# Centimeter-Level Precise Orbit Determination for the Luojia-1A Satellite Using BeiDou Observations
## 3 BeiDou Multipath Modeling with Luojia-1A Observations
### Data Collection  
In this study, the Luojia-1A onboard BDS data of 2018 DOY 159 were collected with a 1-s sample rate. The onboard BDS data include both B1I and B2I frequency data. To demonstrate the effectiveness of BDS based orbit determination, the onboard BDS observations of Luojia-1A are analyzed in this section.  
The statistical details of BDS observations are shown in Figure 2. The left panel shows the number of observations tracked during the observation period, and the right panel shows the percentage of three types of BeiDou satellites. The observation condition of the Luojia-1A satellite depends on the altitude of the satellite. The figure indicates that the Luojia-1A tracks the most observations from the C03 and the C07 satellites. Regarding the observation ratio, it concludes that the observations from the GEO satellite contribute to 42.18%, which is nearly the same as IGSO satellites. It should be noticed that GEO and IGSO satellites contribute to more than 80% observations, while these satellites are only available in Asia-Pacific and surrounding regions. The MEO satellites contribute fewer observations due to fewer MEO satellites and faster change of relative geometry between MEO and LEO satellites.  
Figure 1: The appearance of the Luojia-1A satellite.  
The onboard BDS receiver equipped on the Luojia-1A satellite supports 12 channels for each frequency, which is abundant for Beidou-2 signal tracking. As the BeiDou-3 satellite deployment, more channels are necessary for future receivers capable of tracking BeiDou-2 and BeiDou-3 signals. The time series of observed satellite number of the epoch and its statistic results are shown in Figure 3. The figure indicates that the Luojia-1A suffers mild intermittent interruption during BDS satellite signals tracking, and the reason is worth further investigation. The right panel indicates that the Luojia-1A can track five or seven satellites per epoch in most cases. There is only a 57.8% chance for Luojia-1A to track more than four BDS satellites simultaneously. This is mainly because most BeiDou satellites are located above the Asia-Pacific region, which is also challenging for obtaining continuous and precise orbit with only Beidou-2 observations.  
The sky view of GEO satellites, IGSO satellites, and MEO satellites from the Luojia-1A is shown in Figure 4. In the figure, different colors mean different satellite types. The sky view of the BDS satellites is relative to the antenna reference frame (ARF) of the Luojia-1A satellite. The azimuth angle is started from the +X axis in the SBF. Referring to the sky view of C02 and C03 satellites, it is apparent that the Luojia-1A has a better observational condition for GEO satellites without a noticeable data breach. As for the C08 satellite, the azimuth varies from 0\({}^{\circ}\) to 180\({}^{\circ}\), and the observations are more concentrated. Moreover, there are data outages of the C10 satellite observation arc. As for the MEO satellites shown in the figure, the observation arc is shorter than that of GEO and IGSO satellites, and the continuity is not as good as that of GEO and IGSO satellites.  
Figure 3: The number of observed satellites (**a**) and the statistic result (**b**).  
Figure 2: Statistics of BDS observations. (**a**) The number of observations for BDS satellites. (**b**) The percentage of different BeiDou satellite types.