# A Sensitivity Study of POD Using Dual-Frequency GPS for CubeSats Data Limitation and Resources
## 3 Orbit Determination under Different Scenarios
### Length of Arc  
The orbital period of a LEO satellite is typically around 1.5 h, depending on its altitude from the Earth's surface. Taking the GRACE FO-1 as an example, based on the semi-major axis estimated in the final reference orbit, its orbital period is approximately 1 h 34 min 29 s for the test day. A 24 h arc for data analysis thus contains about roughly 15.2 orbital periods. By reducing the length of the processed arc in case of rapid processing, the amount of the data used for estimation of the orbital parameters may cover, e.g., only several orbital cycles. For an observation model with a good strength, e.g., having data with a high sampling rate, a high duty-cycle, a relatively loose latency requirement, and a high number of observed satellites, the influence of the arc length could be small. However, a long arc might be essential for scenarios with weaker model strengths. To analyze this correlation, this section presents results of a varying arc length from 24 h to 12 h and 6 h. The influences of the arc length on different scenarios are investigated in detail. Using the best scenario with a duty-cycle of 100%, a mean satellite number of 9, and an observation sampling interval of 10 s, the 3D RMSE of the final orbits are given in Table 5 for different arc lengths and using different IGS products. For arcs shorter than 24 h, multiple arcs were processed covering the entire test day. Figure 12: 3D orbital errors not applying the antenna attitude information. The IGS final products were used for observations with a duty-cycle of 100%, a sampling interval of 10 s, and a mean satellite number of 9. From Table 5 it can be observed that in case of good data condition, the accuracy differences are very small when reducing the arc length. Having a closer look at the 3D orbital errors with an arc length of 6 h and 12 h using, e.g., the IGS final products (see Figure 13a), border effects of the short arcs, i.e., the degradation of the orbital accuracy at the edges of the corresponding arcs, are the main reason of the degradation [11]. Applying the IGS rapid products (see Figure 13b), the degradation at borders is less obvious due to the generally much larger orbital errors. For cases with lower data availability, the degradation caused by shortening the arcs could be higher. For scenarios simulating different data conditions, the increase in the 3D RMSE when shortening the arc length from 24 h to 12 h is given in Table 6 as an example applying the IGS final products. While most of the increase is still at millimeters, increase of several centimeters is also observed for the cases with very limited data. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Duty-Cycle/Mean \# Satellite** & **8 Satellites** & **7 Satellites** & **5 Satellites** \\
**Sampling Interval [s]** & **10/20/30/60/120** & **10/20/30/60/120** & **10/20/30/60/120** \\ \hline
100\% & 0.6/0.2/0.1/0.2/–0.1 & 0.1/0.1/0.2/0.2/0.2 & 0.1/0.0/0.1/0.1/0.2 \\ \hline
80\% & 0.2/0.1/0.5/0.4/–0.4 & 0.1/0.1/0.2/0.2/0.5 & 0.2/0.2/0.2/0.3/0.4 \\ \hline
60\% & 0.1/0.0/0.3/1.0/–0.4 & 0.1/0.1/0.2/0.2/0.5 & 0.0/0.1/0.1/0.1/0.1 \\ \hline
40\% & 0.2/0.3/0.3/0.6/0.8 & 0.2/0.0/0.2/0.7/1.7 & 0.2/0.3/0.5/2.0/3.5 \\ \hline
20\% & 2.0/2.2/8.3/– & 1.6/2.2/3.0/3.6/– & 2.9/2.0/3.4/4.8/– \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Increase in the 3D RMSE (in cm) of phase-based reduced-dynamic orbits when shortening the arc length from 24 h to 12 h. The IGS final products were used. Figure 13: 3D orbital errors computed with different arc lengths using **(a)** the IGS final products and **(b)** the IGS rapid products. A duty-cycle of 100%, an observation interval of 10 s, and a mean satellite number of 9 were assumed for the processing. The arc length experiment here refers to the processing using e.g., \(k\) hours of data in each processing round, and in each hour of these \(k\) hours, data are tracked in X% of the time.