Figures & data
Figure 1. Illustration of DYB (Sun-fixed) and XYZ (body-fixed) orthogonal frames (Rodriguez-Solano, Hugentobler, and Steigenberger Citation2012).
![Figure 1. Illustration of DYB (Sun-fixed) and XYZ (body-fixed) orthogonal frames (Rodriguez-Solano, Hugentobler, and Steigenberger Citation2012).](/cms/asset/a931cce3-652a-4cd2-a7fc-8dfae42554c5/tgsi_a_2071177_f0001_c.jpg)
Table 1. Values of parameters in the a priori SRP model for BDS GEO satellites (Wang et al. Citation2019; units: nm/s2; angle in degrees).
Figure 2. Distributions of MGEX (blue) and iGMAS (red) stations used in ultra-rapid orbit prediction experiment.
![Figure 2. Distributions of MGEX (blue) and iGMAS (red) stations used in ultra-rapid orbit prediction experiment.](/cms/asset/cefb23a1-4f59-44cf-a224-09e392412752/tgsi_a_2071177_f0002_c.jpg)
Table 2. Orbit dynamic models.
Figure 3. Correlations between empirical along-track acceleration and SRP parameters with 24-h, 48-h, and 72-h orbit arc lengths. Other BDS GEO satellites show similar performances.
![Figure 3. Correlations between empirical along-track acceleration and SRP parameters with 24-h, 48-h, and 72-h orbit arc lengths. Other BDS GEO satellites show similar performances.](/cms/asset/9b9eb339-10d2-4e76-8b24-b55b68190b3c/tgsi_a_2071177_f0003_c.jpg)
Figure 5. Daily OBDs time series of observed orbits for strategies 1, 2, and 3 in the radial (R), cross-track (C), and along-track (A) directions for BDS C01 satellite (unit: m). The gray blocks indicate the satellite eclipse seasons. The black lines indicate the elevation angle of the Sun above the satellite orbital plane. Other BDS GEO satellites showed similar performance.
![Figure 5. Daily OBDs time series of observed orbits for strategies 1, 2, and 3 in the radial (R), cross-track (C), and along-track (A) directions for BDS C01 satellite (unit: m). The gray blocks indicate the satellite eclipse seasons. The black lines indicate the elevation angle of the Sun above the satellite orbital plane. Other BDS GEO satellites showed similar performance.](/cms/asset/b03e620e-b193-4fa8-a90b-183ff4905182/tgsi_a_2071177_f0005_c.jpg)
Table 3. The daily OBDs RMS values of BDS GEO satellites.
Figure 6. SLR residual time series of observed orbits for strategies 1–3 for BDS C01 satellite (unit: m).
![Figure 6. SLR residual time series of observed orbits for strategies 1–3 for BDS C01 satellite (unit: m).](/cms/asset/e9ed6d7a-dd2f-4ad7-b3f1-90fb92efba45/tgsi_a_2071177_f0006_c.jpg)
Table 4. Mean and STD of SLR residuals for observed orbits for BDS C01 satellite (unit: m), as determined by strategies 1–3.
Figure 7. Daily RMS of BDS C01 orbit overlap differences in the radial, cross-track, and along-track directions for the fitting arc lengths of 24-h, 48-h, and 72-h with different strategies. Other BDS GEO satellites show similar performances.
![Figure 7. Daily RMS of BDS C01 orbit overlap differences in the radial, cross-track, and along-track directions for the fitting arc lengths of 24-h, 48-h, and 72-h with different strategies. Other BDS GEO satellites show similar performances.](/cms/asset/461a199f-1cae-4c3f-91ca-727bdfe575c9/tgsi_a_2071177_f0007_c.jpg)
Figure 8. Correlations between SRP parameters and the PX, PY, PZ (satellite position parameter in the X, Y and Z direction of the celestial reference frame) parameters, VX, VY VZ (satellite velocity parameter in the X, Y and Z direction of the celestial reference frame) parameters of 48-h orbit arc length for BDS C01 satellite when β is equal to 21 degrees, parameter correlations of 24-h and 72-h orbit arc length show similar characteristics.
![Figure 8. Correlations between SRP parameters and the PX, PY, PZ (satellite position parameter in the X, Y and Z direction of the celestial reference frame) parameters, VX, VY VZ (satellite velocity parameter in the X, Y and Z direction of the celestial reference frame) parameters of 48-h orbit arc length for BDS C01 satellite when β is equal to 21 degrees, parameter correlations of 24-h and 72-h orbit arc length show similar characteristics.](/cms/asset/dfdf6d5c-96f5-4a7d-a48a-45fabd3c6dc0/tgsi_a_2071177_f0008_b.gif)
Table 5. Average RMS values of all BDS GEO satellites in the three directions and the 3D component for strategies 1–3 with fitting arc lengths of 24-h, 48-h, and 72-h for eclipse (E) and non-eclipse (NE) seasons (unit: m).
Figure 9. Time series of SLR residuals for predicted orbits with 24-h, 48-h, and 72-h fitting arc lengths of BDS C01 satellites (unit: m). Other BDS GEO satellites show similar performances.
![Figure 9. Time series of SLR residuals for predicted orbits with 24-h, 48-h, and 72-h fitting arc lengths of BDS C01 satellites (unit: m). Other BDS GEO satellites show similar performances.](/cms/asset/5408d7c8-1164-4299-979d-a7a7610d9303/tgsi_a_2071177_f0009_c.jpg)
Table 6. Means and STDs of SLR residuals of orbit prediction for the three strategies (unit: m).
Figure 10. Estimated SRP parameters (D0,Y0,B0,BC, and BS) time series with fitting arc lengths of 24-h, 48-h, and 72-h for strategies 1–3 for BDS C01. Other BDS GEO satellites show similar performances.
![Figure 10. Estimated SRP parameters (D0,Y0,B0,BC, and BS) time series with fitting arc lengths of 24-h, 48-h, and 72-h for strategies 1–3 for BDS C01. Other BDS GEO satellites show similar performances.](/cms/asset/257b718e-5616-4b6e-b6db-891fc6265ad1/tgsi_a_2071177_f0010_c.jpg)
Figure 11. Correlations coefficients between the Y0 and BS parameters of BDS C01. The black lines indicate the elevation angle of the Sun.
![Figure 11. Correlations coefficients between the Y0 and BS parameters of BDS C01. The black lines indicate the elevation angle of the Sun.](/cms/asset/eddb305b-7306-4a22-a446-f8aa1a59caa2/tgsi_a_2071177_f0011_c.jpg)