# A Sensitivity Study of POD Using Dual-Frequency GPS for CubeSats Data Limitation and Resources
## 2 Processing Strategy
\begin{table}
\begin{tabular}{l l} \hline \hline \multirow{3}{*}{**Measurement Model**} & GPS code P1 + P2, phase L1 + L2 \\ \cline{2-3}  & IF linear combination \\ \cline{2-3}  & Sampling interval: 10 s, 20 s, 30 s, 60 s, 120 s \\ \cline{2-3}  & Elevation mask: 5\({}^{\circ}\), 15\({}^{\circ}\), 25\({}^{\circ}\) (for different mean satellite numbers) \\ \cline{2-3}  & Arc length: 6 h, 12 h, 24 h \\ \cline{2-3}  & GPS orbits and clocks: IGS final, rapid, real-time products \\ \hline \multirow{3}{*}{**Dynamic Model**} & Earth gravity: EGM2008 [39], Earth potential degree: 120 \\ \cline{2-3}  & N-body gravity: JPL DE405 [40] (Planetary ephemeris) \\ \cline{2-3}  & Solid Earth tides: IERS Conventions 2010 \\ \cline{2-3}  & Pole tides: IERS Conventions 2010 [41] \\ \cline{2-3}  & Ocean tides: FES2004 [42] \\ \cline{2-3}  & General relativistic term \\ \hline \multirow{2}{*}{**Reference Frame**} & IGS14, J2000.0 (Julian epoch) \\ \cline{2-3}  & Nutation and precession: IAU2000R06 [34] \\ \cline{2-3}  & Sub-daily pole variations: IERS Conventions 2010 [41] \\ \cline{2-3}  & Earth rotation parameters: IGS final, rapid, ultra-rapid products \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Processing details for the reduced-dynamic orbit determination. Figure 2: Flow-diagram of the processing procedure and the estimated parameters. \(n\) and \(m\) are the numbers of the stochastic parameter vectors considered during the estimation in Step 3 and 4, respectively. In this study, the data from the LEO satellite of the GRACE Follow-on mission [43], the GRACE FO-1, which continuously tracked dual-frequency code and phase GPS observations on L1 and L2, are used for different scenarios simulating conditions with limited data and resources on 22 August 2018. For the purpose of consistency, the processed orbits are differenced with the best-case scenario in this study (as the reference for comparison), i.e., the phase-based reduced dynamic orbits with a duty-cycle of 100%, an observation sampling interval of 10 s, an elevation mask of 5 degrees (default setting in Bernese for LEO processing), using the IGS final products and processed in a 24 h arc. The use of our best-case scenario as a reference for comparing different tested cases is justified by comparing it with the reference orbits provided by the Jet Propulsion Laboratory (JPL) [44] for the same day, where good consistency with a 3-dimentional (3D) root-mean-squared error (RMSE) of below 2 cm was achieved. Nevertheless, it should be noted that in this study, the 3D RMSE computed under different scenarios refer to the accuracy difference compared with the best-case scenario, but not the absolute orbital accuracy. Note that for LEO missions, independent technics like the satellite laser ranging (SLR) and the K-band ranging (KBR) are often utilized to validate the accuracy of reference orbits. As a large number of variants with respect to different observation sampling rates, duty-cycles, satellite numbers, latencies, availability of the attitude information, and arc lengths are tested, this study does not attempt to study long-term variation of results. As a consistency check, the POD results of the best-case scenario from 14 to 21 August 2018 were compared with the JPL reference orbits, and no significant difference from those of the test day in this study can be observed, i.e., at a few millimeters. As such, we consider the simulations based on the test day are representative.