# Application of Multi-System Combination Precise Point Positioning in Landslide Monitoring

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## Abstract

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## 1. Introduction

## 2. PPP Model and Evaluation Index

- S = satellite system;
- IF = ionospheric cancellation combination;
- P = observation value of pseudo-distance;
- L = phase observation;
- $\rho $ = geometric distance;
- c = speed of light;
- ${T}^{S}$ = tropospheric delay;
- $d{\overline{t}}^{S}$ = receiver clock difference;
- ${\lambda}^{S}$ = wavelength;
- ${\overline{N}}^{S}$ = ambiguity;
- $\epsilon \left({P}_{IF}^{S}\right)$ = pseudo-range observation noise;
- $\epsilon \left({L}_{IF}^{S}\right)$ = phase observation noise.

- B = reference satellite system;
- S
_{i}= rest of the constellations except the base system, i = 1,2,3; - $IB{S}^{B,{S}_{i}}$ = system deviation between the base system and the rest of the system.

- ${\sigma}_{P,0}^{2}$ = prior variances of pseudo-range;
- ${\sigma}_{L,0}^{2}$ = phase observations;
- $\alpha $ = the height of the angle threshold (30°).

- ${\sigma}_{B,P}$ = standard deviation of pseudo-range observations of reference system (3 m);
- ${\sigma}_{{S}_{i},P}$ = standard deviation of pseudo-range observations of auxiliary system (6 m);
- ${\sigma}_{B,L}$ = standard deviation of phase observation of reference system (0.003 m);
- ${\sigma}_{{S}_{i},L}$ = standard deviation of phase observation of auxiliary system (0.006 m).

## 3. Quantitative Evaluation Index

#### 3.1. Convergence Time

- CT = convergence time (min);
- SI = sampling interval;
- L = the number of epochs required from the beginning of the first epoch until the calculation accuracy meets the limitation requirements.

#### 3.2. Root Mean Square Error

- k = initial epoch at the time of convergence time;
- n = total epoch;
- P
_{i}= parameter to be estimated; - $\widehat{P}$ = the reference value.

## 4. Overview of the Study Area

#### 4.1. Basic Characteristics of Landslides in the Study Area

#### 4.2. Location of Monitoring Points

## 5. Application of Multi-System Combination PPP in Landslide Monitoring

#### 5.1. Analysis of Convergence Time

#### 5.2. Analysis of Positioning Accuracy

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Table 1.**The PPP positioning results compared with the results of static relative positioning difference and the RMSE.

Combination | Date | Deviation/cm | RMSE | ||||
---|---|---|---|---|---|---|---|

(Year/Month/Day) | E | N | U | E | N | U | |

2019/6/18 | 0.79 | 0.69 | 3.37 | 1.32 | 0.55 | 2.85 | |

2019/7/18 | −0.22 | 0.58 | −2.93 | 1.53 | 0.58 | 2.79 | |

2019/8/18 | 1.72 | 0.68 | −2.71 | 1.61 | 0.56 | 2.77 | |

G/R/C | 2019/9/18 | −2.15 | −0.7 | −4.1 | 1.34 | 0.57 | 2.68 |

2019/10/18 | −2.02 | 0.71 | 2.96 | 1.48 | 0.53 | 2.55 | |

2019/11/18 | −1.39 | 0.97 | −1.64 | 1.73 | 0.61 | 2.93 | |

2019/12/18 | −1.49 | 0.98 | −1.69 | 1.49 | 0.53 | 2.67 | |

2020/1/18 | 1.45 | −0.52 | −2.38 | 1.33 | 0.51 | 3.03 | |

2019/6/18 | 0.41 | 0.31 | 3.01 | 1.40 | 0.46 | 2.77 | |

2019/7/18 | −0.68 | 0.62 | −2.89 | 1.70 | 0.57 | 2.75 | |

2019/8/18 | −1.66 | 0.75 | −2.65 | 1.54 | 0.64 | 2.80 | |

G/R/E | 2019/9/18 | −1.96 | −0.51 | −3.9 | 1.34 | 0.61 | 2.79 |

2019/10/18 | −2.42 | 0.31 | 2.56 | 1.50 | 0.56 | 2.52 | |

2019/11/18 | −1.04 | 1.31 | −1.3 | 1.67 | 0.73 | 2.95 | |

2019/12/18 | −1.33 | −0.82 | −1.53 | 1.52 | 0.56 | 2.66 | |

2020/1/18 | 1.71 | −0.26 | −2.12 | 1.47 | 0.54 | 3.10 | |

2019/6/18 | 0.94 | 0.84 | 3.52 | 1.14 | 0.59 | 2.88 | |

2019/7/18 | −0.28 | 0.52 | −2.99 | 1.35 | 0.55 | 2.79 | |

2019/8/18 | −1.63 | 0.78 | −2.61 | 1.41 | 0.56 | 2.79 | |

G/R/E/C | 2019/9/18 | −2.21 | −0.76 | −4.16 | 1.14 | 0.59 | 2.68 |

2019/10/18 | −2.14 | 0.59 | 2.84 | 1.23 | 0.57 | 2.54 | |

2019/11/18 | −1.52 | 0.84 | −1.77 | 1.52 | 0.65 | 2.91 | |

2019/12/18 | −1.58 | −1.07 | −1.79 | 1.29 | 0.54 | 2.65 | |

2020/1/18 | 1.48 | −0.49 | −2.35 | 1.15 | 0.51 | 3.01 |

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**MDPI and ACS Style**

Lin, C.; Wu, G.; Feng, X.; Li, D.; Yu, Z.; Wang, X.; Gao, Y.; Guo, J.; Wen, X.; Jian, W.
Application of Multi-System Combination Precise Point Positioning in Landslide Monitoring. *Appl. Sci.* **2021**, *11*, 8378.
https://doi.org/10.3390/app11188378

**AMA Style**

Lin C, Wu G, Feng X, Li D, Yu Z, Wang X, Gao Y, Guo J, Wen X, Jian W.
Application of Multi-System Combination Precise Point Positioning in Landslide Monitoring. *Applied Sciences*. 2021; 11(18):8378.
https://doi.org/10.3390/app11188378

**Chicago/Turabian Style**

Lin, Chen, Guanye Wu, Xiaomin Feng, Dingxing Li, Zhichao Yu, Xuanwei Wang, Yonggang Gao, Jinyun Guo, Xiaole Wen, and Wenbin Jian.
2021. "Application of Multi-System Combination Precise Point Positioning in Landslide Monitoring" *Applied Sciences* 11, no. 18: 8378.
https://doi.org/10.3390/app11188378