Gravity Gradient Tensor Eigendecomposition for Spacecraft Positioning

TL;DR

This paper introduces a novel spacecraft positioning method using gravity gradient tensor eigendecomposition, transforming measurements into position estimates without initial guesses, leveraging eigenvalues and eigenvectors for direct localization.

Contribution

The paper presents a new approach to spacecraft positioning based on GGT inversion and eigen-decomposition, eliminating the need for initial position guesses and inertial navigation aid.

Findings

Method effectively estimates spacecraft position from GGT eigenvalues and eigenvectors.

Suitable for space navigation with negligible terrain effects at higher frequencies.

Uses J2 gravity model for simplified yet accurate positioning.

Abstract

In this Note, 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 then 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 simplespecific functions of spherical coordinates of the observation position. without the need of an initial position. Unlike the strategy of inertial navigation aiding, no prediction or first guess of the spacecraft position is needed. The method makes use of the J2 gravity model, and is suitable for space navigation where higher frequency terrain contributions to the GGT signals can be neglected.