# Centimeter-Level Orbit Determination of GRACE-C Using IGS-RTS Data

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Real-Time Orbit and Clock Recovery

#### 2.1.1. Real-Time Orbit Recovery

#### 2.1.2. Real-Time Clock Recovery

#### 2.2. Clock Evaluation

#### 2.2.1. Coordinate Frame Unification

#### 2.2.2. Time Frame Unification

- 1.
- Trend Error Correction

- 2.
- Systematic Bias Correction

## 3. Accuracy Evaluation of SSR Products

#### 3.1. Integrity

#### 3.2. Continuity

#### 3.3. Accuracy

#### 3.3.1. Orbit Accuracy

#### 3.3.2. Clock Error Accuracy

## 4. Space-Borne POD Experiment and Accuracy Analysis

#### 4.1. Reduced-Dynamic Precise Orbit Determination

#### 4.2. Kinematic Precise Orbit Determination

## 5. Conclusions

- (1)
- By studying the real-time orbit and clock correction products provided by 11 research institutions, including BKG, CAS, CNES, DLR, ESA, GFZ, GMV, IGS, NRC, SHA, and WHU, we concluded that the product integrity of BKG, CAS, and NRC needs to be improved, and the product continuity of NRC and WHU needs to be strengthened.
- (2)
- Compared with IGS final precise products, the numerical results showed that the RTS orbit accuracy of all ACs reached the centimeter level and the RMS in the radial direction was better than 0.02 m. Among the ACs, the orbit accuracy of IGS, SHA, and WHU was relatively high. The real-time clock error STD was 30 ps overall; WHU and CNES performed best, with STDs of 15.65 ps and 16.98 ps, respectively. In addition, the clock error accuracy was related to the Block. It was verified that the accuracy of Block IIR and Block IIR-M was slightly worse than that of Block IIF and Block IIIA.
- (3)
- Using RTS orbit and clock products, the radial accuracy of the GRACE-C space-borne GPS orbit determination based on the reduced-dynamic and kinematic methods reached the centimeter level and the average three-dimensional position accuracy values were 3.8 cm and 10.6 cm, respectively. As expected, the reduced-dynamic orbit was more robust and less affected by product integrity and continuity. It is advised that RTS products are used to carry out large-scale ultra-rapid orbit determinations for LEO satellites in the future.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**The root mean square (RMS) values in the radial (R), along-track (A), and cross-track (C) directions of GPS real-time orbits from different IGS ACs (the mean RMS of orbit errors for all GPS satellites is shown in each subplot).

**Figure 5.**The standard deviations (STDs) of real-time GPS clock errors from different ACs (the mean STD of the clock errors for all GPS satellites is shown in each subplot).

**Figure 6.**Scatterplots of IGS-RTS clock errors: PRN 16, Block IIR (

**a**); PRN 29, Block IIR-M (

**b**); PRN 30, Block IIF (

**c**); and PRN 14, Block IIIA (

**d**).

**Figure 7.**RMS of GRACE-C (GRCC) reduced-dynamic orbit products in the R, A, and C directions from JPL precise orbit ephemeris (POE) (the mean RMS of orbit errors for each AC is shown in each subplot).

**Figure 8.**RMS of GRCC kinematic orbit products in the R, A, and C directions from JPL POE (the mean RMS of the orbit errors for each AC is shown in each subplot).

**Figure 9.**Orbit differences of GRCC kinematic results with JPL POE in the R, A, and C directions: (

**a**) DLR result for DOY 147 of 2022; (

**b**) CAS result for DOY 147 of 2022.

AC | Mount Point | Supported System | Interval for Orbit and Clock Corrections (s) |
---|---|---|---|

BKG | SSRA00BKG0 | G | 60, 5 |

CAS | SSRA00CAS0 | GREC | 5, 5 |

CNE | SSRA00CNE0 | GREC | 5, 5 |

DLR | SSRA00DLR0 | GREC | 30, 5 |

ESA | SSRA00ESA0 | G | 5, 5 |

GFZ | SSRA00GFZ0 | GREC | 5, 5 |

GMV | SSRA00GMV0 | GRE | 5, 5 |

IGS ^{1} | SSRA01IGS0 | G | 5, 5 |

SSRA02IGS0 | GR | 60, 10 | |

SSRA03IGS0 | GREC | 60, 10 | |

NRC | SSRA00NRC0 | G | 5, 5 |

SHA | SSRA00SHA0 | GREC | 5, 5 |

WHU | SSRA00WHU0 | GREC | 5, 5 |

^{1}SSRA01IGS0 is a single-epoch solution; SSRA02IGS0 and SSRA03IGS0 are Kalman filter solutions.

ACs | Block IIR | Block IIR-M | Block IIF | Block IIIA |
---|---|---|---|---|

BKG | 25.02 | 23.88 | 21.67 | 22.96 |

CAS | 31.89 | 30.08 | 22.26 | 22.77 |

CNE | 17.86 | 17.66 | 16.03 | 17.05 |

DLR | 19.34 | 20.93 | 21.09 | 18.65 |

ESA | 19.8 | 19.89 | 17.79 | 19.03 |

GFZ | 26.95 | 24.86 | 21.51 | 21.41 |

GMV | 35.83 | 37.38 | 24.23 | 24.17 |

IGS01 | 36.94 | 43.16 | 23.9 | 22.19 |

NRC | 21.13 | 20.93 | 18.22 | 19.70 |

SHA | 20.88 | 22.19 | 17.42 | 18.47 |

WHU | 16.75 | 16.59 | 14.36 | 15.91 |

Mean | 24.76 | 25.23 | 19.86 | 20.21 |

Reference Frame | Description |
---|---|

Protocol inertial reference system | Geocenter inertial reference system in J2000 |

Precession and nutation model | IAU2000 R06 |

Earth orientation parameter | IERS C04 |

Dynamic model | Description |

N-body gravity | JPL DE421 |

Gravity field of the earth | GOCO06S |

Relativity effect | IERS 2010 Conventions |

Solid tide | IERS 2010 Conventions |

Ocean tide | FES2004 |

Radiation pressure | Empirical force model |

Observation model | Description |

Measurements | L3 P3 undifferenced ionosphere-free |

Arc length and interval | 24 h, 30 s |

Cut-off elevation (°) | 5 |

GPS satellite orbits and clocks | RTS-recovered products |

Receiver antenna PCO/PCV | Pre-calibrated values |

Parameter estimation | Description |

Initial state | Initial position and velocity |

Receiver clock error | Estimated as white noise, one bias per epoch |

Ambiguity | Float solution |

Pseudo-stochastic pulses | One group in the R, A, and C directions every 6 min |

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**MDPI and ACS Style**

Li, D.; Zhou, X.; Li, K. Centimeter-Level Orbit Determination of GRACE-C Using IGS-RTS Data. *Remote Sens.* **2023**, *15*, 1832.
https://doi.org/10.3390/rs15071832

**AMA Style**

Li D, Zhou X, Li K. Centimeter-Level Orbit Determination of GRACE-C Using IGS-RTS Data. *Remote Sensing*. 2023; 15(7):1832.
https://doi.org/10.3390/rs15071832

**Chicago/Turabian Style**

Li, Duoduo, Xuhua Zhou, and Kai Li. 2023. "Centimeter-Level Orbit Determination of GRACE-C Using IGS-RTS Data" *Remote Sensing* 15, no. 7: 1832.
https://doi.org/10.3390/rs15071832