Gravity Gradient Tensor Eigendecomposition for Spacecraft Positioning

Pei Chen1, Xiucong Sun2, and Chao Han3 Beihang University, Beijing, 100191, People’s Republic of China Nomenclature U = gravitational potential, m2/s2 T = gravity gradient tensor (GGT), E TECEF = GGT in ECEF, E TENU = GGT in ENU, E TEIG = GGT in the Eigen frame, E T0 = GGT in GRF, E LA→B = rotation matrix from A to B r = observation position, m x, y, z = cartesian coordinates of r r, φ, λ = spherical coordinates of r Q = rotation matrix from GRF to inertial frame W = rotation matrix from inertial frame to ECEF μ = geocentric gravitational constant, m3/s2 J2 = unnormalized second zonal harmonic R = equatorial radius of the Earth, m ξ, η = eigenvalue and eigenvector θ = rotation angle from ENU to the Eigen frame, rad