# A Method to Determine BeiDou GEO/IGSO Orbital Maneuver Time Periods
## 3 Experimental Validation
### Orbital Maneuver Period Detection
#### 3.2.1 Orbital Maneuver Period Detection for GEO Satellites
Whether or not orbital maneuvers occur, pseudo-range observations are also closer to the real distance between the station and the satellite, which are not influenced by orbit maneuvering. The biases of the red section are significantly greater than normal conditions because the backward predicted orbit is inaccurate before the start time. It gradually decreases because the backward predicted orbit is gradually closer to the real orbit. From Figure 8, it is obvious that the difference between the real orbit and the backward predicted orbit gradually decreases. The backward predicted orbit is correct after the end time of the orbit maneuver. However, the variation of pseudo-range observations is small during the period of orbit maneuvering. Thus, the biases calculated by the backward orbit reach normal levels at the start time of orbit maneuvering. Figure 9 shows the detected end time of orbit maneuvering. The blue marks represent the series before the detected end time, and the red marks represent the series after the detected end time. The biases of the red section are significantly greater than normal conditions because the forward predicted orbit is inaccurate after the end time of maneuvering. It gradually increases because the forward predicted orbit gradually deviates from the real orbit. From Figure 2, it is obvious that the difference between the real orbit and forward predicted orbit gradually increases. The forward predicted orbit is correct before the start time of orbital maneuvering, and the variation of pseudo-range observation is small during the period of orbit maneuvering. Thus, the biases calculated by forward orbit over normal levels mark the end time of orbit maneuvering. Figure 8: Spatial bias of pseudo-range single point positioning (SPP) coordinates on 9 January 2017. Coordinates are calculated by backward predicted orbit using the precise products on the day after orbital maneuvers. The red line is the series before the start time determined of maneuvering. The blue line is the series after the start time determined of maneuvering. Although the biases of SPP using the data of the nearby reference station are consistent with the orbital maneuver period detection results, it cannot be proved that the biases are only caused by the satellite orbit maneuvers. It is necessary to eliminate the influence of common nonmaneuvering errors. Considering that the orbital semimajor axis will change suddenly before and after the orbital maneuver of the satellite [19], this orbital element could be used as evidence to prove that the orbital maneuver period detected is correct. The time series of orbital semimajor axis from the satellite broadcast ephemeris is shown in Figure 10.  
In Figure 10, A is the semimajor axis and the blue points are values of A. The orbital semimajor axis of C01 had several jumps in 2017, caused by the satellite propulsion system changing the original position of the satellite. In the plot on the right, the blue, red, and black marks represent the series of A on days 008, 009, and 010, respectively. Because the position of C01 was changed by orbit maneuvering, the orbital semimajor axis of C01 changed suddenly on days 009. In summary, it can be considered validated that the period (5:05:30 to 5:33:00) of orbit maneuvering for C01 is correct. The correctness of the method proposed for detecting the orbital maneuver period of GEO satellites is also validated in this study. Figure 10: Time series of orbital semimajor axis of C01 in 2017. Graph on the right shows detailed information of the red box (days 008–010) in the plot on the left. Figure 9: Spatial bias of pseudo-range SPP coordinates for 9 January 2017. Coordinates are calculated by forward predicted orbit using the precise products on the day before orbital maneuvers. The blue line is the series before the end time determined of maneuvering. The red line is the series after the end time determined of maneuvering.