Preliminary Orbit Determination of Artificial Satellites: A Vectorial Sixth-Order Approach

Abstract

A modified classical method for preliminary orbit determination is presented. In our proposal, the spread of the observations is considerably wider than in the original method, as well as the order of convergence of the iterative scheme involved. The numerical approach is made by using matricial weight functions, which will lead us to a class of iterative methods with a sixth local order of convergence. This is a process widely used in the design of iterative methods for solving nonlinear scalar equations, but rarely employed in vectorial cases. The numerical tests confirm the theoretical results, and the analysis of the dynamics of the problem shows the stability of the proposed schemes.