# A Sensitivity Study of POD Using Dual-Frequency GPS for CubeSats Data Limitation and Resources
## 3 Orbit Determination under Different Scenarios
### Duty Cycling and Satellite Numbers  
As mentioned before, due to the constraints of the CubeSats on the power, the data storage, and the time of active attitude control possibly during the sunlight, the GNSS observations might have breaks, and are collected in pieces of different length [20]. In this study, observation data are assumed to be collected with different duty-cycles, i.e., with the power turned on only for a part of the time. The duty-cycle \(D\) is defined here as a percentage of time data was available out of the total time considered. The sensitivity analysis is performed assuming the \(D\) varying from 20% to 100%. In our tests, a duty-cycle implies that the data are available in the first \(60\times D\) min of each hour. The 3D orbital errors are shown in Figure 4 with varying \(D\). The observation sampling interval was 10 s. Recall that the phase-based reduced-dynamic orbit with a duty-cycle of 100% was our best-case scenario and was used as the reference for comparison as mentioned in Section 2. The RMSE increases from about 1.6 cm with a \(D\) of 80% to about 3.5 cm with a \(D\) of 20%. Note that the RMSE is computed from the beginning of the first power-on period to the end of the last power-on period of the test day. Figure 4: 3D orbital errors for different duty-cycles (from 20% to 80%) of the phase-based reduced-dynamic orbits using data of GRACE FO-1 with a sampling interval of 10 s. The elevation mask was set to 5 degrees with a mean satellite number of about 9. Figure 3: 3D orbital errors of the code-based kinematic (red) and reduced-dynamic daily arc (blue) with a sampling interval of 10 s. The IGS final products were used for the GPS satellites. As shown in Figure 1 and discussed in [19], the number of satellites that can be properly tracked (at least for the P1 and P2 observations) by the CubeSat receiver could be lower than expected due to different reasons, such as the antenna stabilization problems or specific channel assignment. Therefore, to resemble this practical issue, a simplified approach is performed in this simulation to reduce the number of satellites observed under good conditions by excluding satellites with low elevation angles. The elevation mask is increased from 5 to 25 degrees in the test, resulting in a reduction of the mean satellite number from about 9 to 6 (see Table 2). The Figure 5a illustrates the distribution of the satellite numbers applying different elevation masks for GRACE FO-1 for the test period. A gradual reduction of the satellite numbers can be observed when increasing the elevation mask. The percentile of valid SPP solutions is reduced correspondingly from nearly 100% to about 83% due to the reduction in redundancy. Having a duty-cycle of 100%, as shown in Figure 5b, decreasing the number of the received satellites from, e.g., 7 to 6, degrades the RMSE from about 1.1 to 2.1 cm. Note that the case with the mean satellite number of 9 having an elevation mask of 5 degrees is our best-case scenario and is used as the reference for comparison, in other words, the RMSE represent the solution discrepancy between the cases of using 7 or 6 satellites and when using 9 satellites. Although the differences observed in Figures 4 and 5 are not large, coupling a reduction in the duty-cycle with a reduction in the number of received satellites would cause larger problems. Table 3 shows the 3D RMSE of the orbits applying different duty-cycles and mean satellite numbers, assuming an observation sampling interval of 10 s still. As mentioned earlier, the solution obtained with a duty-cycle of 100% and the mean satellite number of 9 is used as the reference for assessing the solutions by computing their discrepancies. It can be observed that with a duty-cycle equal or above 60%, even when the observed satellites are limited, the RMSE is still below 3 cm. With lower