# Accuracy Evaluation of Ionospheric Delay from Multi-Scale Reference Networks and Its Augmentation to PPP during Low Solar Activity

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## Abstract

**:**

## 1. Introduction

## 2. Methods

## 3. Data and Models

## 4. Results

#### 4.1. Convergence Analysis of Ambiguity-Float and Ambiguity-Fixed PPP

#### 4.2. Ionospheric Delays Retrival from the Ambiguity-Fixed PPP

#### 4.3. Using of CODE Global Ionosphere Products for PPP Ambiguity Resolution

#### 4.4. PPP-RTK Using Ionospheric Delay from Multi-Scale Networks

## 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 1.**Un-differenced satellite narrow-lane phase biases for all GPS (

**left**) and Galileo (

**right**) satellites. Each color represents a different satellite.

**Figure 3.**Comparison of the ambiguity fixing rate of the static PPP using GFZ/GOP and CNES products at different stations.

**Figure 4.**Horizontal positioning errors achieved from PPP ambiguity-float (

**left**) and ambiguity-fixed (

**right**) solution using GFZ/GOP products: all errors (green) and errors at the 50% percentile (red).

**Figure 5.**Horizontal positioning errors achieved from PPP ambiguity-float (

**left**) and ambiguity-fixed (

**right**) solution using CNES products: all errors (green), and errors at the 50% percentile (red).

**Figure 6.**The indices of Kp during the period of 2019. The selected period for the analysis are represented as the gray area between two vertical dashed lines.

**Figure 7.**Single-difference ionospheric residuals from ambiguity float PPP at two collocated stations.

**Figure 8.**Single-difference ionospheric residuals from ambiguity fixed PPP at two collocated stations and the corresponding Kp index (bottom).

**Figure 9.**Single-difference ionospheric residuals from ambiguity float (

**top**), ambiguity fixed (

**middle**) PPP at two collocated stations and the corresponding Kp index (

**bottom**).

**Figure 10.**RMS of the ionospheric delay interpolated from IONEX product w.r.t. the ionospheric delays computed from PPP-AR as reference on DOY 001, 2019.

**Figure 11.**Horizontal positioning errors (50% percentile) of hourly PPP solutions using different a priori constraints for external ionospheric corrections.

**Figure 16.**Position errors of ambiguity-fixed PPP without external ionospheric delays and with ionospheric corrections estimated at nearby station GOPE.

**Figure 17.**Positioning errors for ambiguity-fixed PPP using ionospheric corrections from nearby station GOPE and corrections interpolated from selected reference stations.

**Figure 19.**Position errors for ambiguity-fixed PPP without external ionospheric delays and using ionospheric corrections interpolated from stations in distances above 209 km.

**Figure 21.**Performance of Galileo-only ambiguity-fixed PPP without and with external ionospheric corrections.

Modeling | Strategies |
---|---|

Observation combination | Raw double-frequency |

Orbits/Clocks/Phase bias | GFZ final orbit/clock products, estimated biases CNES real-time orbit/clock/biases products |

Ionosphere corrections | Iono-No: estimated as unknown parameter Iono-Interp: Interpolated from network side |

Zenith troposphere delay | Estimated as random walk parameter |

Satellite DCB | Corrected using products provided by DLR [24] |

Receiver DCB | Estimated as random unknown parameter |

Elevation cutoff | 7° |

Sampling | 30 s |

Attitude corrections | Steering attitude model for GFZ products Nominal attitude model for CNES PPP |

Ambiguity resolution | Partial ambiguity resolution |

Coordinates | Service side: Static User side: Kinematic |

Station | Receiver Type | Antenna Type | Lon | Lat | Dist. (m) |
---|---|---|---|---|---|

YARR | SEPT POLARX5 | LEIAT504 NONE | 115.3472 | 29.0465 | 20.2 |

YAR3 | SEPT POLARX5 | LEIAR25 NONE | |||

GOP6 | SEPT POLARX5 | LEIAR25.R4 LEIT | 14.7856 | 49.9137 | 4.1 |

GOPE | TRIMBLE SPS855 | TPSCR.G3 TPSH | |||

PRD2 | TPS NET-G5 | NOV750.R4 NONE | −114.2929 | 50.8713 | 77.6 |

PRD3 | TPS NET-G5 | TPSCR.G3 NONE |

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**MDPI and ACS Style**

Zhao, L.; Douša, J.; Václavovic, P.
Accuracy Evaluation of Ionospheric Delay from Multi-Scale Reference Networks and Its Augmentation to PPP during Low Solar Activity. *ISPRS Int. J. Geo-Inf.* **2021**, *10*, 516.
https://doi.org/10.3390/ijgi10080516

**AMA Style**

Zhao L, Douša J, Václavovic P.
Accuracy Evaluation of Ionospheric Delay from Multi-Scale Reference Networks and Its Augmentation to PPP during Low Solar Activity. *ISPRS International Journal of Geo-Information*. 2021; 10(8):516.
https://doi.org/10.3390/ijgi10080516

**Chicago/Turabian Style**

Zhao, Lewen, Jan Douša, and Pavel Václavovic.
2021. "Accuracy Evaluation of Ionospheric Delay from Multi-Scale Reference Networks and Its Augmentation to PPP during Low Solar Activity" *ISPRS International Journal of Geo-Information* 10, no. 8: 516.
https://doi.org/10.3390/ijgi10080516