# New Orbit Determination Method for GEO Satellites Based on BeiDou Short-Message Communication Ranging

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## Abstract

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## 1. Introduction

## 2. Measurement Model of RDSS

## 3. Orbit Determination Method for GEO Satellite Based on RDSS Data

#### 3.1. Principles of Orbit Determination

#### 3.2. Principles of Calibrating Time Delay for RDSS Equipments Based on SLR Data

#### 3.3. Program Design

## 4. Experiment and Analysis

#### 4.1. Accuracy Analysis of RDSS Time Delay

#### 4.2. Observation Residuals of RDSS Data

#### 4.3. Overlap Orbit Differences (OOD)

#### The OOD Comparisons in the Orbital Arc

#### 4.4. Orbit Accuracy Analysis in Radial Direction Based on the SLR Data

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Yang, Y.; Mao, Y.; Sun, B. Basic performance and future developments of BeiDou global navigation satellite system. Satell. Navig.
**2020**, 1, 1–8. [Google Scholar] [CrossRef] - Yang, Y.; Yang, Y.; Hu, X.; Tang, C.; Zhao, L.; Xu, J. Comparison and analysis of two orbit determination methods for BDS-3 satellites. Acta Geod. Cartogr. Sin.
**2019**, 48, 831–839. [Google Scholar] - Yang, Y.; Gao, W.; Guo, S.; Mao, Y.; Yang, Y. Introduction to BeiDou-3 navigation satellite system. Navig. J. Inst. Navig.
**2019**, 66, 7–18. [Google Scholar] [CrossRef] - Tan, S. Innovative development and forecast of BeiDou system. Acta Geod. Et Cartogr. Sin.
**2017**, 46, 1284–1289. [Google Scholar] - Tan, S. The Engineering of Satellite Navigation and Positioning; National Defense Industry Press: Arlington, VA, USA, 2011; Volume 1, pp. 12–27. [Google Scholar]
- Tan, S. The Comprehensive RDSS Global Position and Report System; National Defense Industry Press: Arlington, VA, USA, 2011; Volume 1, pp. 26–32. [Google Scholar]
- Tan, S. Theory and application of comprehensive RDSS position and report. Acta Geod. Cartogr. Sin.
**2009**, 38, 1–5. [Google Scholar] - Zheng, J. Design of general aviation emergency communication, surveillance and rescue service system based on RDSS. Mod. Navig.
**2016**, 1, 1–5. [Google Scholar] - Li, X.; Zhou, J.; Hu, X.; Liu, L.; Guo, R.; Zhou, S. Orbit determination and prediction for Beidou GEO satellites at the time of the spring/autumn equinox. Sci. China Phys. Mech. Astron.
**2015**, 58, 089501. [Google Scholar] [CrossRef] - Li, X.; Guo, R.; Hu, X.; Tang, C.; Wu, S.; Chang, Z.; Liu, S. Construction of a BDSPHERE solar radiation pressure model for BeiDou GEOs at vernal and autumn equinox periods. Adv. Space Res.
**2018**, 62, 1717–1727. [Google Scholar] [CrossRef] - Zhou, S.; Hu, X.; Wu, B. Orbit Determination and Time Synchronization for a GEO/IGSO Satellite Navigation Constellation with Regional Tracking Network. Sci. China Phys. Mech. Astron.
**2011**, 54, 1089–1097. [Google Scholar] [CrossRef] - Tang, C.; Hu, X.; Zhou, S.; Guo, R.; He, F.; Liu, L.; Zhu, L.; Li, X.; Wu, S.; Zhao, G.; et al. Improvement of orbit determination accuracy for Beidou Navigation Satellite System with Two-way Satellite Time Frequency Transfer. Adv. Space Res.
**2016**, 58, 1390–1400. [Google Scholar] [CrossRef] - Chen, J.; Hu, X.; Tang, C.; Zhou, S.; Yang, Y.; Pan, J.; Ren, H.; Ma, Y.; Tian, Q.; Wu, B.; et al. SIS accuracy and service performance of the BDS-3 basic system. Sci. China Phys. Mech. Astron.
**2020**, 63, 269511. [Google Scholar] [CrossRef] - Yang, Y.; Yang, Y.; Hu, X.; Chen, J.; Guo, R.; Tang, C.; Zhou, S.; Zhao, L.; Xu, J. Inter-Satellite Link Enhanced Orbit Determination for BeiDou-3. J. Navig.
**2020**, 73, 115–130. [Google Scholar] [CrossRef] - Li, X.; Zhu, Y.; Zheng, K.; Yuan, Y.; Liu, G.; Xiong, Y. Precise orbit and clock products of Galileo, BDS and QZSS from MGEX since 2018: Comparison and PPP validation. Remote Sens.
**2020**, 12, 1415. [Google Scholar] [CrossRef] - Lv, Y.; Geng, T.; Zhao, Q.; Xie, X.; Zhou, R. Initial assessment of BDS-3 preliminary system signal-in-space range error. GPS Solut.
**2020**, 24, 16. [Google Scholar] [CrossRef] - Wang, C.; Zhao, Q.; Guo, J.; Liu, J.; Chen, G. The contribution of intersatellite links to BDS-3 orbit determination: Model refinement and comparisons. Navigation
**2019**, 66, 71–82. [Google Scholar] [CrossRef] - Li, X.; Zhou, J.; Guo, R. High-precision orbit prediction and error control techniques for COMPASS navigation satellite. Chin. Sci. Bull.
**2014**, 59, 2841–2849. [Google Scholar] [CrossRef] - Xing, N.; Tang, C.; Li, X.; Zhang, T.; Ren, H.; Guo, R.; Hu, X. Precision analysis of BDS-3 GEO satellite orbit determination using RDSS. Sci. China Phys. Mech. Astron.
**2021**, 51, 019510. [Google Scholar] - Li, X.; Hu, X.; Guo, R.; Tang, C.; Zhou, S.; Liu, S.; Chen, J. Orbit and Positioning Accuracy for the New Generation Beidou Satellites during the Earth Eclipsing Period. J. Navig.
**2018**, 71, 1069–1087. [Google Scholar] [CrossRef] - Xing, N.; Su, R.; Zhou, J.; Hu, X.; Gong, X.; Liu, L.; He, F.; Guo, R.; Ren, H.; Hu, G. Analysis of RDSS positioning accuracy based on RNSS wide area differential technique. Sci. China Phys. Mech. Astron.
**2013**, 56, 1995–2001. [Google Scholar] [CrossRef] - Yuan, Y.; Huang, J.; Wu, P. Research on the method of satellite selecting in BDS TDOA position reporting. J. Navig. Position.
**2014**, 2, 15. [Google Scholar] - Yuan, Y.; Huang, J.; Tao, J. A Beidou RDSS positioning model and its error analysis without elevation. Comput. Appl. Softw.
**2017**, 34, 114–118. [Google Scholar] - Li, X.; Hu, X.; Guo, R.; Tang, C.; Liu, S.; Huang, S.; Xin, J.; Pu, J.; Chen, J. A new time delay calibration method to improve the service performance of RDSS in the BDS. Adv. Space Res.
**2020**, 66, 2365–2377. [Google Scholar] [CrossRef] - Pang, J.; Zhang, Y.; Zhan, J.; Ou, G. Research on key techniques of the Beidou RDSS receiver test system. J. Astronaut. Metrol. Meas.
**2016**, 36, 95–100. [Google Scholar] - Liang, G. Research on EIRP calibration method of RDSS closed-loop test system. Foreign Electron. Meas. Technol.
**2017**, 36, 18–20. [Google Scholar] - Montenbruck, O.; Steigenberger, P.; Hauschild, A. Broadcast versus precise ephemerides: A multi-GNSS perspective. GPS Solut.
**2015**, 19, 321–333. [Google Scholar] [CrossRef] - Steigenberger, P.; Hugentobler, U.; Hauschild, A.; Montenbruck, O. Orbit and clock analysis of Compass GEO and IGSO satellites. J. Geod.
**2013**, 87, 515–525. [Google Scholar] [CrossRef] - Montenbruck, O.; Steigenberger, P.; Prange, L.; Deng, Z.; Zhao, Q.; Perosanz, F.; Romero, I.; Noll, C.; Stürze, A.; Weber, G. The Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS)–achievements, prospects and challenges. Adv. Space Res.
**2017**, 59, 1671–1697. [Google Scholar] [CrossRef]

**Figure 5.**Evaluation of the OOD comparisons in the orbital arc. The red arc segments represent the overlapping arc segments.4.3.2. The OOD Comparisons in the 2-h Orbital Prediction Arc.

**Figure 6.**Evaluation of the OOD comparisons in the 2-h orbital prediction arc. The red arc segments represent the overlapping arc segments.

POD Methods by RDSS and SLR Data | |
---|---|

Satellite | 8 GEO: C01, C02, C03, C04, C05 in BDS-2 system C59, C60, C61 in BDS-3 system |

Stations | Seven RDSS calibration stations deployed in Beijing, Sichuan, Hainan, Southeast China, and Northeast China, and two in Xinjiang One SLR station: Beijing |

Arc length | 3 days, sampling interval: RDSS data: 60 s SLR data: 1 s |

observation | RDSS data in Seven RDSS calibration stations SLR data in Beijing station |

Estimated parameter | GEO Initial orbit of the satellite, solar radiation pressure parameters and RDSS equipment time delay parameters |

Parameter estimation method | Least squares algorithm |

Gravitational field model | EGM 2008 12 × 12 |

Sun, Moon gravity and the gravitational force of the other planets | Jet Propulsion Laboratory Development Ephemeris 405 (JPL DE405) |

Solar radiation pressure (SRP) | An empirical SRP model which is similar to BERNESE ECOM 9 parameter model |

Solid tides, ocean tide perturbation | IERS Convention 2003 |

Precession and nutation | IAU2000R06 |

EOP parameters | Constraints to the International Earth Rotation and Reference Systems Service (IERS) C04 model |

Satellites | R | T | N | Positions | SISRE (Orbit) |
---|---|---|---|---|---|

C01 | 0.47 | 6.05 | 1.81 | 6.33 | 0.74 |

C02 | 0.41 | 5.35 | 1.74 | 5.64 | 0.65 |

C03 | 0.38 | 5.37 | 1.62 | 5.63 | 0.63 |

C05 | 0.43 | 6.97 | 0.63 | 7.01 | 0.76 |

C59 | 0.48 | 5.99 | 1.86 | 6.29 | 0.74 |

C60 | 0.39 | 5.32 | 1.77 | 5.62 | 0.64 |

C61 | 0.34 | 5.30 | 1.59 | 5.54 | 0.60 |

Mean Values | 0.41 | 5.76 | 1.57 | 6.01 | 0.68 |

Satellites | R | T | N | Positions | SISRE (Orbit) |
---|---|---|---|---|---|

C01 | 0.56 | 6.73 | 2.25 | 7.12 | 0.85 |

C02 | 0.53 | 6.49 | 2.78 | 7.09 | 0.82 |

C03 | 0.40 | 5.55 | 2.54 | 6.12 | 0.68 |

C05 | 0.58 | 7.91 | 2.56 | 8.34 | 0.94 |

C59 | 0.57 | 6.77 | 2.28 | 7.17 | 0.86 |

C60 | 0.51 | 6.46 | 2.74 | 7.03 | 0.81 |

C61 | 0.36 | 5.47 | 2.5 | 6.03 | 0.65 |

Mean Values | 0.50 | 6.48 | 2.52 | 6.99 | 0.80 |

**Table 4.**Orbit accuracy in Short-arc orbit determination for GEO satellites based on RDSS data (unit: m).

Satellites | R | T | N | Positions | SISRE (Orbit) |
---|---|---|---|---|---|

C01 | 1.95 | 8.76 | 5.33 | 10.44 | 2.16 |

C02 | 2.21 | 9.78 | 6.05 | 11.71 | 2.44 |

C03 | 2.14 | 9.32 | 6.14 | 11.29 | 2.36 |

C04 | 2.80 | 10.14 | 7.60 | 12.98 | 3.02 |

C05 | 2.78 | 10.06 | 7.55 | 12.88 | 3.00 |

C59 | 1.90 | 8.65 | 5.13 | 10.23 | 2.10 |

C60 | 1.78 | 8.14 | 4.89 | 9.66 | 1.97 |

C61 | 1.67 | 8.13 | 5.03 | 9.71 | 1.88 |

Mean values | 2.15 | 9.12 | 5.97 | 11.11 | 2.37 |

Satellites | 2 July 2019 | 1 June to 31 July 2021 |
---|---|---|

C01 | 0.55 | 0.56 |

C02 | 0.57 | 0.54 |

C03 | 0.51 | 0.50 |

C04 | - | 0.55 |

C05 | 0.62 | 0.57 |

Mean values | 0.56 | 0.54 |

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**MDPI and ACS Style**

Li, X.; Guo, R.; Chen, J.; Liu, S.; Chang, Z.; Xin, J.; Guo, J.; Tian, Y. New Orbit Determination Method for GEO Satellites Based on BeiDou Short-Message Communication Ranging. *Remote Sens.* **2022**, *14*, 4602.
https://doi.org/10.3390/rs14184602

**AMA Style**

Li X, Guo R, Chen J, Liu S, Chang Z, Xin J, Guo J, Tian Y. New Orbit Determination Method for GEO Satellites Based on BeiDou Short-Message Communication Ranging. *Remote Sensing*. 2022; 14(18):4602.
https://doi.org/10.3390/rs14184602

**Chicago/Turabian Style**

Li, Xiaojie, Rui Guo, Jianbing Chen, Shuai Liu, Zhiqiao Chang, Jie Xin, Jinglei Guo, and Yijun Tian. 2022. "New Orbit Determination Method for GEO Satellites Based on BeiDou Short-Message Communication Ranging" *Remote Sensing* 14, no. 18: 4602.
https://doi.org/10.3390/rs14184602