# Gravity Field Recovery Using High-Precision, High-Low Inter-Satellite Links
## 4 Results  
### Gravity Field Retrieval Performance Due to Instrument Errors  
At first the impact of the instrument errors on the gravity field retrieval were quantified. For this task, we performed simulations where each error source according to the assumptions described in Section 2.2 was treated individually. Figure 5 shows the gravity field retrieval performance in terms of equivalent water height (EWH) errors per SH degree per coefficient for the low-low pair constellation and the MOBILE concept. Furthermore, the results were quantified using global RMS values of the errors in the recovered signal expressed in terms of cm of EWH, listed in Table 3 (see part: instrument errors). If only white-noise positioning errors were considered (Figure 5, green curves), the gravity field retrieval performance mainly depended on the observation geometry. The comparison between both satellite concepts revealed strongly reduced retrieval errors for MOBILE, which benefited from multi-directional observations. In the case of accelerometer noise in combination with star camera errors (Figure 5, blue curves), the MOBILE constellation showed reduced error behavior compared to the low-low pair as well. This was mainly caused by the observation geometry, but also by the improved accelerometers (\(\approx\)23%) with 3D capabilities to certain parts in the case of MOBILE. In contrast, the retrieval performance of the low-low pair benefits from the nanometer accuracy of the laser interferometer compared to the micrometer accuracy of MOBILE's laser link sensor for the most part of the spectrum (>5H degree 10). This became evident when only laser interferometer noise was considered (Figure 5, red curves). However, in the very low degrees, the MOBILE concept performed better than GRACE, which was again owed to the fact of an improved observation geometry. When considering all instrument error sources together, the retrieval errors of the low-low satellite pair are dominated by the accelerometer plus star camera sensor performance, while for the MOBILE constellation, the laser link error was the dominating error source for SH degrees higher than 20, and the accelerometer plus star camera noise only dominated the spectrum in the lower degrees. These results led to the conclusion that the gravity field retrieval based on instrument error sources showed smaller errors below SH degree 40 for the MOBILE concept compared to the low-low pair, but increased errors in the higher frequency spectrum due to the lower accuracy of the laser interferometer. Figure 5: Degree (error) standard deviations after 1 month of full AOHIS signal (black), low–low pair formation (dashed curves), and MOBILE constellation (continuous curves), when including only distance measurement errors (red), acceleration plus star camera errors (blue), and orbit errors (green). Next to the estimation of SH coefficients, we estimated their formal errors as well, shown in Figure 6. The noise of the different sensors in combination with the observation geometry reveal the performance of a specific satellite concept. In our case, they demonstrated the impact of the MOBILE high-low tracking concept by showing an almost uniform (isotropic) error spectrum and a high sensitivity in the sectorial coefficients (SH degree equal to SH order). In case of the low-low pair configuration especially, the sectorial coefficients were less well-determined than the zonal coefficients (SH order equal to zero). Figure 6b,d gave a closer view of the formal errors located in the long wavelength (low-degree) spectrum. The comparison between MOBILE and the low-low pair led to the assumption that the determination of the very low SH coefficients could be accomplished with a higher sensitivity through the MOBILE concept. In contrast to the observations in the along-track direction of the low-low pearl-string configuration, the multi-directional observations of the high-low tracking concept with a strong dominance of the radial component enabled an improved estimation of the very low SH coefficients.