# New Adaptable All-in-One Strategy for Estimating Advanced Tropospheric Parameters and Using Real-Time Orbits and Clocks

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Assessment of Available RT Orbit and Clock Products and RT ZTDs

#### 2.1. Assessment of Real-Time Orbit and Clock Corrections

#### 2.2. Impact of IGS RTS Products on ZTD Estimates

#### 2.3. Long-Term Quality of Operational RT ZTD Production

## 3. New Adaptable Strategy for RT and NRT Troposphere Monitoring

#### 3.1. Epoch-Wise Filtering vs. Batch Processing, PPP vs. Network Approach

#### 3.2. Combining RT and NRT Processing Supported by Observations from Files or Streams

#### 3.3. Estimating High-Resolution ZTDs and Horizontal Gradients

_{N}) and East (G

_{E}) using an azimuth (A), which direction is counted from the North [43]

#### 3.4. Retrieving Slant Tropospheric Delays from Both RT and NRT Processing

## 4. Assessment of New Method Compared to the Existing E-GVAP Processing

## 5. Impact Assessments on Estimated Parameters at Collocated Stations

#### 5.1. Impact of Backward Smoothing on Adaptable RT/NRT Solutions

#### 5.2. Tropospheric Parameters from Multi-GNSS Analyses

#### 5.3. Impact of Precise Products on ZTD and Gradient Estimates

#### 5.4. Carrier-Phase Post-Fit Residuals and Slant Delays

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 8.**Stochastic modeling of the troposphere represented by real-time Kalman filter (white points), hourly backward smoothing (blue points), and 45 min postponed hourly backward smoothing (red points).

**Figure 9.**Real time (red), near-real time (green, blue) and reference (gray, black) ZTD estimates during a fast change in the troposphere.

**Figure 10.**Elevation-dependent absolute (

**a**) and normalized (

**b**) statistics for slant delay differences at POTM and POTS stations using real-time (RT), post-processing (PP) product, Kalman filter (F), backward smoothing (S). Line types indicates model SD (solid), clean SD (dashed), raw SD (dotted).

**Figure 11.**Elevation-dependent absolute (

**a**) and normalized (

**b**) statistics for GOP slant delay differences at POTM and POTS stations using post-processing (PP) product and Kalman filter (F) or backward smoothing (S), GFZ slant delays and old GOP product (GOP_S). Line types indicates model SD (solid), clean SD (dashed), raw SD (dotted).

**Figure 12.**ZTD standard deviations and biases for 13 EUREF stations and six processing strategies compared to the reference EUREF product.

**Figure 13.**Standard deviations for ZTDs (

**a**) and east gradients (

**b**) using different delays in backward smoothing at two dual-stations—Zimmerwald (

**top**) and Matera (

**bottom**).

**Figure 14.**Time series of ZTD (

**top**), north gradient (

**middle**) and east gradient (

**bottom**) differences at Zimmerwald dual-station when using the Kalman filter (

**a**) and the backward smoothing (

**b**).

**Figure 15.**Carrier-phase post-fit residuals from the Kalman filter (

**a**) and the backward smoothing (

**b**) using COM (

**top**) and GBM (

**bottom**) products at ZIM2 station.

RMSE | SDEV | |||||
---|---|---|---|---|---|---|

Radial | Along | Cross | 3D | Clock | Clock | |

IGS01 | 1.84 | 2.83 | 2.38 | 4.34 | 5.72 | 2.95 |

IGS02 | 2.35 | 3.71 | 3.04 | 5.63 | 10.08 | 3.52 |

IGS03 | 2.41 | 3.82 | 3.10 | 5.70 | 10.28 | 3.03 |

CNS91 | 2.68 | 3.07 | 2.47 | 5.01 | 11.16 | 2.29 |

**Table 2.**Summary statistics from the comparison of PPP ZTD results using two inputs (IGS01 RT vs. IGS final)

G-Nut/Tefnut PPP Input Precise Products | ZTD Reference Product | Bias (mm] | STD (mm) | RMS (mm] |
---|---|---|---|---|

IGS final (SP3 files) | GOP final (Bernese/DD) | +0.9 | 5.1 | 5.2 |

IGS01 RT corrections | GOP final (Bernese/DD) | +2.4 | 5.8 | 6.4 |

IGS final (SP3 files) | GFZ final (EPOS/PPP) | +0.4 | 4.1 | 4.2 |

IGS01 RT corrections | GFZ final (EPOS/PPP) | +2.8 | 4.9 | 5.7 |

**Table 3.**Summary statistics over 18 stations from routine RT product using GPS and GPS + GLO data w.r.t. EUREF reprocessing.

Solution Description | BIAS (mm) mean ± sdev | SDEV (mm) mean ± sdev | RMSE (mm) mean ± sdev |
---|---|---|---|

GOPQ—GPS+GLO | 1.8 ± 2.9 | 6.7 ± 1.2 | 7.5 ± 2.5 |

GOPR—GPS | 2.0 ± 2.8 | 7.2 ± 1.0 | 7.9 ± 1.5 |

**Table 4.**Summary statistics of three processing strategies and six ZTD solutions compared to EUREF combined tropospheric product.

Solution | Software | Strategy Description | Latency | Mean BIAS | Mean SDEV |
---|---|---|---|---|---|

RT PPP (HR:59) | G-Nut/Tefnut | Kalman filter in simulated real-time solution | <5 min | 2.4 mm | 5.7 mm |

NRT PPP (HR:00) | G-Nut/Tefnut | Hourly backward smoothing in real time | ~60 min | 2.5 mm | 4.6 mm |

PP PPP (HR:59) | G-Nut/Tefnut | Kalman filter in offline processing, IGS final | <5 min | 0.1 mm | 4.7 mm |

PP PPP (HR:00) | G-Nut/Tefnut | Hourly backward smoothing with IGS final | ~60 min | −0.2 mm | 3.6 mm |

NRT DD (HR:59) | Bernese V52 | Last ZTD of hourly PW linear LSQ | ~90 min | 0.4 mm | 4.9 mm |

NRT DD (HR:00) | Bernese V52 | First ZTD of hourly PW linear LSQ | ~30 min | 0.2 mm | 3.7 mm |

Station Pair | GNSS | BIAS ± SDEV ZTD (mm) | BIAS ± SDEV N-GRD (mm) | BIAS ± SDEV E-GRD (mm) |
---|---|---|---|---|

ZIM2-ZIMJ | G | +2.8 ± 1.4 | +0.08 ± 0.17 | −0.02 ± 0.14 |

ZIM2-ZIMJ | GR | +2.4 ± 1.3 | +0.02 ± 0.14 | −0.02 ± 0.12 |

ZIM2-ZIMJ | GRE | +2.0 ± 1.3 | +0.03 ± 0.14 | −0.04 ± 0.13 |

MAT1-MATE | G | −0.5 ± 2.4 | −0.03 ± 0.18 | +0.18 ± 0.25 |

MAT1-MATE | GR | +0.1 ± 2.3 | +0.01 ± 0.15 | +0.14 ± 0.22 |

MAT1-MATE | GRE | +0.1 ± 2.2 | +0.00 ± 0.15 | +0.13 ± 0.21 |

Station Pair | GNSS | BIAS ± SDEV ZTD (mm) | BIAS ± SDEV N-GRD (mm) | BIAS ± SDEV E-GRD (mm) |
---|---|---|---|---|

ZIM2-ZIMJ | G | +2.7 ± 1.1 | +0.11 ± 0.12 | −0.02 ± 0.10 |

ZIM2-ZIMJ | GR | +2.3 ± 1.0 | +0.06 ± 0.11 | −0.02 ± 0.09 |

ZIM2-ZIMJ | GRE | +1.9 ± 1.0 | +0.07 ± 0.12 | −0.04 ± 0.09 |

MAT1-MATE | G | −1.3 ± 1.6 | −0.04 ± 0.15 | +0.22 ± 0.19 |

MAT1-MATE | GR | +0.6 ± 1.4 | +0.00 ± 0.12 | +0.16 ± 0.17 |

MAT1-MATE | GRE | +0.5 ± 1.4 | -0.01 ± 0.11 | +0.16 ± 0.16 |

**Table 7.**Summary statistics for dual stations using different products: real-time (IGS01, IGS03) and final MGEX (COM, GBM), the Kalman filter and, in addition, the backward smoothing.

Station Pair | Products | Kalman/Smoother ZTD SDEV (mm) | Kalman/Smoother N-GRD SDEV (mm) | Kalman/Smoother E-GRD SDEV (mm) |
---|---|---|---|---|

ZIM2-ZIMJ | IGS01 | 3.3/2.7 | 0.34/0.26 | 0.32/0.25 |

ZIM2-ZIMJ | IGS03 | 2.3/1.9 | 0.25/0.23 | 0.25/0.21 |

ZIM2-ZIMJ | COM MGEX | 1.4/1.1 | 0.17/0.12 | 0.14/0.10 |

ZIM2-ZIMJ | GFZ MGEX | 1.4/1.1 | 0.18/0.12 | 0.14/0.10 |

MAT1-MATE | IGS01 | 4.8/3.6 | 0.41/0.36 | 0.42/0.33 |

MAT1-MATE | IGS03 | 3.4/2.6 | 0.31/0.33 | 0.39/0.32 |

MAT1-MATE | COM MGEX | 2.5/1.6 | 0.18/0.15 | 0.25/0.19 |

MAT1-MATE | GFZ MGEX | 2.5/1.6 | 0.19/0.15 | 0.24/0.19 |

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**MDPI and ACS Style**

Douša, J.; Václavovic, P.; Zhao, L.; Kačmařík, M.
New Adaptable All-in-One Strategy for Estimating Advanced Tropospheric Parameters and Using Real-Time Orbits and Clocks. *Remote Sens.* **2018**, *10*, 232.
https://doi.org/10.3390/rs10020232

**AMA Style**

Douša J, Václavovic P, Zhao L, Kačmařík M.
New Adaptable All-in-One Strategy for Estimating Advanced Tropospheric Parameters and Using Real-Time Orbits and Clocks. *Remote Sensing*. 2018; 10(2):232.
https://doi.org/10.3390/rs10020232

**Chicago/Turabian Style**

Douša, Jan, Pavel Václavovic, Lewen Zhao, and Michal Kačmařík.
2018. "New Adaptable All-in-One Strategy for Estimating Advanced Tropospheric Parameters and Using Real-Time Orbits and Clocks" *Remote Sensing* 10, no. 2: 232.
https://doi.org/10.3390/rs10020232