# Hybrid Electrostatic-Atomic Accelerometer for Future Space Gravity Missions
## 3 Results and Discussions  
### Numerical Gravity Performance Simulations  
#### 3.1.1 Instrument Noise Impact  
It is clearly observed in Figure 11 that a higher EA corner frequency allows for a larger impact of the CAI, but simultaneously lowers the overall performance of gravity field retrieval. This is not observable for _Case 4_, where the CAI performance is equal to the EA noise floor. Not all hybridization scenarios lead to an improvement of the solution quality compared to a stand-alone EA. Indeed, looking for instance at Figure 11, no significant differences can be observed between the coefficient residuals of the reference EA scenario and _Case 1_ and only a slight improvement can be seen for _Case 2_, in the disadvantageous scenario, for the EA, presenting a 3 mHz corner frequency. This behavior can be attributed to the fact that the obtained accelerometer improvement lies below the frequency bandwidth that is relevant for gravity field retrieval. The lower boundary of this frequency band is defined by the satellites orbital frequency, which is approximately \(1.8\times 10^{-4}\) Hz (equivalent to complete revolution in about 90 min) for both the polar and the inclined pair. In _Case 2_, for an EA corner frequency of 1 mHz, the hybridization of the EA occurs at a frequency that is very close to the edge of the retrieval band, and therefore, no significant improvement could be achieved. This is no longer the situation if now an EA corner frequency of 3 mHz is assumed. Considering a 1 mHz EA corner frequency, we can observe only significant improvements with respect to a stand-alone EA scenario when assuming a hybrid accelerometer compatible with _Case 3_ and _Case 4_. The degree RMS of the residuals improves by up to a factor three in the SH degrees below \(n=10\) for _Case 3_ and, in the same spectrum area, by roughly one order of magnitude for _Case 4_. Considering now a Bender-type configuration (cf. Figure 12), we can see that the overall level of the coefficient residuals is significantly lower than for a GRACE-type one. This highlights one of the interests of a Bender-type mission, which improves the observation geometry and allows, amongst others, registering the east-west components of the gravity field. The accelerometer stability plays here a much smaller role towards the solution quality than in the case of a single-pair mission. Considering the optimistic scenario of _Case 4_ and an EA corner frequency of 1 mHz, the performance gain is now only limited to degrees below \(n=20\). Nevertheless, it allows for improvements of up to one order of magnitude in the very low degrees up to \(n=5\), which is still substantial with regard to time-variable gravity applications. It is important to note that the retrieval performance gain that could be achieved through hybridization is not limited to the frequency bands specified in Figure 6, but instead extends into the high-degree spectrum of the gravity field solution (cf. Figures 11-13). This behavior arises from the fact that a one-to-one relation between the instrument's frequency spectrum, related to the time domain of the orbit track, and the spherical harmonic spectrum, related to the space domain of the sphere, only holds for zonal coefficients, while coefficients of high orders contain significant amounts of low-frequency information [70]. Therefore, if the quality of low-frequency observation increases, then, consequently, the retrieval quality of the sectoral and tesseral coefficients is also improved. Figure 13a,c show the relative improvements made in analyzing the formal error triangles of _Case 3_ and _Case 4_ with respect to the reference EA scenario. We can see that the hybridization may significantly influence high-degree sectoral coefficients, as well as high-order tesseral coefficients.