GPS or GLONASS satellites were comparable, but in most cases, the GPS solutions performed better. Some other Scholars have also, discussed the combined methods of leveling in an attempt to evaluate height differences between points on ground surface (Wang & Soler, 2015;Tata & Olatunji, 2020;Kemboi & Odera, 2016;Peprah & Kumi, 2017;Paar, Novakovic, & Kolovrat, 2014). While these earlier works laid much emphasis on determining, which method is more accurate, among two or more leveling techniques, this present work seeks to investigate the extent of the difference between the height differences obtained by spirit and trigonometric leveling, by subjecting this difference to a test of hypothesis, based on field observed survey data Chen, 2022;Maverick, 2021;Bhandar, 2022;Turney, 2022).…”