Harmonic analysis of the earth's gravitational field from kinematic CHAMP orbits based on numerically derived satellite accelerations

Abstract

Based on very accurate kinematic CHAMP orbits, a new CHAMP gravitational field model was computed by means of a (point-wise) acceleration approach. In order to implement such an acceleration approach, the satellite's acceleration has to be derived from the kinematic CHAMP orbits by means of interpolation and subsequent numerical differentiation. The iterative method of preconditioned conjugate gradients is implemented to solve the large linear system of equations for the spherical harmonic coefficients. If appropriate preconditioning is applied, convergence can be reached within 7 - 15 iterations. An important topic concerning the accuracy of the gravity field solutions is the detection and filtering or down-weighting of spikes, jumps, outliers and inaccurate data in the kinematic orbits. These problems are adressed by data-preprocessing or robust estimation. Different gravity field solutions up to degree and order 90 were computed, where validation exhibits a signal-to-noise (S/N) ratio per degree of S/N ≥ 1 for coefficients up to degree 80 and S/N ≥ 2 for coefficients up to degree 70. Comparisons to different CHAMP-models, which were obtained by application of alternative algorithms, prove that the acceleration approach can compete with other methods of gravity field determination. © 2006 Springer-Verlag Berlin Heidelberg.