# Accuracy Analysis of Real-Time Precise Point Positioning—Estimated Precipitable Water Vapor under Different Meteorological Conditions: A Case Study in Hong Kong

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Sources

#### 2.2. Data Processing Method

#### 2.2.1. PPP Functional Model

#### 2.2.2. PPP PWV Calculation Method

^{−1}, (3.776 ± 0.014) × 105 K2∙hPa

^{−1}, and 461 J∙(Kg∙K)

^{−1}; ρ is the water vapor constant; and Tm is the atmospheric weighted temperature. Its mathematical expression is:

#### 2.2.3. Precision Evaluation Index

## 3. Results

#### 3.1. Real-Time Static PPP Accuracy Analysis

#### 3.2. Accuracy Analysis of Real-Time PPP-Estimated ZTD

#### 3.3. Accuracy Analysis of Real-Time PPP PWV

## 4. Discussion

## 5. Limitations and Future Direction of the Research

## 6. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**(

**a**) Comparison of PPP-ZTD and IGS-ZTD at HKSL station during nonrainfall periods; (

**b**) Comparison of PPP-ZTD and IGS-ZTD at HKSL station during rainfall; (

**c**) Comparison of PPP-ZTD and IGS-ZTD at HKWS station during nonrainfall periods; (

**d**) Comparison of PPP-ZTD and IGS-ZTD at HKWS station during rainfall.

Station | Latitude (°) | Longitude (°) | Antenna |
---|---|---|---|

HKCL | 22.2958 | 113.9077 | TRM59800.00 |

HKFN | 22.4946 | 114.1381 | LEIAT504 |

HKKT | 22.3678 | 114.3119 | TRM59800.00 |

HKKS | 22.4449 | 114.0665 | LEIAR25.R4 |

HKLM | 22.2189 | 114.1200 | TRM59800.00 |

HKLT | 22.4181 | 113.9966 | LEIAR25.R4 |

HKMW | 22.2558 | 114.0031 | LEIAR25.R4 |

HKNP | 22.2490 | 113.8938 | LEIAR25.R4 |

HKOH | 22.2476 | 114.2285 | LEIAR25.R4 |

HKPC | 22.2849 | 114.0378 | LEIAR25.R4 |

HKQT | 22.2910 | 114.2132 | TRM59800.00 |

HKSC | 22.3222 | 114.1411 | LEIAR25.R4 |

HKSL | 22.3720 | 113.9279 | LEIAR25.R4 |

HKSS | 22.4310 | 114.2693 | LEIAR25.R4 |

HKST | 22.3952 | 114.1842 | LEIAR25.R4 |

HKTK | 22.5465 | 114.2232 | TRM59800.00 |

HKWS | 22.4342 | 114.3353 | LEIAR25.R4 |

T430 | 22.4947 | 114.1382 | TRM59800.00 |

Observation | Combination of observation | IF |

Elevation mask angle | 10° | |

Stochastic model | Elevation weighting | |

Error correction | Phase wrapping | Correction |

Phase center variation | Igs14.atx | |

Atmospheric loading | Leave out | |

Tide correction | Solid tide, polar tide, and ocean tide | |

Relativistic correction | Correction | |

Tropospheric delay | Parameter estimation | |

Parameter estimation | Tropospheric mapping function | NMF |

Site coordinates | Constant | |

Station receiver clock error | White noise | |

Ambiguity | Float ambiguity | |

Filtering method | Extended Kalman filter |

Station | E (cm) | N (cm) | U (cm) | Convergence Time (min) | E (cm) | N (cm) | U (cm) | Convergence Time (min) |
---|---|---|---|---|---|---|---|---|

During Rainfall | During Nonrainfall | |||||||

HKSL | 1.94 | 0.77 | 2.34 | 47 | 1.38 | 0.88 | 1.88 | 37.5 |

HKWS | 1.43 | 0.83 | 2.4 | 78 | 1.31 | 0.83 | 2.06 | 33 |

Station | E (cm) | N (cm) | U (cm) | Convergence Time (min) | E (cm) | N (cm) | U (cm) | Convergence Time (min) |
---|---|---|---|---|---|---|---|---|

During Rainfall | During Nonrainfall | |||||||

HKSL | 1.77 | 0.83 | 2.59 | 38 | 1.35 | 0.86 | 1.71 | 34 |

HKWS | 1.19 | 0.57 | 2.13 | 50.5 | 1.06 | 0.87 | 1.43 | 28 |

Station | Bias (mm) | STDEV (mm) | RMS (mm) | Bias (mm) | STDEV (mm) | RMS (mm) |
---|---|---|---|---|---|---|

During Rainfall | During Nonrainfall | |||||

HKSL | 5.43 | 9.14 | 10.52 | 2.1 | 9.72 | 9.91 |

HKWS | 4.08 | 8.91 | 9.88 | 2.42 | 8.85 | 9.13 |

Station | Bias (mm) | STDEV (mm) | RMS (mm) | Bias (mm) | STDEV (mm) | RMS (mm) |
---|---|---|---|---|---|---|

During Rainfall | During Nonrainfall | |||||

HKCL | 12.02 | 18.24 | 15.47 | 8.84 | 14.57 | 11.42 |

HKFN | 13.23 | 17.75 | 16.85 | 9.06 | 13.44 | 12.25 |

HKKS | 12.24 | 20.65 | 15.86 | 9.32 | 14.35 | 12.07 |

HKKT | 12.07 | 17.66 | 15.21 | 8.44 | 12.23 | 11.35 |

HKLM | 10.74 | 18.64 | 14.15 | 9.08 | 15.91 | 11.36 |

HKLT | 12.95 | 17.37 | 16.66 | 8.54 | 11.58 | 10.83 |

HKMW | 15.66 | 18.65 | 19.14 | 14.29 | 11.05 | 17.24 |

HKNP | 10.11 | 13.96 | 13.08 | 9.14 | 11.27 | 11.75 |

HKOH | 15.25 | 19.37 | 18.67 | 9.26 | 11.16 | 11.56 |

HKPC | 11.53 | 16.74 | 14.74 | 7.84 | 9.94 | 9.91 |

HKQT | 14.17 | 22.36 | 17.95 | 8.36 | 12.83 | 10.82 |

HKSC | 11.88 | 18.19 | 14.66 | 8.15 | 11.54 | 10.05 |

HKSS | 13.02 | 18.74 | 16.74 | 8.55 | 13.01 | 11.35 |

HKST | 12.64 | 16.55 | 15.55 | 8.64 | 10.83 | 10.92 |

HKTK | 13.76 | 22.06 | 17.46 | 10.95 | 15.45 | 14.66 |

T430 | 13.12 | 17.83 | 16.97 | 9.06 | 12.81 | 12.24 |

Station | Bias (mm) | STDEV (mm) | RMS (mm) | Bias (mm) | STDEV (mm) | RMS (mm) |
---|---|---|---|---|---|---|

During Rainfall | During Nonrainfall | |||||

HKSC | 3.45 | 1.79 | 3.85 | 0.93 | 1.21 | 1.18 |

Station | Bias (mm) | STDEV (mm) | RMS (mm) | Bias (mm) | STDEV (mm) | RMS (mm) |
---|---|---|---|---|---|---|

During Rainfall | During Nonrainfall | |||||

HKCL | 1.89 | 2.87 | 2.43 | 1.4 | 2.3 | 1.81 |

HKFN | 2.09 | 2.79 | 2.65 | 1.42 | 2.12 | 1.93 |

HKKS | 1.93 | 2.51 | 2.5 | 1.47 | 2.1 | 1.9 |

HKKT | 1.93 | 3.25 | 2.5 | 1.47 | 2.27 | 1.9 |

HKLM | 1.89 | 2.78 | 2.4 | 1.33 | 1.93 | 1.79 |

HKLT | 1.7 | 2.93 | 2.22 | 1.42 | 2.53 | 1.78 |

HKMW | 2.03 | 2.73 | 2.62 | 1.34 | 1.81 | 1.72 |

HKNP | 2.45 | 2.93 | 3.01 | 2.24 | 1.74 | 2.71 |

HKOH | 1.59 | 2.19 | 2.04 | 1.42 | 1.77 | 1.83 |

HKPC | 2.39 | 3.04 | 2.92 | 1.45 | 1.76 | 1.82 |

HKQT | 1.82 | 2.64 | 2.32 | 1.24 | 1.57 | 1.56 |

HKSL | 2.23 | 3.52 | 2.84 | 1.32 | 2.03 | 1.71 |

HKSS | 1.89 | 2.68 | 2.37 | 1.33 | 1.85 | 1.77 |

HKST | 2.06 | 2.95 | 2.64 | 1.35 | 2.06 | 1.79 |

HKTK | 1.97 | 2.59 | 2.44 | 1.36 | 1.7 | 1.72 |

HKWS | 2.16 | 3.48 | 2.75 | 1.73 | 2.44 | 2.31 |

T430 | 2.21 | 3.05 | 2.79 | 1.53 | 1.89 | 2.04 |

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**MDPI and ACS Style**

Xu, Y.; Ma, L.; Zhang, F.; Chen, X.; Yang, Z. Accuracy Analysis of Real-Time Precise Point Positioning—Estimated Precipitable Water Vapor under Different Meteorological Conditions: A Case Study in Hong Kong. *Atmosphere* **2023**, *14*, 650.
https://doi.org/10.3390/atmos14040650

**AMA Style**

Xu Y, Ma L, Zhang F, Chen X, Yang Z. Accuracy Analysis of Real-Time Precise Point Positioning—Estimated Precipitable Water Vapor under Different Meteorological Conditions: A Case Study in Hong Kong. *Atmosphere*. 2023; 14(4):650.
https://doi.org/10.3390/atmos14040650

**Chicago/Turabian Style**

Xu, Ying, Lin Ma, Fangzhao Zhang, Xin Chen, and Zaozao Yang. 2023. "Accuracy Analysis of Real-Time Precise Point Positioning—Estimated Precipitable Water Vapor under Different Meteorological Conditions: A Case Study in Hong Kong" *Atmosphere* 14, no. 4: 650.
https://doi.org/10.3390/atmos14040650