# Precise Orbit Determination and Maneuver Assessment for TH-2 Satellites Using Spaceborne GPS and BDS2 Observations

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## Abstract

**:**

## 1. Introduction

## 2. TH-2 Spaceborne GNSS Data Assessment

#### 2.1. Spaceborne Receiver Feature

#### 2.2. Tracking Ability of GNSS Satellites

#### 2.3. Quality of GNSS Observations

#### 2.3.1. Carrier-to-Noise Ratio

_{0}), which shows the ratio of the carrier signal power to the noise power in a 1 Hz bandwidth [25]. Figure 5 indicates that the average C/N

_{0}values of all signals increase as the elevation angle increases. For the GPS, the C/N

_{0}values of the L1 frequency are larger than those of the L2 at all elevations, which is attributed to the differences in their tracking method. For the BDS2, the B3 frequency has about 2–4 dB∙Hz larger C/N

_{0}values than the B1. In addition, it can be noted that the C/N

_{0}values for the MEOs are slightly larger than for the GEOs and IGSOs, which may be due to the higher free-space loss of the GEOs and IGSOs than for the MEOs.

#### 2.3.2. Pseudorange Multipath Combination

#### 2.3.3. Noise Level of Carrier Phase

## 3. POD Strategy

## 4. Maneuver Assessment and POD Results

#### 4.1. Maneuver Assessment by POD

#### 4.2. POD Performance of Single GNSS

#### 4.3. GPS and BDS2 Fused Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Yang, C. LM-4B sends Tianhui 2 satellite into orbit. Aerosp. China
**2019**, 20, 59. [Google Scholar] - Lou, L.; Liu, Z.; Zhang, H.; Qian, F.; Huang, Y. TH-2 satellite engineering design and implementation. Acta Geod. Car-Tographica Sin.
**2020**, 49, 1252–1264. [Google Scholar] [CrossRef] - Qian, F.; Chen, G.; Lu, J.; Chen, X.; Lou, L.; Jiang, T.; Liu, W.; Wang, S. Correcting method of slant-range error for the TH-2 satellites. Remote. Sens. Lett.
**2021**, 12, 142–149. [Google Scholar] [CrossRef] - Birmingham, W.P.; Miller, B.L.; Stein, W.L. Experimental Results of Using the GPS for Landsat 4 Onboard Navigation. Navigation
**1983**, 30, 244–251. [Google Scholar] [CrossRef] - Kang, Z.; Tapley, B.; Bettadpur, S.; Ries, J.; Nagel, P.; Pastor, R. Precise orbit determination for the GRACE mission using only GPS data. J. Geod.
**2006**, 80, 322–331. [Google Scholar] [CrossRef] - Ijssel, J.V.D.; da Encarnacao, J.T.; Doornbos, E.; Visser, P. Precise science orbits for the Swarm satellite constellation. Adv. Space Res.
**2015**, 56, 1042–1055. [Google Scholar] [CrossRef] - Moon, Y.; Koenig, R.; Michalak, G.; Rothacher, M. Precise orbit and baseline determination for TerraSAR-X and TanDEM-X. In Proceedings of the 2008 IEEE International Geoscience and Remote Sensing Symposium, Boston, MA, USA, 7–11 July 2008. [Google Scholar]
- Arnold, D.; Montenbruck, O.; Hackel, S.; Sośnica, K. Satellite laser ranging to low Earth orbiters: Orbit and network validation. J. Geod.
**2018**, 93, 2315–2334. [Google Scholar] [CrossRef] [Green Version] - Li, M.; Li, W.; Shi, C.; Jiang, K.; Guo, X.; Dai, X.; Meng, X.; Yang, Z.; Yang, G.; Liao, M. Precise orbit determination of the Fengyun-3C satellite using onboard GPS and BDS observations. J. Geod.
**2017**, 91, 1313–1327. [Google Scholar] [CrossRef] [Green Version] - Xiong, C.; Lu, C.; Zhu, J.; Ding, H. Orbit determination using real tracking data from FY3C-GNOS. Adv. Space Res.
**2017**, 60, 543–556. [Google Scholar] [CrossRef] - Li, X.; Zhang, K.; Meng, X.; Zhang, Q.; Zhang, W.; Li, X.; Yuan, Y. LEO–BDS–GPS integrated precise orbit modeling using FengYun-3D, FengYun-3C onboard and ground observations. GPS Solut.
**2020**, 24, 48. [Google Scholar] [CrossRef] - Qing, Y.; Lin, J.; Liu, Y.; Dai, X.; Lou, Y.; Gu, S. Precise Orbit Determination of the China Seismo-Electromagnetic Satellite (CSES) Using Onboard GPS and BDS Observations. Remote Sens.
**2020**, 12, 3234. [Google Scholar] [CrossRef] - Lou, Y.; Zheng, F.; Gu, S.; Wang, C.; Guo, H.; Feng, Y. Multi-GNSS precise point positioning with raw single-frequency and dual-frequency measurement models. GPS Solut.
**2015**, 20, 849–862. [Google Scholar] [CrossRef] - Zhao, W.; Chen, H.; Gao, Y.; Jiang, W.; Liu, X. Evaluation of Inter-System Bias between BDS-2 and BDS-3 Satellites and Its Impact on Precise Point Positioning. Remote Sens.
**2020**, 12, 2185. [Google Scholar] [CrossRef] - Zeng, A.; Yang, Y.; Ming, F.; Jing, Y. BDS–GPS inter-system bias of code observation and its preliminary analysis. GPS Solut.
**2017**, 48, 1573–1581. [Google Scholar] [CrossRef] - Cai, Y.; Bai, W.; Wang, X.; Sun, Y.; Du, Q.; Zhao, D.; Meng, X.; Liu, C.; Xia, J.; Wang, D.; et al. In-orbit performance of GNOS on-board FY3-C and the enhancements for FY3-D satellite. Adv. Space Res.
**2017**, 60, 2812–2821. [Google Scholar] [CrossRef] - Jäggi, A.; Montenbruck, O.; Moon, Y.; Wermuth, M.; König, R.; Michalak, G.; Bock, H.; Bodenmann, D. Inter-agency comparison of TanDEM-X baseline solutions. Adv. Space Res.
**2012**, 50, 260–271. [Google Scholar] [CrossRef] - Allende-Alba, G.; Montenbruck, O.; Ardaens, J.-S.; Wermuth, M.; Hugentobler, U. Estimating maneuvers for precise relative orbit determination using GPS. Adv. Space Res.
**2017**, 59, 45–62. [Google Scholar] [CrossRef] - Beutler, G.; Jäggi, A.; Hugentobler, U.; Mervart, L. Efficient satellite orbit modelling using pseudo-stochastic parameters. J. Geod.
**2006**, 80, 353–372. [Google Scholar] [CrossRef] [Green Version] - Yoon, Y.; Montenbruck, O.; Kirschner, M. Precise maneuver calibration for remote sensing satellites. In Proceedings of the 19th international symposium on space flight dynamics, Kanazawa, Japan, 4–11 June 2006; pp. 607–612. [Google Scholar]
- Ju, B.; Gu, D.; Herring, T.A.; Allende-Alba, G.; Montenbruck, O.; Wang, Z. Precise orbit and baseline determination for maneuvering low earth orbiters. GPS Solut.
**2015**, 21, 53–64. [Google Scholar] [CrossRef] [Green Version] - Woo, K. Optimum Semi-Codeless Carrier Phase Tracking of L2. NAVIGATION. J. Inst. Navig.
**2000**, 47, 82–99. [Google Scholar] [CrossRef] - Montenbruck, O.; Garcia-Fernandez, M.; Williams, J. Performance comparison of semicodeless GPS receivers for LEO satellites. GPS Solut.
**2006**, 10, 249–261. [Google Scholar] [CrossRef] - Yang, Y.; Xu, Y.; Li, J.; Yang, C. Progress and performance evaluation of BeiDou global navigation satellite system: Data analysis based on BDS-3 demonstration system. Sci. China Earth Sci.
**2018**, 61, 614–624. [Google Scholar] [CrossRef] - Teunissen, P.J.; Kleusberg, A. GPS for Geodesy; Springer: Berlin/Heidelberg, Germany, 1998. [Google Scholar]
- Zhang, X.; Wu, M.; Liu, W.; Li, X.; Yu, S.; Lu, C.; Wickert, J. Initial assessment of the COMPASS/BeiDou-3: New-generation navigation signals. J. Geod.
**2017**, 91, 1225–1240. [Google Scholar] [CrossRef] - Wanninger, L.; Beer, S. BeiDou satellite-induced code pseudorange variations: Diagnosis and therapy. GPS Solut.
**2015**, 19, 639–648. [Google Scholar] [CrossRef] [Green Version] - Pan, L.; Guo, F.; Ma, F. An Improved BDS Satellite-Induced Code Bias Correction Model Considering the Consistency of Multipath Combinations. Remote Sens.
**2018**, 10, 1189. [Google Scholar] [CrossRef] [Green Version] - Montenbruck, O.; Kroes, R. In-flight performance analysis of the CHAMP BlackJack GPS Receiver. GPS Solut.
**2003**, 7, 74–86. [Google Scholar] [CrossRef] - Wu, S.C.; Yunck, T.P.; Thornton, C.L. Reduced-dynamic technique for precise orbit determination of low earth satellites. J. Guid. Control. Dyn.
**1991**, 14, 24–30. [Google Scholar] [CrossRef] - Gu, D.; Ju, B.; Liu, J.; Tu, J. Enhanced GPS-based GRACE baseline determination by using a new strategy for ambiguity resolution and relative phase center variation corrections. Acta Astronaut.
**2017**, 138, 176–184. [Google Scholar] [CrossRef] - Tian-Yi, H.; Qing-Lin, Z. Adams-Cowell integrator with a first sum. Chin. Astron. Astrophys.
**1993**, 17, 205–213. [Google Scholar] [CrossRef] - Zhang, Q.; Liu, L. The comparison between Adams-Cowell method and KSG integrator. Publ. Purple Mt. Obs.
**1998**, 17, 19–27. [Google Scholar] - Prince, P.; Dormand, J. High order embedded Runge-Kutta formulae. J. Comput. Appl. Math.
**1981**, 7, 67–75. [Google Scholar] [CrossRef] [Green Version] - Jäggi, A.; Dach, R.; Montenbruck, O.; Hugentobler, U.; Bock, H.; Beutler, G. Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination. J. Geod.
**2009**, 83, 1145–1162. [Google Scholar] [CrossRef] [Green Version] - Steigenberger, P.; Montenbruck, O. Consistency of MGEX Orbit and Clock Products. Engineering
**2020**, 6, 898–903. [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] - Uhlemann, M.; Gendt, G.; Ramatschi, M.; Deng, Z. GFZ Global Multi-GNSS Network and Data Processing Results. In Gravity, Geoid and Height Systems; Springer: Singapore, 2015; pp. 673–679. [Google Scholar]
- Rebischung, P.; Schmid, R. IGS14/igs14.atx: A new framework for the IGS products. In Proceedings of the American Geo-physical Union Fall Meeting 2016, San Francisco, CA, USA, 12–16 December 2016. [Google Scholar]
- Dilssner, F.; Springer, T.; Schönemann, E.; Enderle, W. Estimation of satellite antenna phase center corrections for BeiDou. In Proceedings of the IGS Workshop, Pasadena, CA, USA, 23–27 June 2014. [Google Scholar]
- Wu, J.-T.; Wu, S.C.; Hajj, G.A.; Bertiger, W.I.; Lichten, S.M. Effects of antenna orientation on GPS carrier phase. In Proceedings of the AAS/AIAA Astrodynamics Conference, Hilton Head, SC, USA, 10–12 August 1992; pp. 1647–1660. [Google Scholar]
- Wang, N.; Yuan, Y.; Li, Z.; Montenbruck, O.; Tan, B. Determination of differential code biases with multi-GNSS observations. J. Geod.
**2016**, 90, 209–228. [Google Scholar] [CrossRef] - Ries, J.C.; Eanes, R.; Kang, Z.; Ko, U.; McCullough, C.; Nagel, P.; Bettadpur, S.; Pie, N.; Poole, S.; Richter, T.; et al. The Devel-opment And Evaluation of The Global Gravity Model GGM05; Center for Space Reseach of University of Texas: Austin, TX, USA, 2016. [Google Scholar]
- Petit, G.; Luzum, B. IERS Conventions (2010). IERS Tech. Note
**2010**, 36, 1. [Google Scholar] - Standish, E.M. JPL Planetary and Lunar Ephemerides, DE405/LE405. Interoffice Memorandum IOM 312, F-98-048. Jet Propulsion Laboratory, Pasadena. 1998. Available online: https://www.iers.org/IERS/EN/Publications/TechnicalNotes/tn36.html (accessed on 2 September 2021).
- Jacchia, L.G. Revised Static Models of the Thermosphere and Exosphere with Empirical Profiles; Smithsonian Astrophysical Observatory: Cambridge, MA, USA, 1971. [Google Scholar]
- Li, X.; Zhang, K.; Meng, X.; Zhang, W.; Zhang, Q.; Zhang, X.; Li, X. Precise Orbit Determination for the FY-3C Satellite Using Onboard BDS and GPS Observations from 2013, 2015, and 2017. Engineering
**2019**, 6, 904–912. [Google Scholar] [CrossRef] - Wang, L.; Xu, B.; Fu, W.; Chen, R.; Li, T.; Han, Y.; Zhou, H. Centimeter-Level Precise Orbit Determination for the Luojia-1A Satellite Using BeiDou Observations. Remote Sens.
**2020**, 12, 2063. [Google Scholar] [CrossRef] - Montenbruck, O.; van Helleputte, T.; Kroes, R.; Gill, E. Reduced dynamic orbit determination using GPS code and carrier measurements. Aerosp. Sci. Technol.
**2005**, 9, 261–271. [Google Scholar] [CrossRef] - Van Diggelen, F. Method and Apparatus for Time-Free Processing of GPS Signals. U.S. Patent No. 6,417,801, 9 July 2002. [Google Scholar]
- Montenbruck, O.; Steigenberger, P.; Hauschild, A. Comparing the ‘Big 4′-A User’s View on GNSS Performance. In Proceedings of the 2020 IEEE/ION Position, Location and Navigation Symposium (PLANS), Portland, OR, USA, 20–23 April 2020; pp. 407–418. [Google Scholar]

**Figure 3.**Average number of GPS (

**left panel**) and BDS2 (

**right panel**) satellites observed along TH-2A orbits from DOY 305 to 310 in 2019.

**Figure 4.**Statistics of the average number of available GPS and BDS2 satellites per epoch for TH-2A and TH-2B.

**Figure 6.**Multipath combinations of GPS and BDS2 pseudorange observations from TH-2A as a function of the elevation angle.

**Figure 7.**Noise levels of GPS and BDS2 carrier phase observations from TH-2A as a function of the elevation angle.

**Figure 8.**LC residuals of GPS-based POD for TH-2A without maneuver estimation (

**top panel**) and those with maneuver estimation (

**bottom panel**) on DOY 314, 2019. The vertical bars denote the centers of the thrust execution periods. Residuals beyond ±6 cm are not shown in the top panel.

**Figure 9.**LC residuals of BDS2-based POD for TH-2A without maneuver estimation (

**top panel**) and those with maneuver estimation (

**bottom panel**) on DOY 314, 2019. The vertical bars denote the centers of thrust execution periods. Residuals beyond ±6 cm are not shown in the top panel.

**Figure 11.**Orbit differences between BDS2- and GPS-based POD during the arcs with and without BDS2 data.

**Figure 12.**Orbit differences between BDS2- and GPS-based POD in radial, along-track, normal, and 3D directions for TH-2A (

**top panel**) and TH-2B (

**bottom panel**).

**Figure 13.**Clock offsets of TH-2A (on DOY 308, 2019) obtained from POD based on GPS observations (

**top panel**) and BDS2 observations without correction (

**bottom panel**). Blue and red points show the estimated clock offsets when radar is in operation and powered off, respectively.

**Figure 14.**Cumulative percentages of the PDOP values of GPS-only and GPS + BDS2 along the trajectories of TH-2A.

**Figure 15.**Differences of GPS and GC combined SPP solutions with respect to GPS-based POD when the PDOP values of GPS exceed 3. (

**top panel**) is TH-2A and (

**bottom panel**) is TH-2B.

**Figure 16.**3D RMS of overlap comparisons of BDS2-only, GPS-only, and GC combined POD for TH-2A (

**top panel**) and TH-2B (

**bottom panel**).

Models | Description |
---|---|

Observation models | |

Observation | Undifferenced ionosphere-free pseudorange and carrier phase; |

Weight | A priori sigma 2 m for the pseudorange and 0.5 cm for the carrier phase observations, with function 2 sin(θ) when the elevation angle θ is below 30°; |

Orbit arc length/Interval | 30 h/10 s; |

GNSS ephemeris and clock | GeoForschungsZentrum (GFZ) products [38]; |

GPS satellite PCO/PCV | igs14_2062.atx [39]; |

BDS2 satellite PCO/PCV | Models from the European Space Agency (ESA) [40]; |

Receiver antenna PCO | Nominal values; |

Receiver antenna PCV | In-flight estimated PCV maps; |

LEO attitude | Star tracker data; |

Antenna phase windup | Phase wind-up correction [41]; |

DCB correction | Chinese Academy of Sciences (CAS) multi-GNSS differential code biases (DCB) products [42]; |

Dynamical models | |

Gravity field | GGM05S(120 × 120) [43]; |

Solid-earth, pole, and ocean tides | IERS 2010 [44]; |

Third body gravity | Luni-solar-planetary gravity [45]; |

Relativity | Only the Schwarzschild item; |

Atmospheric drag | Jacchia 71 density model [46], one drag coefficient per 3 h; |

Solar radiation pressure | Cannonball model, one solar radiation coefficient per 30 h; |

Empirical acceleration | Constant accelerations in radial direction; piecewise linear accelerations at 15 min interval in along-track and normal directions; |

Maneuver acceleration | Constant thrust model over predefined maneuver durations. |

**Table 2.**Average RMS of PC and LC residuals of GPS- and BDS2-based POD for TH-2A (without maneuver estimation), TH-2A (with maneuver estimation), and maneuver-free TH-2B.

Residual | Observation | TH-2A (without Maneuver Estimation) | TH-2A (with Maneuver Estimation) | TH-2B (Maneuver-Free) |
---|---|---|---|---|

LC RMS (cm) | GPS | 0.93 | 0.58 | 0.58 |

BDS2 | 1.53 | 0.58 | 0.58 | |

PC RMS (m) | GPS | 0.84 | 0.81 | 0.81 |

BDS2 | 0.72 | 0.56 | 0.57 |

Sat | Overlap Comparison (cm) | |||
---|---|---|---|---|

Radial | Along-Track | Normal | 3D | |

TH-2A | 0.32 | 0.46 | 0.35 | 0.68 |

TH-2B | 0.31 | 0.46 | 0.33 | 0.66 |

Sat | Region | Orbit Difference (cm) | |||
---|---|---|---|---|---|

Radial | Along-Track | Normal | 3D | ||

TH-2A | Asia-Pacific | 2.75 | 5.51 | 2.30 | 6.57 |

Beyond Asia-Pacific | 2.59 | 7.91 | 3.21 | 8.91 | |

TH-2B | Asia-Pacific | 2.98 | 5.36 | 2.38 | 6.58 |

Beyond Asia-Pacific | 2.53 | 7.65 | 3.12 | 8.64 |

**Table 5.**Average RMS of orbit differences of GPS-only and GC combined SPP solutions with respect to GPS-based POD for TH-2A and TH-2B.

Sat | Solution | Orbit Difference (m) | |||
---|---|---|---|---|---|

Radial | Along-Track | Normal | 3D | ||

TH-2A | GPS SPP | 1.86 | 0.74 | 0.59 | 2.09 |

GC combined SPP | 1.71 | 0.69 | 0.57 | 1.93 | |

TH-2B | GPS SPP | 1.84 | 0.74 | 0.59 | 2.07 |

GC combined SPP | 1.72 | 0.70 | 0.57 | 1.94 |

Residual | Observation | TH-2A | TH-2B |
---|---|---|---|

LC RMS (cm) | GPS | 0.59 | 0.58 |

BDS2 | 0.64 | 0.66 | |

PC RMS (m) | GPS | 0.81 | 0.81 |

BDS2 | 0.53 | 0.55 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, H.; Gu, D.; Ju, B.; Shao, K.; Yi, B.; Duan, X.; Huang, Z.
Precise Orbit Determination and Maneuver Assessment for TH-2 Satellites Using Spaceborne GPS and BDS2 Observations. *Remote Sens.* **2021**, *13*, 5002.
https://doi.org/10.3390/rs13245002

**AMA Style**

Zhang H, Gu D, Ju B, Shao K, Yi B, Duan X, Huang Z.
Precise Orbit Determination and Maneuver Assessment for TH-2 Satellites Using Spaceborne GPS and BDS2 Observations. *Remote Sensing*. 2021; 13(24):5002.
https://doi.org/10.3390/rs13245002

**Chicago/Turabian Style**

Zhang, Houzhe, Defeng Gu, Bing Ju, Kai Shao, Bin Yi, Xiaojun Duan, and Zhiyong Huang.
2021. "Precise Orbit Determination and Maneuver Assessment for TH-2 Satellites Using Spaceborne GPS and BDS2 Observations" *Remote Sensing* 13, no. 24: 5002.
https://doi.org/10.3390/rs13245002