## 2 Models and Assumptions
### Assumed Receiver Characteristics  
As mentioned, in this study we assumed the characteristics of the spaceborne receiver \"SANAG\" [12] under development in our laboratory, which is designed to acquire L1 C/A signals with a sensitivity of 15 dB-Hz (when aided by an orbital filter) and to track both L1 C/A and L5Q signals, respectively with a tracking sensitivity of 15 dB-Hz and 12 dB-Hz. In particular, note that the tracking strategy adopted includes the use of ionosphere-free observations combinations for some of the signals crossing the ionosphere, in order to mitigate their ionospheric delay. More detailed information about the tracking strategy adopted in the SANAG receiver can be found in [12].  
The SANAG receiver observations are processed by an orbit determination filter, described in detail in [7; 13], able to significantly improve the achievable navigation accuracy.  
The SANAG receiver is assumed to be completely autonomous, able to provide orbit determination without the need for any additional external information, which is not an integral part of the GPS signal data message. Therefore only code-based observations are assumed, while we did not consider the use of more accurate carrier phase observations, since only their fractional part is measured by the receiver and therefore they would rely on additional corrections (not part of the data message) to solve their unknown integer ambiguities. However, it is important to mention that signals transmitted by the satellite based augmentation system (SBAS) geostationary satellites may also be processed by an orbiting spaceborne receiver to improve the navigation performance. Firstly they could be used as a source of real-time precise orbit and clock corrections, allowing for the processing of carrier-phase observations and then for precise orbit determination (POD). Moreover, the number of collected ranging observations could be increased (increasing the availability) as well as the integrity (since SBAS signals contain information about the GNSS signals that should not be tracked because affected by larger errors) and therefore the achievable navigation accuracy eventually.  
The signal power received at the receiver position is modeled as follows, taking into account the gain patterns of both transmitter and receiver antennas and the free space signal propagation losses:  
\[P_{o}=P_{ICD}+\ O_{G}+LFS-L_{TX}(\varphi,\phi)-L_{RX}\ (dBm) \tag{1}\]  
where \(P_{ICD}\) is the guaranteed minimum signal level for a receiver on Earth (as specified in signal-in-space specifications document); \(O_{G}\) is the global offset (set to match the same level of signals as when real ones are received), \(LFS\) is the free space loss; \(L_{TX}\) and \(L_{RX}\) are the loss due to the transmitter's antenna pattern and receiver's antenna pattern, respectively; and \(\varphi,\phi\) represent the elevation and azimuth of the transmitter antenna pattern, respectively. Note that in the rest of the paper, the elevation is meant to be the angle from the antenna boresight, while the azimuth is the angle around the antenna boresight.  
The \(P_{ICD}\) for GPS L1 C/A and GPS L5Q was assumed to be \(-128.5\) dBm and \(-127\) dBm, respectively, according to the interface control document (ICD) documents [4; 14]; in addition, a global offset of 3 dB for both signals was assumed to account for the difference between the minimum power transmitted and the real one [6].  
It should also be mentioned that a Spinent simulator has some bounds on the available signal power level range that can be generated. Indeed, the upper and lower bound are \([P_{ICD}+O_{G}+20]\) dBmand \([P_{ICD}+O_{G}-49.9]\) dBm, respectively. Thus, the available signal powers would belong to the interval (\(-175.4\), \(-105.5\)) dBm and (\(-173.9000\), \(-104\)) dBm for GPS L1 C/A and GPS L5, respectively.  
The GPS observations were modeled as in our previous study [9]. Table 1 summarizes the assumptions used in the models.