Estimation of the parameters of the map's projection using the quasi-Newton method : hybrid Broyden-Fletcher-Goldfarb-Shanno method
Abstract
Detection of the map's projection based on the quasi-Newton method: the hybrid Broyden-Fletcher-Goldfarb-Shanno method with the inexact length step. Our software supports the detection of 5-9 parameters of the projection using the weighted non-linear least squares solution.
It provides a symmetric positive definite update of the Hessian matrix leading to the fast convergence rate (the fastest from all proposed methods). The global convergence is ensured from the Wolfe sufficient decrease condition.
The method is also applicable to early maps geoereference.