# Preliminary Results on Tropospheric ZTD Estimation by Smartphone

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. ZTD Estimation from GNSS

_{S}and δ

^{R}are the satellite and receiver clock errors, respectively, ${\mathrm{N}}_{\mathrm{R}}^{\mathrm{S}}$ is the unknown initial phase ambiguity, ${\mathrm{I}}_{\mathrm{R}}^{\mathrm{S}}$ is the ionospheric (slant) delay, ${\mathrm{T}}_{\mathrm{R}}^{\mathrm{S}}$ is the tropospheric (slant) delay, MP is the multipath effect, and ε contains all the remaining unmodelled errors.

_{S}and δ

^{R}can be eliminated using the double differences strategy or can be modelled in PPP, ${\mathrm{N}}_{\mathrm{R}}^{\mathrm{S}}$ is resolved in the initialization phase, and ${\mathrm{I}}_{\mathrm{R}}^{\mathrm{S}}$ can be eliminated using the iono-free dual frequencies combination for double-frequency receivers, or it can be modelled for single-frequency receivers. The multipath effect MP can be mitigated by choosing an antenna position that is far from reflecting objects, installing special antennas (e.g., choke-ring antennas), masking low elevation signals, or by using techniques and models designed to recognize the reflected signals and discard them [37].

#### 2.2. Case Study: Materials, Methods and Processing

#### 2.2.1. Case Study 1

#### 2.2.2. Case Study 2

## 3. Results

#### 3.1. Case Study 1

#### 3.2. Case Study 2

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**ZTD values for TORI (estimated, blue) and TOSM (Xiaomi Mi 8—modelled, orange) obtained with CSRS-PPP.

**Figure 4.**Differences between estimated and reference coordinates for TORI (blue) and TOSM (Xiaomi Mi 8—orange) receivers, obtained with RTKLIB.

**Figure 6.**Residuals of positioning components for TORI with respect to the reference position, as obtained with RTKLIB.

**Figure 7.**Residuals of positioning components for TOSM with respect to the reference position, as obtained with RTKLIB.

**Figure 8.**Comparison of ZTD values for TOSM considering CSRS-PPP (modelled, blue) and RTKLIB (estimated, orange).

**Figure 14.**ZTD values for GENU (estimated, blue) and GESM (Xiaomi Mi8—modelled, orange) obtained with CSRS-PPP software.

**Figure 16.**Differences between estimated and reference coordinates for GENU (blue) and GESM (Xiaomi Mi 8—orange) receivers, obtained with RTKLIB.

**Figure 17.**Differences between estimated and reference coordinates for GENU and GESM estimated with RTKLIB.

**Figure 18.**Residuals of positioning components for GENU with respect to the reference position, as obtained with RTKLIB.

**Figure 19.**Residuals of positioning components for GESM with respect to the reference position, as obtained with RTKLIB.

**Figure 21.**Comparison of ZTD values for GENU considering CSRS-PPP (orange, modelled) and RTKLIB (blue, estimated) software. The green dots represent GENO CORS ZTD estimates provided by EUREF.

**Figure 22.**Comparison of ZTD estimates for GESM considering RTKLIB (blue). The green dots represent GENO CORS ZTD estimates provided by EUREF.

RINEX format | RINEX 3 |

Cut-off angle | 7.5° |

Ephemeris | Final (MGEX) |

Clocks | Final (MGEX) |

Ionosphere | Iono-free |

OTL | Based on Chalmers grid solution |

Ambiguity resolution | PPP-AR |

**Table 2.**Statistical parameters for the position outputs for TORI and TOSM with respect to the corresponding reference positions.

Average (m) | Standard Deviation (m) | Root Mean Square (m) | ||
---|---|---|---|---|

TORI | E-W | 0.16 | 0.29 | 0.33 |

N-S | −0.10 | 0.20 | 0.22 | |

U-D | −0.04 | 0.14 | 0.14 | |

TOSM | E-W | −0.45 | 0.56 | 0.72 |

N-S | 0.30 | 0.34 | 0.45 | |

U-D | 0.85 | 1.36 | 1.60 |

Receiver | Mean (m) | Standard Deviation (m) |
---|---|---|

TOSM | 0.170 | 0.114 |

TORI | 0.007 | 0.011 |

**Table 4.**Statistical parameters for the positions output for GENU and GESM with respect to the corresponding reference positions.

Average (m) | Standard Deviation (m) | Root Mean Square (m) | ||
---|---|---|---|---|

GENU | E-W | −0.03 | 0.02 | 0.03 |

N-S | 0.02 | 0.01 | 0.02 | |

U-D | −0.08 | 0.04 | 0.09 | |

GESM | E-W | 0.23 | 0.35 | 0.42 |

N-S | 0.07 | 0.23 | 0.24 | |

U-D | 0.02 | 0.18 | 0.18 |

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**MDPI and ACS Style**

Benvenuto, L.; Dabove, P.; Ferrando, I.; Sguerso, D.
Preliminary Results on Tropospheric ZTD Estimation by Smartphone. *Remote Sens.* **2021**, *13*, 4567.
https://doi.org/10.3390/rs13224567

**AMA Style**

Benvenuto L, Dabove P, Ferrando I, Sguerso D.
Preliminary Results on Tropospheric ZTD Estimation by Smartphone. *Remote Sensing*. 2021; 13(22):4567.
https://doi.org/10.3390/rs13224567

**Chicago/Turabian Style**

Benvenuto, Lorenzo, Paolo Dabove, Ilaria Ferrando, and Domenico Sguerso.
2021. "Preliminary Results on Tropospheric ZTD Estimation by Smartphone" *Remote Sensing* 13, no. 22: 4567.
https://doi.org/10.3390/rs13224567