Page - 95 - 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

0.1 1 10 100 Frequency [mHz] 10−11 10−9 10−7 10−5 KBR LRI Figure 7.7: Real data. Propagation of orbit noise to range rate measurement ρ˙. Solid black is a noise model for the GRACE KBR and ACC instrument noise, Dashed black is a noise model for the GRACE-FO LRI and ACC instruments. The other colours are the same as in figs. 7.4 to 7.6. range-rate error smaller than the precision of the current KBR instrument on GRACE (solid black line) across the entire frequency spectrum. Inthebranchoftheerrorspectrumthat isdominatedbytheKBRnoise,above≈10mHz, the accuracy of the configuration using no reference motion (brown) as well as the uncertainty of both the Kepler configurations (pink and green) are well above the performance estimate for the LRI (dashed black line). Both configurations using equinoctial elements (purple and orange) are below the LRI noise level over the complete spectrum. As could be expected, the equinoctial configuration based on the best-fit reference ellipse (orange) also shows the lowest noise in this domain. The KBR noise spectrum in fig. 7.7 is based on spectral analysis of real GRACE SST residuals. The performance estimate for the LRI is based on real GRACE ACC data, a description of the noise characteristics of the LRI (Heinzel et al., 2012), and an optimistic assumption of a 50-fold improvement of the ranging accuracy with regard to the KBR instrument (Flechtner, 2012). 7.4 Discussion An improved algorithm for dynamic orbit determination was developed, paying particular attention to its applicability to GRACE-FO data processing. The existing methodology was refined by applying Encke’s method, directly eliminating the large contribution of the central term of Earth’s gravitational potential on the numerically integrated accelerations. Encke’s method was then refined in two separate ways: First, the osculating reference ellipse proposed by Encke was replaced by a rigorously optimized best-fit reference ellipse. Such a best-fit ellipse significantly reduces the 7.4 Discussion 95