# Performance Analysis of the Korean Positioning System Using Observation Simulation
## 3 Simulations
### Precise Orbit Simulation  
In this study, we first evaluate KPS and GPS POD performance with simulated data on the PANDA software. To investigate the performance of KPS/GPS POD, we also consider 11 temporary KPS monitoring stations (KPSMS) and 10 additional Multi-GNSS Experiment (MGEX) stations to simulate ground-based observations for three days, day 140-142, 2018. The sampling intervals of the simulated observations are set to 30 s for ground stations. Figure 1 shows the distribution of KPSMS and MGEX stations selected temporarily for the KPS/GPS POD simulations. The filled blue circles and red triangles represent the MGEX and KPSMS stations, respectively. In batch least squares (LSQ) mode, we use 24 h data for one POD solution. In the solution, the ionospheric free linear combinations are used to eliminate the first-order ionospheric delay, and the unknown parameters to be estimated include initial position and velocity, solar radiation parameters,the satellite clock offsets, station coordinates, which are usually tightly constrained though they are estimated as parameters, receiver clock offsets, integer ambiguities, and zenith wet delays (ZWD). Table 2 presents the force and observation models applied for KPS/GPS POD simulation. Figure 2 shows the ground tracks of KPS and GPS satellites. KPS IGSO satellites have repeating analemma ground tracks with north-south asymmetry. This is very similar to the ground tracks of QZSS IGSO satellites. KPS GEO satellites are placed at regular intervals near the Earth's equator. In addition, the ground tracks for 24 GPS satellites are marked with solid green lines, as shown in Figure 2.  
Figure 1: The distribution of 11 KPS monitoring stations (KPSMS) and 10 Multi-GNSS Experiment (MGEX) stations selected for the KPS/GPS precise orbit determination (POD) simulations. The filled blue circles and red triangles denote locations of the MGEX and KPSMS stations, respectively. A background is produced by the [PERSON] projection in M_Map [28]. Figure 2: The ground trajectories for the designed KPS and GPS satellites. The red crosses and solid red line represent the ground tracks of the KPS geostationary Earth orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites, respectively. The solid green lines indicate the ground tracks of the GPS satellites. A background is produced by the [PERSON] projection in M_Map [28]. Figure 3 presents the averaged orbit root mean square (RMS) errors in the along-track, cross-track, and radial directions for seven KPS satellites. The orbit errors of all components were compared with the true orbits that we have simulated. For the KPS GEO satellites (PRN K01 \(\sim\) K03) in regional coverage, it is feasible to obtain the orbit accuracy in terms of three dimensional RMS at about 50 cm, while the orbit accuracy of the KPS IGSO satellites (PRN K04 \(\sim\) K07) to be achieved is about 10 cm. As seen in Figure 3, the RMS values of the GEO satellites are much larger in the along-track direction than in the others. In addition, the RMS of the POD solution for KPS GEO satellites is less than 10 cm in the cross-track and radial directions. The averaged RMS values in the radial direction are the smallest, while the averaged RMS value in the along-track direction reaches up to nearly 50 cm. [PERSON] et al. (2019) reported that the weak tracking geometry of GEO satellites results in large orbit errors in the along-track directions. Moreover, [PERSON] et al. (2019) indicated that the orbit errors of GEO satellites in the along-track are highly correlated with the ambiguity solutions. [PERSON] et al. (2019) showed that the RMS value in the along-track direction is about 46-73 cm for BDS GEO satellites with ground tracking observations only. In addition, the RMS values in all directions for BDS IGSO satellites were less than 20 cm. Although KPS and BDS differ slightly in the designed orbital elements, the KPS orbit simulation results are very similar to those presented by [PERSON] et al. (2019).