# Hybrid Electrostatic-Atomic Accelerometer for Future Space Gravity Missions
## 2 Materials and Methods  
### Numerical Gravity Performance Simulations  
Gravity performance simulations were performed aiming to assess the added value of such a hybrid accelerometer for future geodesy missions. Some additional details concerning the performed simulations can be found in [42]. In brief, a series of simulations was conducted on IAPG's closed-loop reduced-scale simulation software, described in [64], to study the hybrid accelerometer's impact on the performance of gravity field retrieval. Due to several simplifications implemented in these reduced-scale simulations as a trade-off for improved computation time, their results were validated by a comparison to IAPG's full-scale simulation tool [65], where all relevant aspects of a real gravity field mission simulation and the subsequent gravity retrieval can be taken into account. The reduced-scale results exhibit a highly consistent behavior with the full-scale ones [42]. Although the total amplitude of the residuals differ slightly between full- and reduced-scale simulations, the relative behavior among the solutions is very similar and proves the validity of the reduced-scale simulation results. All the results that are presented in the following derive from reduced-scale simulations in the case of a GRACE-type and a Bender-type satellite flight formation. The GRACE-type constellation consists of a pair of identical satellites, which follow each other on a near-polar orbit, while Bender features an additional GRACE-type satellite pair on an inclined orbit (see Figure 5). Here, both the orbit altitudes and the initial mean anomalies (respectively mean anomaly differences of the satellites within one pair) were chosen to closely match the corresponding average values of the actual GRACE, respectively GRACE-FO, missions (450-500 km orbit altitude, 200 km inter-satellite distance). The retrieval period was set to a total of 30 days, enabling one full repeat cycle of the polar pair and nearly three full repeat cycles of the inclined one. For the instrument noise, only the two most dominant contributors to the error budget were taken into account, which were, on the one hand, the accelerometer and, on the other hand, the inter-satellite ranging instrument. For the  
Figure 5: Illustration of a GRACE-type (**left**) and a Bender-type (**right**) flight formation. This figure is extracted from [66]. latter, the performance specifications of the laser raging interferometer (LRI) implemented on GRACE-FO were assumed [67]. For the hybrid accelerometer, a number of possible performance scenarios were predefined, based on the CAI's overall noise floor (4 cases; cf. Table 2), the EA's noise increase in the low observation frequencies (stemming primarily from thermal fluctuations), and the extent of the EA's designated measurement bandwidth defined by the corner frequency at which the temperature-dependent effects in the low frequencies become the major error source. The model specifications are presented in Table 2, and a selection is visualized in Figure 6, where, in this case, the EA was assumed to present a \(1/f^{3}\) noise slope at a low frequency and a corner frequency of \(1\,\mathrm{mHz}\). For the CAI, we assumed different noise levels ranging from _Case 1_, corresponding to achieved on-ground sensitivities with state-of-the-art cold atom gravimeters [23, 24, 44], to _Case 4_, corresponding roughly to performance foreseen in future challenging space projects with cold atom inertial sensors [6, 13]. Note that, in the following, the results assume a hybridization in just one axis that can be considered as aligned along the line-of-sight between the two satellites, pointing from one satellite's center of mass to the other's [42]. A selection of simulation results is presented based on specific parameters to show the impact of hybridization in gravity retrieval. In the first group of simulation results we disregard temporal gravity signals and, thus, temporal aliasing errors and only take into account instrument errors of the