# A Sensitivity Study of POD Using Dual-Frequency GPS for CubeSats Data Limitation and Resources
## 3 Orbit Determination under Different Scenarios
### Sampling Rate of the Observations  
In Section 3.1, the GPS observations onboard the LEO satellite with a sampling interval of 10 s were used for producing the reduced-dynamic orbits. Depending on the capacity of the CubeSat missions, the data might need to be stored and transferred to the GPC with a lower sampling rate. A compromise thus needs to be considered between the duty-cycles, the data completeness, and the sampling rate. Figure 6 illustrates the 3D RMSE of the orbits with the sampling interval varying from 10 to 120 s and the duty-cycle varying from 100% to 20%. The cases having mean satellite numbers of 9, 7, and 6 are given between each pair of dashed lines. Recall that the number of satellites is controlled by adjusting the elevation mask (Section 3.1). In the case of a duty-cycle of 20%, the orbits generated with an observation sampling interval of 120 s (red line) are not produced due to the extremely low number of continuous observations in each data patch. Note that all the RMSE are computed based on orbits resampled to 10 s sampling intervals.  
From Figure 6 it can be observed that the values in general gradually increase from the left to the right side, i.e., from the cases with good data continuity, completeness, to those with bad data conditions. With less data available for the processing in the Steps 3 and 4 (Section 2), the estimable parameters, including the six Keplerian elements, the additional dynamic parameters, and the stochastic parameters, are determined with lower precision. This results in a lower accuracy of the numerically integrated  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Duty-Cycle/Mean \# Satellite** & **9 Satellites** & **7 Satellites** & **6 Satellites** \\ \hline
100\% & – & 1.1 & 2.1 \\ \hline
80\% & 1.6 & 1.9 & 2.4 \\ \hline
60\% & 2.0 & 2.1 & 2.7 \\ \hline
40\% & 2.6 & 2.9 & 3.5 \\ \hline
20\% & 3.5 & 3.9 & 4.8 \\ \hline \hline \end{tabular}
\end{table}
Table 3: 3D RMSE (in cm) of the phase-based reduced-dynamic orbits under different duty-cycles and mean satellite numbers.  
Figure 6: 3D RMSE of the reduced-dynamic orbits under different duty-cycles, observation sampling intervals, and mean satellite numbers using the IGS final products. The cases having 9, 7, and 6 satellites (on average) are given between each pair of the dashed lines.  
orbits. At the same time, it can also be observed that the differences between having observation sampling intervals of 10 s (green), 20 s (yellow), and 30 s (magenta) are small. This can be attributed to the 30 s GPS clocks provided in the IGS final products, where interpolation into high-sampled time epochs would introduce biases within a higher percentage of the processing time (to be discussed in the next subsection). Provided that the receiver has a high duty-cycle not lower than 60%, even with a limited number of observed satellites and a high sampling interval of 120 s, the 3D RMSE is still below or around 3 cm. However, with lower duty-cycles, the degradation of the orbit accuracy could be dramatic when the observations are only available with a low sampling rate and when the observed satellites are limited.