Gravity gradient tensor eigendecomposition for spacecraft positioning

A study is conducted to present a new approach to spacecraft positioning based on GGT inversion is presented. The gravity gradient tensor is initially measured in the gradiometer reference frame (GRF) and transformed to the Earth-centered Earth-fixed (ECEF) frame via attitude information as well as Earth rotation parameters. Matrix Eigen-Decomposition is introduced to directly translate GGT into position based on the fact that the eigenvalues and eigenvectors of GGT are specific functions of spherical coordinates of the observation position.