# GPS/BDS-2/Galileo Precise Point Positioning Ambiguity Resolution Based on the Uncombined Model

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. Basic Code and Carrier Phase Observation Equation

#### 2.2. Uncombined PPP with Ambiguity Resolution

**X**for the uncombined multi-GNSS PPP model is presented as:

#### 2.3. FCB Estimation

## 3. Data and Processing Strategy

## 4. Analysis Results

#### 4.1. ISB Stability

#### 4.2. FCB Results

#### 4.2.1. GPS FCB Results

#### 4.2.2. BDS-2 FCB Results

#### 4.2.3. Galileo FCB Results

#### 4.3. Positioning Results

#### 4.3.1. PPP AR Accuracy

#### 4.3.2. Convergence Time

#### 4.3.3. Ambiguity Success Fixing Rate

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Distribution of the 24 stations that were used for the precise point positioning (PPP) processing and the inter-system bias (ISB) analysis.

**Figure 2.**One day (3 September 2019) ISB means for BDS-2 and Galileo at the 24 stations. Stations with different receivers are separated by a red dashed line and are marked as “A” (JAVAD TRE_3 DELTA), “B” (JAVAD TRE_3), “C” (SEPT POLARX5), “D” (TRIMBLE NETR9), and “E” (TRIMBLE ALLOY).

**Figure 3.**One day (3 September 2019) ISB series for BDS-2, first with the mean removed (left panel), and then, with both the mean and the common trend term removed (right panel).

**Figure 5.**STD of each station’s one day (3 September 2019) ISB series for BDS-2 and Galileo. The STD of the original ISB series for BDS-2 is marked as “BDS1”, and the new solution with the variation trend removed is marked as “BDS2.”.

**Figure 6.**Global distribution of the stations in the fractional cycle bias (FCB) estimation network for GPS (yellow), BDS-2 (red), and Galileo (blue).

**Figure 7.**Distribution of the a posteriori residuals of the GPS FCB estimation with integer linear-combined float ambiguities. RMS, root mean square.

**Figure 8.**One day (3 September 2019) GPS FCB time series of the narrow-lane (NL) and wide-lane (WL) combinations.

**Figure 9.**STD of the one day (3 September 2019) GPS FCB time series for each satellite NL and WL combination.

**Figure 10.**Distribution of the a posteriori residuals of the BDS-2 FCB estimation with integer linear-combined float ambiguities.

**Figure 11.**One day (3 September 2019) BDS-2 FCB time series of the NL and WL combinations for the inclined geosynchronous orbit (IGSO) and medium Earth orbit (MEO) satellites.

**Figure 12.**STD of the one day (3 September 2019) BDS-2 FCB time series for each satellite NL and WL combination.

**Figure 13.**Distribution of the a posteriori residuals of the Galileo FCB estimation with integer linear-combined float ambiguities.

**Figure 15.**STD of the one day (3 September 2019) Galileo FCB time series for each satellite NL and WL combination.

**Figure 16.**Averaged RMSs of the positioning for “G”, “GC”, “GE”, and “GCE” with float and ambiguity resolution (AR) solutions in the eastward, northward, upward, and three-dimensional (3D) directions for 3 h static PPPs on 3 September 2019.

**Figure 17.**Convergence of the positioning bias for “G”, “GC”, “GE”. and “GCE” systems in the ambiguity-float and ambiguity-fixed solutions with 1.5 h data.

Receiver Type | Sum of Stations | Mean (ns) | STD (ns) | ||
---|---|---|---|---|---|

BDS-2 | Galileo | BDS-2 | Galileo | ||

A | 2 | 43.16 | 2.85 | 2.38 | 2.46 |

B | 3 | 40.77 | 8.85 | 2.12 | 1.85 |

C | 8 | 22.32 | 11.99 | 5.48 | 7.76 |

D | 9 | 84.32 | 29.64 | 5.67 | 8.75 |

E | 2 | 119.54 | 37.20 | 14.45 | 12.18 |

System | 3D Positioning Accuracy (cm) at Different Processing Intervals | ||||||
---|---|---|---|---|---|---|---|

10 min | 20 min | 30 min | 60 min | 120 min | 180 min | ||

G | Float | 19.8 | 11.2 | 7.8 | 4.3 | 2.5 | 1.9 |

AR | 10.9 | 3.9 | 2.4 | 1.7 | 1.4 | 1.3 | |

Improvement | 45% | 65% | 69% | 61% | 43% | 30% | |

GC | Float | 19.7 | 10.2 | 6.5 | 3.7 | 2.4 | 1.8 |

AR | 9.0 | 2.7 | 1.8 | 1.6 | 1.4 | 1.2 | |

Improvement | 54% | 74% | 72% | 57% | 44% | 32% | |

GE | Float | 15.6 | 8.4 | 5.7 | 3.2 | 2.1 | 1.7 |

AR | 6.9 | 2.6 | 1.8 | 1.5 | 1.3 | 1.2 | |

Improvement | 55% | 69% | 69% | 53% | 38% | 28% | |

GCE | Float | 15.4 | 7.9 | 5.2 | 3.0 | 2.0 | 1.6 |

AR | 5.7 | 2.0 | 1.6 | 1.4 | 1.2 | 1.1 | |

Improvement | 63% | 75% | 70% | 53% | 39% | 30% |

System | Float (min) | AR (min) | Improvement |
---|---|---|---|

G | 22 | 10.5 | 52% |

GC | 20.5 | 9.5 | 54% |

GE | 16.5 | 8 | 52% |

GCE | 16 | 7.5 | 53% |

Time (min) | Ambiguity Success Fixing Rate | |||
---|---|---|---|---|

G | GC | GE | GCE | |

10 | 75.5% | 94.3% | 86.5% | 99.0% |

20 | 91.1% | 99.0% | 96.4% | 99.0% |

30 | 93.8% | 100.0% | 97.4% | 100.0% |

60 | 97.9% | 99.5% | 100.0% | 99.5% |

120 | 99.5% | 100.0% | 99.5% | 100.0% |

180 | 97.9% | 99.5% | 99.5% | 100.0% |

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## Share and Cite

**MDPI and ACS Style**

Wang, J.; Huang, G.; Zhang, Q.; Gao, Y.; Gao, Y.; Luo, Y.
GPS/BDS-2/Galileo Precise Point Positioning Ambiguity Resolution Based on the Uncombined Model. *Remote Sens.* **2020**, *12*, 1853.
https://doi.org/10.3390/rs12111853

**AMA Style**

Wang J, Huang G, Zhang Q, Gao Y, Gao Y, Luo Y.
GPS/BDS-2/Galileo Precise Point Positioning Ambiguity Resolution Based on the Uncombined Model. *Remote Sensing*. 2020; 12(11):1853.
https://doi.org/10.3390/rs12111853

**Chicago/Turabian Style**

Wang, Jin, Guanwen Huang, Qin Zhang, Yang Gao, Yuting Gao, and Yiran Luo.
2020. "GPS/BDS-2/Galileo Precise Point Positioning Ambiguity Resolution Based on the Uncombined Model" *Remote Sensing* 12, no. 11: 1853.
https://doi.org/10.3390/rs12111853