Estimating the seven transformational parameters between two geodetic datums using the steepest descent algorithm of machine learning

Abstract

This study evaluates the steepest descent algorithm as a tool for root mean square (RMS) error optimization in geodetic reference systems to improve the integrity of transformation. With an initial RMS error estimate of 0.01830m, the negative gradient direction was applied through the steepest optimization leading to a final RMS error estimate of 0.00051m. Using the exact line search mode with a one-point step size of 0.1, we achieved the minimum values in less than sixty iterations, regardless of the slow convergence rate of the steepest descent algorithm.