Analysis of the Earth’s Gravitational Field from Semi-Continuous Ephemeris of a Low Earth Orbiting GPS-Tracked Satellite of Type CHAMP, GRACE or GOCE

The aim is to present and to examine an algorithm for the orbit analysis of a low-Earthorbiting GPS-tracked satellite to determine the spherical harmonic coefficients of the Earth’s gravitational field. By means of Newton’s interpolation scheme the accelerations acting on the satellite are derived from the satellite’s GPSpositions x(t _k ), y(t _k ), z(t _k ) or position differences Δx,(t _k-1 k), Δy(t _k-1 k), Δz(t _k-1 k). This is done in a quasiInertial Reference Frame to avoid frame accelerations. The acceleration vector is balanced due to Newton’s equation of motion by the gravitational force vector, namely the gradient of the gravitational potential. The coordinates of the gradient of the gravitational potential, which are given in a Cartesian representation, also have to be transformed to the quasi-Inertial Reference Frame. The resulting equation system is then solved by means of a Gauss-Markov model. In order to get a more stable solution for higher resolutions a regularization method (Tikhonov, Kaula) can be applied.