# Analysing the Zenith Tropospheric Delay Estimates in On-line Precise Point Positioning (PPP) Services and PPP Software Packages

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}of precipitable water.

#### 1.1. Tropospheric Delay

_{1}= 77.689 K·h·Pa

^{−1}, k

_{2}= 71.295 K·h·Pa

^{−1}and k

_{3}= 375,463 K

^{2}·h·Pa

^{−1}are empirically determined coefficients [20]. The troposphere causes a delay to the signal ${\Delta}^{PD}$ which can be expressed as an integral of the total refractivity N along the propagation path s from receiver r to the satellite w:

#### 1.2. Precise Point Positioning

#### 1.3. Observation Equations

## 2. Materials and Methods

_{dry}and M

_{wet}are the dry and wet mapping function (Neill mapping function) which does not require any meteorological data. The multiplication of the mapping function and the slant delay yield the Zenith Troposheric Delay.

## 3. Results

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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Parameter | APPS | CSRS-PPP | magicGNSS | gLAB | POINT | RTKLIB |
---|---|---|---|---|---|---|

Version | GIPSY 6.4 | 1.05 | N/A | 5.0.0 | N/A | 2.4.3 |

Mode of calculation | Static/kine-matic | Static/kine-matic | Static/kine-matic | Static/kine-matic | Static/kine-matic | Static/kine-matic |

Constellation | GPS | GPS,GLO | GPS,GLO, Galileo,BDS | GPS, GLO,Galileo | GPS,GLO | GPS,GLO, GPS+GLO |

Frequency | L1,L2 | L1,L2 | L1,L2 | L1,L2 | L1,L2 | L1,L2 |

Type of observation | Code and phase | Code and phase | Code and phase | Code and phase | Code and phase | Code and phase |

Antenna model | Not taken into account | Taken into account | Not taken into account | Taken into account | Taken into account | Taken into account |

Frame of reference | ITRF2008 | ITRF2008 | ITRF2008 | ITRF2008 | ITRF2008 | ITRF2008 |

Orbits and clocks of satellites | JPL final | IGS final | GMV Rapid, IGS Rapid, IGS final | IGS final | IGS final | IGS final |

Cut-off angle | 10° | 10° | 10° | 10° | 10° | 10° |

Mapping Function | GMF | GMF | GMF | NMF | NMF | NMF |

Station | City | Country | Latitude | Longitude | Height |
---|---|---|---|---|---|

ALGO | Algonquin Park | Canada | 45.95861 | −78.0714 | 202 |

REYK | Reykjavik | Iceland | 64.13861 | −21.9553 | 93.1 |

TIXI | Tixi | Russian Federation | 71.63444 | 128.8664 | 46.9847 |

MAL2 | Malindi | Kenya | −2.995833 | 40.1938 | −20.4 |

RIOP | Riobamba | Ecuador | −1.65055 | −78.6508 | 2793.00 |

NAUR | Nauru | Nauru | −0.55167 | 166.9253 | 46.3 |

PARC | Punta Arenas | Chile | −53.1369 | −70.8797 | 22.3 |

MAW1 | Mawson | Antarctica | −67.6047 | 62.87056 | 59.184 |

MAC1 | Macquarie Island | Australia | −54.4994 | 158.9356 | −6.69 |

CSRS [cm] | APPS [cm] | MAGIC [cm] | POINT [cm] | RTKLIB [cm] | GLAB [cm] | |
---|---|---|---|---|---|---|

North 2016 | 0.48 | 8.59 | 0.78 | 3.90 | 8.40 | 4.29 |

Center 2016 | 0.98 | 27.61 | 1.29 | 19.06 | 5.84 | 4.04 |

South 2016 | 0.80 | 7.39 | 0.87 | 20.39 | 18.67 | 2.12 |

North 2017 | 4.92 | 7.64 | 4.96 | 5.32 | 10.93 | 4.12 |

Center 2017 | 6.15 | 25.71 | 6.18 | 17.82 | 6.82 | 3.07 |

South 2017 | 2.55 | 5.15 | 2.77 | 22.36 | 20.46 | 2.13 |

CSRS [cm] | APPS [cm] | MAGIC [cm] | POINT [cm] | RTKLIB [cm] | GLAB [cm] | |
---|---|---|---|---|---|---|

North 2016 | 0.42 | 7.18 | 0.80 | 9.22 | 10.10 | 1.6 |

Center 2016 | 0.60 | 31.26 | 0.86 | 11.66 | 14.62 | 3.99 |

South 2016 | 0.86 | 10.18 | 0.75 | 6.45 | 12.39 | 2.61 |

North 2017 | 0.45 | 8.96 | 0.69 | 3.82 | 8.19 | 3.62 |

Center 2017 | 0.87 | 30.64 | 1.21 | 12.36 | 14.09 | 3.61 |

South 2017 | 0.62 | 4.66 | 0.69 | 9.24 | 13.29 | 4.76 |

CSRS [cm] | APPS [cm] | MAGIC [cm] | POINT [cm] | RTKLIB [cm] | GLAB [cm] | |
---|---|---|---|---|---|---|

North 2016 | 0.60 | 14.89 | 0.98 | 8.85 | 5.76 | 3.17 |

Center 2016 | 0.77 | 20.96 | 1.22 | 20.23 | 11.35 | 1.77 |

South 2016 | 0.68 | 4.45 | 0.75 | 6.97 | 10.22 | 2.03 |

North 2017 | 0.55 | 12.36 | 0.83 | 12.78 | 8.59 | 4.5 |

Center 2017 | 0.57 | 29.70 | 0.75 | 16.88 | 8.71 | 4.71 |

South 2017 | 0.82 | 8.36 | 0.77 | 5.88 | 8.82 | 1.38 |

CSRS [cm] | APPS [cm] | MAGIC [cm] | POINT [cm] | RTKLIB [cm] | GLAB [cm] | |
---|---|---|---|---|---|---|

North 2016 | 0.7 | 21.81 | 1.07 | 5.9 | 3.65 | 3.6 |

Center 2016 | 0.71 | 18.75 | 0.8 | 23.75 | 16.59 | 1.77 |

South 2016 | 0.7 | 26.59 | 0.8 | 8.59 | 2.79 | 4.37 |

North 2017 | 0.41 | 27.93 | 0.87 | 7.92 | 6.54 | 8.94 |

Center 2017 | 0.54 | 24.05 | 0.81 | 18.11 | 15.36 | 3.31 |

South 2017 | 0.7 | 41.32 | 0.8 | 10.53 | 2.06 | 2.73 |

CSRS [cm] | APPS [cm] | MAGIC [cm] | POINT [cm] | RTKLIB [cm] | GLAB [cm] | |
---|---|---|---|---|---|---|

January 27th 2016 | 0.78 | 17.13 | 1.01 | 16.23 | 12.29 | 3.62 |

January 27th 2017 | 4.77 | 15.67 | 4.85 | 16.75 | 13.96 | 3.21 |

April 27th 2016 | 0.65 | 19.45 | 0.80 | 9.36 | 12.51 | 2.91 |

April 27th 2017 | 0.67 | 18.64 | 0.90 | 9.45 | 12.14 | 4.03 |

July 27th 2016 | 0.69 | 15.06 | 1.00 | 13.68 | 9.42 | 2.4 |

July 27th 2017 | 0.66 | 17.39 | 0.78 | 12.67 | 8.71 | 3.85 |

October 26th 2016 | 0.70 | 22.60 | 0.89 | 14.97 | 9.94 | 3.35 |

October 27th 2017 | 0.56 | 31.99 | 0.83 | 12.90 | 9.71 | 5.83 |

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**MDPI and ACS Style**

Mendez Astudillo, J.; Lau, L.; Tang, Y.-T.; Moore, T.
Analysing the Zenith Tropospheric Delay Estimates in On-line Precise Point Positioning (PPP) Services and PPP Software Packages. *Sensors* **2018**, *18*, 580.
https://doi.org/10.3390/s18020580

**AMA Style**

Mendez Astudillo J, Lau L, Tang Y-T, Moore T.
Analysing the Zenith Tropospheric Delay Estimates in On-line Precise Point Positioning (PPP) Services and PPP Software Packages. *Sensors*. 2018; 18(2):580.
https://doi.org/10.3390/s18020580

**Chicago/Turabian Style**

Mendez Astudillo, Jorge, Lawrence Lau, Yu-Ting Tang, and Terry Moore.
2018. "Analysing the Zenith Tropospheric Delay Estimates in On-line Precise Point Positioning (PPP) Services and PPP Software Packages" *Sensors* 18, no. 2: 580.
https://doi.org/10.3390/s18020580