# Analysis of BDS-3 Onboard Clocks Based on GFZ Precise Clock Products

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## Abstract

**:**

## 1. Introduction

## 2. Methods and Data Collection

#### 2.1. Data Collection

#### 2.2. Preprocessing for Clock Offsets

#### 2.3. Satellite Clock Offset Model

## 3. Analysis of Long-Term Clock Bias, Frequency, Drift Rate, and Noise

#### 3.1. Analysis of Clock Bias Series

#### 3.2. Analysis of Frequency Series

#### 3.3. Analysis of Drift Rate Series

#### 3.4. Fitting Precision Analysis of Clock Offset

## 4. Frequency Stability Analysis

- BDS-3 MEO PHM: These clocks have the best frequency stability at 1000 s and 10,000 s among all BDS clocks. The OADEVs are $4{.03\times 10}^{-14},\text{}2{.24\times 10}^{-14},\text{}\mathrm{and}\text{}0{.22\times 10}^{-14}\text{}\mathrm{s}/\mathrm{s}$ at 1000 s, 10,000 s, and 1 day, respectively.
- BDS-3 MEO Rb: It can be seen that the stability of MEO Rb clocks is slightly worse than that of BDS-3 MEO PHMs, with the OADEVs being $4{.3\times 10}^{-14}$, $2{.56\times 10}^{-14},\text{}\mathrm{and}\text{}0{.25\times 10}^{-14}\text{}\mathrm{s}/\mathrm{s}$ at 1000 s, 10,000 s, and 1 day, respectively.
- BDS-3 IGSO PHM: These clocks have the best daily stability, down to $0{.17\times 10}^{-14}\text{}\mathrm{s}/\mathrm{s}$, but the stabilities for 1000-second and 10,000-second variations are $11{.1\times 10}^{-14}$ and $4{.48\times 10}^{-14}\text{}\mathrm{s}/\mathrm{s}$, respectively, which are larger than those of clocks on MEO satellites.
- BDS-3 GEO PHM: Although the newest BDS-3 GEO satellites are equipped with PHMs, their frequency stabilities are much worse than those of MEO clocks, probably resulting from the poor accuracy of precise clock products for GEO satellites. The 1000-second, 10,000-second, and 1-day stabilities are $23{.81\times 10}^{-14}$, $7{.9\times 10}^{-14},$ and $0{.61\times 10}^{-14}\text{}\mathrm{s}/\mathrm{s}$, respectively.
- BDS-2 clocks: Being the older clocks of BDS satellites, their frequency stability is worse than those of BDS-3 clocks. The 1000-second, 10,000-second and 1-day stabilities of BDS-2 satellite onboard clocks are $21{.51\times 10}^{-14}$, $7{.83\times 10}^{-14}$ and $0{.62\times 10}^{-14}\text{}\mathrm{s}/\mathrm{s}$, respectively.

## 5. Spectrum Analysis

## 6. Discussion

## 7. Conclusions

- (1)
- In terms of the BDS-3 system, the performance of PHMs equipped on MEO satellites is slightly better than the performance of Rb clocks. The OADEV of MEO Rb clocks is $4{.3\text{}\times \text{}10}^{-14}\text{}\mathrm{s}/\mathrm{s}$ at 1000 s, which is 7% higher than the $4{.03\text{}\times \text{}10}^{-14}\text{}\mathrm{s}/\mathrm{s}$ of MEO PHMs. Furthermore, the RMS of fitting residuals of Rb clocks is 0.17 ns, which is 13% higher than that of PHMs.
- (2)
- The precise clock offset products of PHMs carried on BDS satellites show different performances when they operate in different types of orbits. The RMS values of the fitting residuals of PHMs on BDS-3 MEO, IGSO, and GEO satellites are 0.15, 0.28, and 0.46 ns, respectively. Moreover, the 1000-second stabilities of PHMs carried on MEO, IGSO, and GEO satellites are $4{.03\text{}\times \text{}10}^{-14}$, $1{.10\text{}\times \text{}10}^{-13},$ and $2{.38\text{}\times \text{}10}^{-13}\text{}\mathrm{s}/\mathrm{s}$, respectively.
- (3)
- Compared to BDS-2, the BDS-3 satellites show great improvements in clock quality. There are fewer frequency jumps in the long-term performance of BDS-3 onboard clocks. Moreover, the drift rates of BDS-3 satellites clocks varies within the range between $-{2\text{}\times \text{}10}^{-18}{\text{}\mathrm{and}\text{}2\text{}\times \text{}10}^{-18}{\text{}\mathrm{s}/\mathrm{s}}^{2}$, which is less than the range between $-{4\text{}\times \text{}10}^{-18}{\text{}\mathrm{and}\text{}4\text{}\times \text{}10}^{-18}{\text{}\mathrm{s}/\mathrm{s}}^{2}$ for BDS-2 clocks. Furthermore, the RMS of fitting residuals of BDS-2 onboard clocks in GEO, IGSO, and MEO satellites are 0.58, 0.53, and 0.33 ns, respectively, while those of BDS-3 onboard clocks in GEO, IGSO, and MEO satellites are 0.46, 0.28, and 0.16 ns, respectively. The frequency stability of BDS-2 clocks is also worse than that of BDS-3 clocks.
- (4)
- The analysis of the periodicity of BDS onboard clocks shows that there are significant periodic signals in BDS satellite clock offsets. The periodicity of the same types of satellite clocks is similar. BDS-3 with PHMs equipped on IGSO and GEO satellites show the same periodic characteristics as BDS-2 IGSO and GEO Rb clocks. The PHMs and Rb clocks carried on BDS-3 MEO satellites show different periodic characteristics. The main periods of the BDS-3 MEO Rb clocks are about 12.88 (1 CPR), 6.44 (2 CPR), and 4.29 h (3 CPR). The main periods of the BDS-3 MEO PHMs are about 6.44 (2 CPR) and 12.88 h (1 CPR).

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Clock bias series of the BDS-2 onboard clocks from DOY 1 to 300, 2021 (units: ${10}^{-4}$ s).

**Figure 2.**Clock bias series of the BDS-3 onboard clocks from DOY 1 to 300, 2021 (units: ${10}^{-4}$ s).

**Figure 3.**Frequency series of the BDS-2 onboard clocks from DOY 1 to 300, 2021 (units: ${10}^{-11}$ s/s).

**Figure 4.**Frequency series of the BDS-3 onboard clocks from DOY 1 to 300, 2021 (units: ${10}^{-11}$ s/s).

**Figure 5.**Drift rate series of the BDS-2 onboard clocks from DOY 1 to 300, 2021 (units: ${10}^{-18}$ s/${\mathrm{s}}^{2}$ ).

**Figure 6.**Drift rate series of the BDS-3 onboard clocks from DOY 1 to 300, 2021 (unit: ${10}^{-18}$ s/${\mathrm{s}}^{2}$).

**Figure 7.**Fitting residual series of the BDS-2 onboard clocks from DOY 1 to 300, 2021 (units: $\mathrm{ns}$).

PRN | Orbit Type | Satellite Type | Clock Type | Launch Date | PRN | Orbit Type | Satellite Type | Clock Type | Launch Date |
---|---|---|---|---|---|---|---|---|---|

C01 | GEO | BDS-2 | Rb | 2019.05 | C26 | MEO | BDS-3 | PHM | 2018.08 |

C02 | GEO | BDS-2 | Rb | 2012.10 | C27 | MEO | BDS-3 | PHM | 2018.01 |

C03 | GEO | BDS-2 | Rb | 2016.06 | C28 | MEO | BDS-3 | PHM | 2018.01 |

C04 | GEO | BDS-2 | Rb | 2010.11 | C29 | MEO | BDS-3 | PHM | 2018.03 |

C05 | GEO | BDS-2 | Rb | 2012.02 | C30 | MEO | BDS-3 | PHM | 2018.03 |

C06 | IGSO | BDS-2 | Rb | 2010.08 | C32 | MEO | BDS-3 | Rb | 2018.09 |

C07 | IGSO | BDS-2 | Rb | 2010.12 | C33 | MEO | BDS-3 | Rb | 2018.09 |

C08 | IGSO | BDS-2 | Rb | 2011.04 | C34 | MEO | BDS-3 | PHM | 2018.10 |

C09 | IGSO | BDS-2 | Rb | 2011.07 | C35 | MEO | BDS-3 | PHM | 2018.10 |

C10 | IGSO | BDS-2 | Rb | 2011.12 | C36 | MEO | BDS-3 | Rb | 2018.11 |

C11 | MEO | BDS-2 | Rb | 2012.04 | C37 | MEO | BDS-3 | Rb | 2018.11 |

C12 | MEO | BDS-2 | Rb | 2012.04 | C38 | IGSO | BDS-3 | PHM | 2019.04 |

C13 | IGSO | BDS-2 | Rb | 2016.03 | C39 | IGSO | BDS-3 | PHM | 2018.06 |

C14 | MEO | BDS-2 | Rb | 2012.09 | C40 | IGSO | BDS-3 | PHM | 2019.11 |

C16 | IGSO | BDS-2 | Rb | 2018.07 | C41 | MEO | BDS-3 | PHM | 2019.12 |

C19 | MEO | BDS-3 | Rb | 2017.11 | C42 | MEO | BDS-3 | PHM | 2019.12 |

C20 | MEO | BDS-3 | Rb | 2017.11 | C43 | MEO | BDS-3 | PHM | 2019.11 |

C21 | MEO | BDS-3 | Rb | 2018.02 | C44 | MEO | BDS-3 | PHM | 2019.11 |

C22 | MEO | BDS-3 | Rb | 2018.02 | C45 | MEO | BDS-3 | Rb | 2019.09 |

C23 | MEO | BDS-3 | Rb | 2018.07 | C46 | MEO | BDS-3 | Rb | 2019.09 |

C24 | MEO | BDS-3 | Rb | 2018.07 | C59 | GEO | BDS-3 | PHM | 2018.11 |

C25 | MEO | BDS-3 | PHM | 2018.08 | C60 | GEO | BDS-3 | PHM | 2020.03 |

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**MDPI and ACS Style**

Geng, T.; Jiang, R.; Lv, Y.; Xie, X.
Analysis of BDS-3 Onboard Clocks Based on GFZ Precise Clock Products. *Remote Sens.* **2022**, *14*, 1389.
https://doi.org/10.3390/rs14061389

**AMA Style**

Geng T, Jiang R, Lv Y, Xie X.
Analysis of BDS-3 Onboard Clocks Based on GFZ Precise Clock Products. *Remote Sensing*. 2022; 14(6):1389.
https://doi.org/10.3390/rs14061389

**Chicago/Turabian Style**

Geng, Tao, Rui Jiang, Yifei Lv, and Xin Xie.
2022. "Analysis of BDS-3 Onboard Clocks Based on GFZ Precise Clock Products" *Remote Sensing* 14, no. 6: 1389.
https://doi.org/10.3390/rs14061389