Page - 97 - in Contributions to GRACE Gravity Field Recovery - Improvements in Dynamic Orbit Integration, Stochastic Modelling of the Antenna Offset Correction, and Co-Estimation of Satellite Orientations

Importantly, this method improves only on the processing of the data, leading to a dynamic orbit that is more compatible with the observations and models used in its integration. The method is not able to compensate for deficiencies in the input data. Given noisy accelerometer data or imperfect background models, application of this method would not lead to dynamic orbits that are necessarily closer to the true position of the spacecraft, but merely fit the noisy observations and models better. Spectral analysis of orbit differences from real GRACE data after convergence shows that some extraneous oscillations remain in the orbits. These oscillations are largest at frequencies at or below one cycle per revolution. They can also be attributed to the static nature of the employed reference ellipse. The presented results are however satisfactory for applications in GRACE processing. For this use, the critical part of the error spectrum begins only at much higher frequencies, where stability better than that expected of the GRACE-FO LRI instrument was achieved (cf. fig. 7.7). The applicability of the often suggested method of rectifying the reference orbit to GRACE dynamic orbit integration is uncertain. Continuous orbit arcs are of high desirability in the context of integrating the variational equations and dynamic orbits, as the number of satellite states to be estimated is kept low. Milani and Nobili (1987) give a refined algorithm for an orbit rectification method which can be used without restarting the integration procedure and thus introducing a new satellite state at that epoch. In the integration method presented in this text, the state transition matrix of the variational equations is modified using corrections computed from the Marussi tensor. Given this circumstance, it is not immediately clear how the method outlined by Milani and Nobili can be applied to the presented modified Encke approach. 7.4 Discussion 97