A comparison between Fukushima-Halley algorithm and Trilateration algorithm for geodetic conversion

Abstract

The geodetic transformation of Cartesian coordinates into their elliptical equivalent is a fundamental problem in geodesy. The Fukushima algorithm accelerated by Halley method (Fukushima-Halley) is considered the standard in this conversion. The Trilateration algorithm is a recent algorithm solving the conversion problem through a computational geometry approach. This study compared the Trilateration algorithm to the Fukushima-Halley algorithm in aspects of accuracy of results, time efficiency, and space efficiency. Also, the parallel version of both algorithms was established using the Master-Slave technique and compared. The Trilateration Algorithm showed a slightly higher accuracy compared to Fukushima-Halley algorithm, which allocated less space in memory, and was 2.6 faster in sequential version compared to 1.9 in the parallel version. The study introduced a benchmark for arithmetic operation on the testing machine to be used in time efficiency comparison.