# Impact of Attitude Model, Phase Wind-Up and Phase Center Variation on Precise Orbit and Clock Offset Determination of GRACE-FO and CentiSpace-1

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## Abstract

**:**

## 1. Introduction

## 2. Testing Spacecrafts and Data Collection

#### 2.1. Testing Spacecrafts

#### 2.2. Data Collection and Quality Analysis

## 3. POCD Platform and Strategy

## 4. Results and Discussion

#### 4.1. Impact of Attitude Model

#### 4.1.1. Attitude Modeling

#### 4.1.2. Validation and Discussion

**e**and the user location. The combined orbit and clock SISRE can be expressed by [7,43]

#### 4.2. Impact of Phase Wind-Up

#### 4.2.1. Carrier Phase Wind-Up Effect

#### 4.2.2. Validation and Discussion

#### 4.3. Impact of PCV

#### 4.3.1. Estimation of PCV Maps

#### 4.3.2. Validation and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Average percentage of observed (

**top**) and useful (

**bottom**) GPS satellites for GRCC and CS01.

**Figure 4.**The difference in phase center vectors in CTS frame using nominal and measured attitude. DOY 273, 2018.

**Figure 6.**The difference in GRCC’s clock offset between solutions using nominal and measured attitude.

**Figure 10.**Azimuth-elevation maps of the 5° × 5° PCV (mm) for the ionosphere-free linear combination of the GRCC (

**left**) and CS01 (

**right**).

Model | Description |
---|---|

Measurement model | |

Observation | Non-differentiated ionosphere-free linear combination |

Arc length and interval | 12 h, 10 s |

Weighting strategy | PC (a priori sigma of 1 m), LC (a priori sigma of 1 cm) |

GPS products | CODE final products [34] |

Elevation cut-off angle | 5° |

GNSS PCO and PCV | igs14.atx [35] |

LEO attitude | Discussed |

Phase wind-up | Discussed |

LEO PCO and PCV | Nominal values; Discussed |

Dynamic model | |

Earth gravity | EIGEN_GL04C, 120 × 120 [36] |

N-body | JPL DE405 [37] |

Relativity | IERS 2010 [38] |

Solid earth tide and pole tide | IERS 2010 [38] |

Ocean tides | FES 2004, 30 × 30 [39] |

Solar radiation pressure | Cannonball model [40] |

Atmospheric drag | NRLMSISE-00 [41], piecewise periodical estimation |

Empirical forces | Piecewise periodical estimation of the sin and cos coefficients in the track and normal directions |

Estimated parameters | |

LEO initial state | Position and velocity at the initial state |

Receiver clock | Epoch-wise estimated |

Ambiguities | Floated solution |

Solar coefficients | One per 3 h |

Drag coefficients | One per 3 h |

Empirical coefficients | One per 3 h |

**Table 2.**The RMS of residual and orbital comparison using nominal and measured attitude for GRCC and CS01.

Spacecraft | Solutions | Residual (mm) | Overlap Comparison (cm) | JPL Comparison (cm) | ||||||
---|---|---|---|---|---|---|---|---|---|---|

R | T | N | 3D | R | T | N | 3D | |||

GRCC | Nominal ATT | 7.95 | 0.75 | 1.56 | 1.25 | 2.15 | 2.07 | 2.08 | 1.15 | 3.18 |

Measured ATT | 7.93 | 0.75 | 1.55 | 1.24 | 2.14 | 2.06 | 2.07 | 1.15 | 3.17 | |

CS01 | Nominal ATT | 9.37 | 0.72 | 1.44 | 1.01 | 1.93 | / | / | / | / |

Measured ATT | / | / | / | / | / | / | / | / | / |

Spacecraft | Solutions | Residual (mm) | Overlap Comparison (cm) | JPL Comparison (cm) | ||||||
---|---|---|---|---|---|---|---|---|---|---|

R | T | N | 3D | R | T | N | 3D | |||

GRCC | without PWU | 7.93 | 0.75 | 1.56 | 1.25 | 2.15 | 2.07 | 2.08 | 1.15 | 3.17 |

with PWU | 7.81 | 0.73 | 1.52 | 1.24 | 2.11 | 1.89 | 1.91 | 1.23 | 2.98 | |

CS01 | without PWU | 9.37 | 0.72 | 1.44 | 1.01 | 1.93 | / | / | / | / |

with PWU | 9.31 | 0.71 | 1.39 | 0.98 | 1.88 | / | / | / | / |

Spacecraft | Solutions | Residual (mm) | Overlap Comparison (cm) | JPL Comparison (cm) | ||||||
---|---|---|---|---|---|---|---|---|---|---|

R | T | N | 3D | R | T | N | 3D | |||

GRCC | without PCV | 7.81 | 0.73 | 1.52 | 1.24 | 2.11 | 1.89 | 1.91 | 1.23 | 2.98 |

with PCV | 7.31 | 0.72 | 1.50 | 1.23 | 2.08 | 1.78 | 1.63 | 1.29 | 2.75 | |

CS01 | without PCV | 9.31 | 0.71 | 1.39 | 0.98 | 1.88 | / | / | / | / |

with PCV | 8.55 | 0.65 | 1.28 | 0.95 | 1.72 | / | / | / | / |

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**MDPI and ACS Style**

Yuan, J.; Zhou, S.; Hu, X.; Yang, L.; Cao, J.; Li, K.; Liao, M.
Impact of Attitude Model, Phase Wind-Up and Phase Center Variation on Precise Orbit and Clock Offset Determination of GRACE-FO and CentiSpace-1. *Remote Sens.* **2021**, *13*, 2636.
https://doi.org/10.3390/rs13132636

**AMA Style**

Yuan J, Zhou S, Hu X, Yang L, Cao J, Li K, Liao M.
Impact of Attitude Model, Phase Wind-Up and Phase Center Variation on Precise Orbit and Clock Offset Determination of GRACE-FO and CentiSpace-1. *Remote Sensing*. 2021; 13(13):2636.
https://doi.org/10.3390/rs13132636

**Chicago/Turabian Style**

Yuan, Junjun, Shanshi Zhou, Xiaogong Hu, Long Yang, Jianfeng Cao, Kai Li, and Min Liao.
2021. "Impact of Attitude Model, Phase Wind-Up and Phase Center Variation on Precise Orbit and Clock Offset Determination of GRACE-FO and CentiSpace-1" *Remote Sensing* 13, no. 13: 2636.
https://doi.org/10.3390/rs13132636