# A Sensitivity Study of POD Using Dual-Frequency GPS for CubeSats Data Limitation and Resources
## 1 Introduction  
Combining strong dynamic models and observations of global navigation satellite system (GNSS) collected onboard, the processing strategies used for the low Earth orbit (LEO) reduced-dynamic precise orbit determination (POD) have been intensively investigated in the last decades [1; 2; 3; 4; 5]. Compared to the dynamic orbits based on the dynamic models only and the kinematic orbits based on the GNSS observations only, the reduced-dynamic orbit determination has the advantage that it is more robust against model deficiencies for the former case, and possible data constraints, e.g., data in-continuity for the latter case. Following the need for the POD by a range of applications, such as the studies in the Earth gravity field [6; 7], the atmospheric sounding [8], the altimetry [9], and the Interferometric Synthetic Aperture Radar (InSAR) [10], the LEO orbital accuracy based on undifferenced GNSS observations can reach a few centimeters [11; 12], and even better at mm-level in case of baseline processing for formation-flying [13; 14; 12]. For undifferenced POD, the highest accuracy is often realizedin postprocessing mode applying good dynamic models, precise GNSS satellite orbits, and clocks, and under the condition that the GPS dual-frequency phase and code data are tracked and collected with a good continuity and completeness. The antenna attitude information is often well monitored by extra sensors like star cameras and inertial measurement unit (IMU), and eventually will be used to correctly apply the antenna sensor offsets, the antenna phase centre offsets (PCOs), and variations (PCVs) [15]. The number of CubeSat missions has dramatically increased in this decade. By April 2020, there are over 1000 CubeSats successfully launched into their low earth orbits [16]. In addition to educational purposes, CubeSats are nowadays also used for the demonstration of new technologies and scientific researches [17; 18]. Compared to large or medium LEO satellites, the CubeSats are mostly cost-effective and occupy a much smaller size and weight, i.e., typically from below 1 kg (0.25U) to more than 20 kg (12U). This often leads to smaller battery volume and smaller size of the solar panels. In addition to the two-line elements (TLEs), other sensors like sun sensors and magnetometers have been used for orbit determination of CubeSats with relatively low accuracy, i.e., at km-level [19]. In the case of higher positioning accuracy requirements, the GNSS-based processing has been demonstrated as a useful method for the CubeSat POD, for which successful postprocessed position fix was achieved with a meter-level accuracy [20]. While the onboard positioning normally utilizes simplified dynamic models due to the limitation of the computational load [21; 22], the data postprocessing allows the usage of comprehensive dynamic models and the estimation of enough additional dynamic parameters to compensate remaining model deficiencies. However, even for the postprocessing mode, strongly constrained satellite size and power need to be shared among all sensors onboard. The capacity for data tracking, storage, and transfer is thus restricted, which limits the accuracy of orbit determination. The GNSS satellites may not be able to be fully tracked continuously due to these limitations, which could yield a duty-cycle smaller than 100% [20; 21; 23], and lead to fewer data available for the processing and more ambiguities to be set up. The size of the data collected between each data dump could also be limited [20]. The collected GNSS observations are most likely to be temporarily stored onboard and transferred back to the ground processing centre (GPC) every orbital cycle or a few cycles during a limited ground contact time, while information of tasks other than positioning is required to be stored and transferred at the same time. This may implicitly limit the GNSS data amount during the downlink.