## 4 Orbit-Tracking and -Determination Algorithm Simulation
### Simulation Results of Orbit-Determination Precision  
Due to the fact that the navigation satellite links conform to the Walker constellation and are evenly distributed globally, the specific timing of expanding user access does not affect the accuracy of orbit determination. The main errors in orbit determination are caused by clock accuracy error, antenna phase center deviation, channel delay error, observation noise, relativistic effects and other errors. After these errors are set to predetermined values, we mainly analyze the impact of the number of time slots and access time per minute on the accuracy of orbit determination. Therefore, we only analyze the duration of access and the  
Figure 4: Clock offset solution accuracy of 20 sets of unidirectional range measurements (* and blue line represent the error value of clock bias calculation). Figure 5: Frequency offset solution accuracy of 20 sets of unidirectional range measurements (* and blue line represent the error value of frequency differences calculation). number of navigation satellites connected each time. The more satellites the extended user accesses with the navigation satellite and the longer the observation arcs are, the higher the measurement precision is. However, the time slot resources for navigation satellite links are limited. Increasing the number of measurement satellites and arcs can burden the navigation satellite links themselves, affecting their normal functions. Therefore, it is necessary to analyze the impact of observation arcs and time slots on orbit-determination precision. The simulation scenario is set for GEO orbit extended users, with initial orbital errors and clock offsets set at 10 km and 5 ms, respectively. The navigation satellites with the best position dilution of precision (PDOP) values are selected for building the link in each link establishment cycle. According to the internal operation strategy of the constellation, a maximum of eight time slot resources per minute are allowed for extended users to use without affecting its own operation. Observations are made for 1 h per day, with three, four and eight link building time slots per minute. Orbit determination and forecasting are conducted using 2 days and 1 day of observation data, respectively, for 24 h and 70 h forecasts, and the maximum three-axis errors are statistically forecasted for 24 h. Orbit determination is performed with 1 h of daily observation and eight time slots per minute, using 1 day of observation data. The results of the orbit-determination simulation are shown in Figure 6. Here, R represents the radial component, T represents the component along the motion trajectory direction, N represents the normal component perpendicular to R and T, and Three-D represents three-dimensional component, respectively. The simulation indicates that the orbit error for a 24 h forecast is 1500 m, and the orbit error for a 72 h forecast is more than 5000 m.  
Observations are made for 1 h each day, with four time slots per minute, using data from a 2 day observation period, and calculations are performed every hour with a sliding window, as shown in Figure 7. The simulation results indicate that the predicted 24 h orbit error is 80 m, and the predicted 72 h orbit error is 205 m.  
Figure 6: One-hour daily observation with 8 time slots per minute, for a 1 day period; the 72 h orbit error chart. Observations are made for 1 h each day, with 3 time slots per minute, using data from a 2 day observation period, and calculations are performed every hour with a sliding window, as shown in Figure 8. The simulation results indicate that the predicted 24 h orbit error is 140 m, and the predicted 72 h orbit error is nearly 300 m.  
We have compiled the simulation results under different conditions, as shown in Table 1. The extended users utilize inter-satellite links to collect unidirectional ranging values, employing a unidirectional orbit-determination strategy. Observations are made for 1 h each day, with four time slots per minute, over a 2 day observation period.