# Improving the Performance of Galileo Uncombined Precise Point Positioning Ambiguity Resolution Using Triple-Frequency Observations

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. UDUC-PPP Observation Equation

#### 2.2. Extra-Wide-Lane Ambiguity Resolution

#### 2.3. Wide-Lane Ambiguity Resolution

#### 2.4. Narrow-Lane Ambiguity Resolution

#### 2.5. Comparison of Dual- and Triple-Frequency UDUC-PPP AR

## 3. Experiment and Results

#### 3.1. Data Processing Strategy and Original UPD Estimation

#### 3.2. Performance Comparison of Dual- and Triple-Frequency Float PPP

#### 3.3. Performance Comparison of Dual- and Triple-Frequency PPP AR

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Linear Combinations of the Original Measurements Theory

## References

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**Figure 1.**A flowchart of the dual- and triple-frequency un-differenced and uncombined precise point positioning (UCUD-PPP) ambiguity resolution.

**Figure 2.**The distribution of the Galileo reference network and user stations. The red stars denote the reference stations for estimating the uncalibrated phase delays (UPDs); the blue stars denote the user stations for testing the performance of PPP.

**Figure 3.**The time series of UPDs for each epoch on day of year (DOY) 201, 2018. (1, 0, 0), (0, 1, 0) and (0, 0, 1) UPD denote the original UPDs of Galileo E1, E5a and E5b signals, respectively. (0, 1, −1) and (1, 0, −1) denote Galileo EWL and WL UPDs.

**Figure 4.**The time series of the position differences for the dual-frequency and triple-frequency float solutions with 0.6-h observations at CPVG station on DOY 201, 2018.

**Figure 5.**The averaged positioning errors of all the test stations in the east, north and up components for dual-frequency and triple-frequency float solutions during the initialization on DOY 201, 2018.

**Figure 6.**The time series of the position differences for the triple-frequency float solutions, dual-frequency WL-NL AR and triple-frequency EWL-WL-NL AR with 1.5-h observations at ASCG station on DOY 201, 2018.

**Figure 7.**The time-to-first-fix (TTFF) of the dual-frequency AR and triple-frequency AR, as well as the convergence time of the triple-frequency float solutions at the user stations on DOY 201, 2018.

**Figure 8.**The RMS of the positioning errors with a 2-h observation for the dual-frequency and triple-frequency AR, as well as the triple-frequency float solutions (unit: cm).

GNSS System | Frequency (MHz) | Carrier Phase | Pseudo Range |
---|---|---|---|

E1/1575.42 | L1C/L1X | C1C/C1X | |

E5a/1176.45 | L5X/L5Q | C5X/C5Q | |

Galileo | E5b/1207.140 | L7X/L7Q | C7X/C7Q |

E5/1191.795 | L8X/L8Q | C8X/C8Q | |

E6/1278.75 | L6C/L6X | C6C/C6X |

Item | Strategies |
---|---|

Estimator | Sequential least square estimator |

Observations | Original triple-frequency carrier-phase and pseudo-range observations |

Signal selection | Galileo: E1/E5a/E5b |

Sampling rate | 30 s |

Elevation cutoff | 15° |

Observations weight | Elevation-dependent weight |

Ionospheric delay | Estimated as random-walk process |

Tropospheric delay | Dry component: corrected with the Saastamoinen) model [30] |

Wet component: estimated as a random-walk process, a Global Mapping Function (GMF) mapping function | |

Receiver clock | Estimated as white noise |

Station displacement | Corrected by IERS Convention 2010, including Solid Earth tide, |

pole tide and ocean tide loading [31] | |

Satellite PCO/PCV | Corrected using an IGS14 ANTEX file |

Receiver PCO/PCV | Corrected using GPS values |

Phase-windup effect | Corrected [32] |

Relativistic effect | Applied |

Station coordinate | Estimated as constants (Static PPP), a white noise (kinematic PPP) |

**Table 3.**The RMS of the positioning errors for three groups of PPP solutions with 2-h observations for all test stations (unit: cm).

Triple Float | WL-NL AR | EWL-WL-NL AR | |
---|---|---|---|

E | 0.36 | 0.28 | 0.17 |

N | 0.24 | 0.21 | 0.15 |

U | 0.46 | 0.38 | 0.29 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Liu, G.; Zhang, X.; Li, P.
Improving the Performance of Galileo Uncombined Precise Point Positioning Ambiguity Resolution Using Triple-Frequency Observations. *Remote Sens.* **2019**, *11*, 341.
https://doi.org/10.3390/rs11030341

**AMA Style**

Liu G, Zhang X, Li P.
Improving the Performance of Galileo Uncombined Precise Point Positioning Ambiguity Resolution Using Triple-Frequency Observations. *Remote Sensing*. 2019; 11(3):341.
https://doi.org/10.3390/rs11030341

**Chicago/Turabian Style**

Liu, Gen, Xiaohong Zhang, and Pan Li.
2019. "Improving the Performance of Galileo Uncombined Precise Point Positioning Ambiguity Resolution Using Triple-Frequency Observations" *Remote Sensing* 11, no. 3: 341.
https://doi.org/10.3390/rs11030341