# Galileo Augmenting GPS Single-Frequency Single-Epoch Precise Positioning with Baseline Constrain for Bridge Dynamic Monitoring

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## Abstract

**:**

## 1. Introduction

## 2. SFSE Double-Differenced GPS/Galileo Mathematical Model

#### 2.1. Single GPS/Galileo Code and Phase Observation Equations

#### 2.2. Integrated GPS/Galileo Code and Phase Observation Equations

#### 2.2.1. GPS/Galileo Loosely Combined Mode (LCM)

#### 2.2.2. GPS/Galileo Tightly Combined Mode (TCM) with Differential Inter-system Biases (DISBs)

#### 2.2.3. GPS/Galileo Tightly Combined Mode (TCM) without Inter-System Biases (ISBs)

#### 2.3. Stochastic Model

#### 2.4. Baseline Length Constraint DD Positioning Method

## 3. Monitoring Data Collecting for the Forth Bridge

#### 3.1. Data Collecting

#### 3.2. Sky Plots

#### 3.3. Availability and PDOP

## 4. Galileo Augmenting GPS SFSE Precise Positioning Experiment

#### 4.1. Evaluation Index

#### 4.2. Experiment Analysis

#### 4.2.1. Experiment 1

#### 4.2.2. Experiment 2

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Abbreviation | Full name |

ADOP | ambiguity dilution of precision |

Asrt | actual success rate |

BCS | Bridge Coordinate System |

BDS | BeiDou Satellite Navigation System |

Bsrt | bootstrapped success rate |

BSSD | between-satellite single-difference |

C/N0 | carrier-to-noise density ratio |

C-GPS | GPS with baseline constraint |

C-GPS/Galileo | GPS/Galileo with baseline constraint |

DD | double-differenced |

DISBs | inter-system biases |

FFT | Fast Fourier Transformation |

Galileo | Galileo Satellite Navigation System |

GeoSHM | The GNSS and Earth Observation for Structural Health Monitoring |

GGTO | GPS-to-Galileo Time Offset |

GNSS | Global Navigation Satellite System |

GPS | Global Positioning System |

GPST | GPS Time |

GST | Galileo System Time |

IOV | In-Orbit Validation |

LCM | loosely combined mode |

NOS | number of satellites |

PDOP | Position Dilution of Precision |

PNT | positioning, navigation and timing |

P-num | the pass rate of visibility |

P-PDOP | the pass rate of PDOP |

QZSS | Quasi-Zenith Satellite System |

RNP | required navigation performance |

RTK | Real-Time Kinematic |

SFSE | single-frequency single-epoch |

TCM | tightly combined mode |

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**Figure 3.**Sky plots (azimuth vs. elevation) for the various satellites systems at station shm1 on 2 May 2018: (

**a**) global positioning system (GPS); (

**b**) Galileo; and, (

**c**) GPS/Galileo.

**Figure 4.**The satellite visibility, Position Dilution of Precision (PDOP), and their pass rate curves of GPS and GPS/Galileo under different cutoff angles (°): (

**a**) The satellite visibility; (

**b**) PDOP; (

**c**) Pass rate of GPS under different cutoff angles (

**d**) Pass rate of GPS/Galileo under different cutoff angles.

**Figure 5.**Position deviation of different strategies for baseline shm1-shm4: (

**a**) GPS, (

**b**) GPS with baseline constraint (C-GPS), (

**c**) GPS/Galileo, and, (

**d**) C-GPS/Galileo.

**Figure 6.**Mean NOS, ADOP, and bootstrapped success rates of different strategies for baseline shm1-shm4: (

**a**) GPS, (

**b**) C-GPS, (

**c**) GPS/Galileo, and (

**d**) C-GPS/Galileo.

**Figure 7.**Position deviation of different strategies for baseline shm1-shm2: (

**a**) GPS, (

**b**) C-GPS, (

**c**) GPS/Galileo, and (

**d**) C-GPS/Galileo.

**Figure 8.**Mean NOS, ADOP, and bootstrapped success rates of different strategies for baseline shm1-shm2: (

**a**) GPS, (

**b**) C-GPS, (

**c**) GPS/Galileo, and (

**d**) C-GPS/Galileo.

Station | Location | Receiver | Sampling (Hz) | Frequency Band | Baseline | Baseline Length (m) |
---|---|---|---|---|---|---|

shm1 | Leica GR10 | 10 | L1, E1 | |||

shm2 | Middle span | Leica GR10 | 10 | L1, E1 | shm1-shm2 | 1529 |

shm4 | South tower | Leica GR10 | 10 | L1, E1 | shm1-shm4 | 1033 |

**Table 2.**The visibility, PDOP and their pass rate of GPS and GPS/Galileo under different cutoff angles (°).

elevation/° | 0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | |
---|---|---|---|---|---|---|---|---|---|---|

GPS | num | 12.0 | 10.6 | 8.9 | 7.7 | 6.7 | 5.9 | 5.1 | 4.4 | 3.6 |

P-num | 100% | 100% | 100% | 100% | 100% | 100% | 95.9% | 78.7% | 44.8% | |

PDOP | 1.336 | 1.545 | 1.883 | 2.365 | 3.277 | 4.929 | 7.146 | 10.25 | 15.19 | |

P-PDOP | 100% | 100% | 100% | 99.6% | 96.5% | 82.2% | 61.5% | 39.7% | 16.8% | |

GPS/Galileo | num | 17.7 | 15.9 | 13.6 | 11.6 | 10.1 | 8.8 | 7.7 | 6.6 | 5.4 |

P-num | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 100% | 98.9% | |

PDOP | 1.084 | 1.241 | 1.48 | 1.854 | 2.416 | 3.063 | 4.27 | 6.536 | 11.3 | |

P-PDOP | 100% | 100% | 100% | 100% | 99.5% | 98.3% | 89.5% | 71.7% | 30.8% |

**Table 3.**NOS, PDOP, ADOP, success rate and position deviation of different strategies for baseline shm1-shm4.

NOS | PDOP | ADOP | Asrt | Bsrt | Horizontal Deviation/cm | Up Deviation/cm | |
---|---|---|---|---|---|---|---|

GPS | 8.8 | 1.93 | 0.465 | 0.7501 | 0.9363 | 1.36 | 1.18 |

C-GPS | 8.8 | 1.93 | 0.389 | 0.9510 | 0.9709 | 1.29 | 1.18 |

GPS/Galileo | 11.9 | 1.50 | 0.252 | 0.9547 | 0.9919 | 1.25 | 1.06 |

C-GPS/Galileo | 11.9 | 1.50 | 0.243 | 0.9912 | 0.9956 | 1.25 | 1.06 |

**Table 4.**NOS, PDOP, ADOP, success rate and position deviation of different strategies for baseline shm1-shm2.

NOS | PDOP | ADOP | Asrt | Bsrt | Horizontal Deviation/cm | Up Accuracy/cm | |
---|---|---|---|---|---|---|---|

GPS | 8.9 | 1.89 | 0.453 | 0.9324 | 0.9499 | 11.57 | 3.23 |

C-GPS | 8.9 | 1.89 | 0.437 | 0.9757 | 0.9619 | 11.66 | 3.24 |

GPS/ Galileo | 12.3 | 1.48 | 0.250 | 0.9842 | 0.9958 | 11.67 | 3.17 |

C-GPS/Galileo | 12.3 | 1.48 | 0.247 | 0.9976 | 0.999 | 11.78 | 3.20 |

Station Name | XB (Longitudinal/Hz) | YB (Lateral/Hz) | ZB (Height/Hz) |
---|---|---|---|

Shm2 | 0.151 | 0.065 0.268 | 0.105 0.205 0.268 |

Shm4 | 0.105 0.151 0.183 | 0.183 | 0.183 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, Q.; Ma, C.; Meng, X.; Xie, Y.; Psimoulis, P.; Wu, L.; Yue, Q.; Dai, X.
Galileo Augmenting GPS Single-Frequency Single-Epoch Precise Positioning with Baseline Constrain for Bridge Dynamic Monitoring. *Remote Sens.* **2019**, *11*, 438.
https://doi.org/10.3390/rs11040438

**AMA Style**

Zhang Q, Ma C, Meng X, Xie Y, Psimoulis P, Wu L, Yue Q, Dai X.
Galileo Augmenting GPS Single-Frequency Single-Epoch Precise Positioning with Baseline Constrain for Bridge Dynamic Monitoring. *Remote Sensing*. 2019; 11(4):438.
https://doi.org/10.3390/rs11040438

**Chicago/Turabian Style**

Zhang, Qiuzhao, Chun Ma, Xiaolin Meng, Yilin Xie, Panagiotis Psimoulis, Laiyi Wu, Qing Yue, and Xinjun Dai.
2019. "Galileo Augmenting GPS Single-Frequency Single-Epoch Precise Positioning with Baseline Constrain for Bridge Dynamic Monitoring" *Remote Sensing* 11, no. 4: 438.
https://doi.org/10.3390/rs11040438