# Precise Orbit Determination and Accuracy Analysis for BDS-3 Satellites Using SLR Observations

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{−7}m/s

^{2}[30]. Analyzing SRP errors is crucial to enhancing the POD of BDS-3 satellites.

## 2. Methods

#### 2.1. Measurement Model for SLR

#### 2.2. POD Strategies

## 3. BDS-3 POD Based on Actual SLR Observations

#### 3.1. SLR Observations of BDS-3 Satellites

#### 3.2. The Orbit Comparison with WUM Orbits

#### 3.3. The Dependency on the Number of SLR Observations and SLR Stations

## 4. Simulation Analysis of BDS-3 POD Accuracy

#### 4.1. SLR Observations Simulation Processing Strategy

#### 4.2. Dependency on the Measurement Errors

#### 4.3. Dependency on the SRP Errors

^{−7}m/s

^{2}, which is the most important influential factor of the orbital model accuracy. In this section, we examine the impact of SRP errors on the precision of orbit determination for the BDS-3 satellite. The detailed simulation idea is as follows:

- Fit 1-day orbit individually, 9 days in total, calculate and stitch together their SRP a1;
- Fit 9-day orbits and calculate their SRP a2;
- Calculate the SRP influence factor C (Equation (5)), and compute the RMS for each direction at the current time;

- 4.
- Add the SRP influence factor C according to the current date in the orbit determination simulation as the SRP errors;
- 5.
- Calculate the magnitude of the SRP influence factor:

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**The distribution of BDS-3 satellite SLR observation stations in 2020 (‘blue and *’ stations refer to the 6 stations that contribute a large number of SLR observations).

**Figure 7.**The relationship between the number of SLR observations and the median RMS values is shown by the red, blue, and black dots, which correspond to the RMS values in the R, T, and N directions, respectively. In addition, the median RMS values are indicated by a hollow circle, with a step size of 2. Subplot (

**a**–

**d**) represents C20, C21, C29, and C30 satellites, respectively.

**Figure 8.**The relationship between the number of stations and the median RMS values. The definitions of different color dots and circles are the same as in Figure 7. Subplot (

**a**–

**d**) represents C20, C21, C29, and C30 satellites, respectively.

Project | Parameters and Models |
---|---|

Observe Elevation Angle Threshold | 10° |

Threshold Residuals of SLR Observations | 300 mm |

Earth Gravity Field | GGM05S, 120 × 120 |

N-body Perturbation | JPL DE430 [32] |

SRP | ECOM 9 [33] |

Precession and Nutation | IERS2010 [34] |

A priori Station Coordinates | ITRF2014 [35] |

Pole and Ocean tides | CSR4.0 [36] |

Relativistic Perturbation | Only Schwarzschild |

A priori Orbital Parameters | The Precise Orbit of WUM |

Orbital Parameters | 6 Orbital Element and 9 ECOM SRP |

**Table 2.**The fundamental information and offsets of LRA’s effective phase center with respect to CoM for BDS-3 satellites [13].

Pseudo-Random Noise (PRN) Number | PCOX (mm) | PCOY (mm) | PCOZ (mm) |
---|---|---|---|

C20 | 594.7 | −86.4 | 1264.4 |

C21 | 598.6 | −86.6 | 1265.0 |

C29 | 664.6 | 424.9 | 642.7 |

C30 | 664.6 | 424.9 | 642.7 |

PRN | Observations | |
---|---|---|

Arcs | NPs | |

C20 | 1209 | 3492 |

C21 | 1211 | 3566 |

C29 | 988 | 2846 |

C30 | 914 | 2755 |

**Table 4.**The number of available SLR NPs, the proportion of the available SLR NPs, and the mean/RMS for SLR validation residuals (unit: cm).

PRN | Available NPs | Proportion | Overall |
---|---|---|---|

C20 | 3476 | 99.37% | 2.78/3.77 |

C21 | 3512 | 98.49% | 2.68/3.71 |

C29 | 2810 | 98.74% | 1.18/3.78 |

C30 | 2680 | 97.28% | 0.42/3.36 |

PRN | The Success Efficiency of POD Solutions (Unit: %) | Average 3D-RMS (Unit: m) | ||||||
---|---|---|---|---|---|---|---|---|

3 d | 5 d | 7 d | 9 d | 3 d | 5 d | 7 d | 9 d | |

C20 | 62.8 | 87.3 | 96.4 | 97.2 | 1.29 | 0.72 | 0.51 | 0.40 |

C21 | 59.2 | 88.1 | 95.6 | 98.0 | 1.08 | 0.75 | 0.48 | 0.42 |

C29 | 51.0 | 79.6 | 90.8 | 94.1 | 1.51 | 0.96 | 0.79 | 0.69 |

C30 | 45.6 | 77.1 | 88.6 | 91.3 | 1.56 | 1.06 | 0.89 | 0.75 |

PRN | VS WUM | |||
---|---|---|---|---|

R | T | N | 3D | |

C20 | 4.8 | 22.1 | 27.9 | 37.7 |

C21 | 4.7 | 22.2 | 27.4 | 37.8 |

C29 | 7.9 | 35.2 | 41.0 | 55.1 |

C30 | 8.2 | 33.2 | 43.8 | 57.0 |

PRN | R | T | N | 3D |
---|---|---|---|---|

C20 | 0.7 | 4.9 | 5.1 | 7.3 |

C21 | 0.7 | 4.9 | 5.2 | 7.6 |

C29 | 0.9 | 6.4 | 6.9 | 9.9 |

C30 | 1.0 | 6.9 | 8.0 | 11.0 |

PRN | R | T | N | 3D |
---|---|---|---|---|

C20 | 1.1 | 6.8 | 7.5 | 10.4 |

C21 | 1.1 | 6.4 | 7.2 | 10.1 |

C29 | 1.3 | 8.7 | 10.1 | 14.1 |

C30 | 1.5 | 9.2 | 10.7 | 15.0 |

PRN | SRP Influence Factor | |||
---|---|---|---|---|

X | Y | Z | Magnitude | |

C20 | 1.8 | 2.5 | 7.9 | 0.6 |

C21 | 1.6 | 2.8 | 7.8 | 0.6 |

C29 | 3.9 | 3.8 | 9.8 | 2.0 |

C30 | 3.7 | 4.2 | 9.9 | 2.1 |

PRN | VS Orbit Modeling Fitting Orbit | |||
---|---|---|---|---|

R | T | N | 3D | |

C20 | 2.0 | 14.8 | 13.9 | 21.7 |

C21 | 2.0 | 14.5 | 14.1 | 20.5 |

C29 | 4.5 | 32.8 | 25.2 | 45.1 |

C30 | 4.4 | 30.8 | 25.3 | 43.3 |

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**MDPI and ACS Style**

An, Z.; Shao, K.; Gu, D.; Wei, C.; Xu, Z.; Tong, L.; Zhu, J.; Wang, J.; Liu, D. Precise Orbit Determination and Accuracy Analysis for BDS-3 Satellites Using SLR Observations. *Remote Sens.* **2023**, *15*, 1833.
https://doi.org/10.3390/rs15071833

**AMA Style**

An Z, Shao K, Gu D, Wei C, Xu Z, Tong L, Zhu J, Wang J, Liu D. Precise Orbit Determination and Accuracy Analysis for BDS-3 Satellites Using SLR Observations. *Remote Sensing*. 2023; 15(7):1833.
https://doi.org/10.3390/rs15071833

**Chicago/Turabian Style**

An, Zicong, Kai Shao, Defeng Gu, Chunbo Wei, Zheyu Xu, Lisheng Tong, Jubo Zhu, Jian Wang, and Daoping Liu. 2023. "Precise Orbit Determination and Accuracy Analysis for BDS-3 Satellites Using SLR Observations" *Remote Sensing* 15, no. 7: 1833.
https://doi.org/10.3390/rs15071833