# Initial Assessment of Precise Point Positioning with LEO Enhanced Global Navigation Satellite Systems (LeGNSS)

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## Abstract

**:**

## 1. Introduction

## 2. The LeGNSS Constellation

## 3. Simulation Configuration

#### 3.1. The Simulation Software

_{s}, and k denote the satellite, receiver, carrier frequency, and epoch, respectively. ${\rho}_{r,k}^{s}$ denotes the geometric distance between the phase centers of satellite and receiver antenna at the signal transmitting and receiving time. $\Delta {t}_{r,k}$ and $\Delta {t}_{k}^{s}$ are the clock biases of receiver and satellite; ${T}_{r,k}^{s}$ is the tropospheric delay; ${I}_{r,{j}_{s},k}^{s}$ is the ionospheric delay at frequency j

_{s}; ${b}_{r,{j}_{s}}$ and ${b}_{{j}_{s}}^{s}$ are code biases of receiver and satellite, respectively; ${\delta}_{r,{j}_{s}}$ and ${\delta}_{{j}_{s}}^{s}$ are the receiver- and satellite-dependent uncalibrated phase delay (UPD) [5]; ${N}_{r,{j}_{s}}^{s}$ is the integer ambiguity with the wavelength ${\lambda}_{{j}_{s}}$; and ${\epsilon}_{{P}_{r,{j}_{s},k}^{s}}$ and ${\epsilon}_{{L}_{r,{j}_{s},k}^{s}}$ denote the measurement noises of code and phase.

#### 3.2. The Adaption of PANDA Software

#### 3.3. Setup

## 4. Assessment and Analysis of LeGNSS Precise Positioning

#### 4.1. Satellite Visibility

#### 4.2. Assessment and Analysis of LeGNSS PPP Performance

#### 4.3. Statistical Analysis of Convergence Time on a Global Scale

## 5. Discussion

## 6. Conclusions

- (1)
- The LEO constellation can improve the availability of the current GNSS system, especially in the polar areas, since LEO are usually polar satellites. With 66 Iridium satellites, it is difficult to provide LEO-only positioning service since there are not enough satellites at medium and low latitudes.
- (2)
- LEO satellites are moving quite fast, flying overhead in minutes compared to the GNSS satellites in hours, which gives rise to improving the geometric condition of ground stations, resulting in the fast convergence time of PPP.
- (3)
- The convergence time of combined G/C/L can be shortened to 5 min in most of the areas of the world with 5 s data while, as far as we are concerned, it is impossible with GNSS to achieve such quick convergence even with 1 s data.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Zumberge, J.F.; Heflin, M.B.; Jefferson, D.C.; Watkins, M.M.; Webb, F.H. Precise point positioning for the efficient and robust analysis of GPS data from large networks. J. Geophys. Res. Solid Earth
**1997**, 102, 5005–5017. [Google Scholar] [CrossRef][Green Version] - Bisnath, S.; Gao, Y. Current state of precise point positioning and future prospects and limitations. In Observing Our Changing Earth; Sideris, M.G., Ed.; Springer: Berlin/Heidelberg, Germany, 2009; Volume 133, pp. 615–623. [Google Scholar]
- Dow, J.M.; Neilan, R.E.; Rizos, C. The International GNSS Service in a changing landscape of Global Navigation Satellite Systems. J. Geodesy
**2009**, 83, 191–198. [Google Scholar] [CrossRef][Green Version] - Collins, P.; Lahaye, F.; Héroux, P.; Bisnath, S. Precise point positioning with ambiguity resolution using the decoupled clock model. In Proceedings of the ION GNSS 2008, Savannah, GA, USA, 16–19 September 2008; pp. 1315–1322. [Google Scholar]
- Ge, M.; Gendt, G.; Rothacher, M.; Shi, C.; Liu, J. Resolution of GPS carrier-phase ambiguities in Precise Point Positioning (PPP) with daily observations. J. Geodesy
**2008**, 82, 389–399. [Google Scholar] [CrossRef] - Geng, J.; Meng, X.; Dodson, A.H.; Ge, M.; Teferle, F.N. Rapid re-convergences to ambiguity-fixed solutions in precise point positioning. J. Geodesy
**2010**, 84, 705–714. [Google Scholar] [CrossRef][Green Version] - Li, B.; Shen, Y.; Feng, Y. Fast GNSS ambiguity resolution as an ill-posed problem. J. Geodesy
**2010**, 84, 683–698. [Google Scholar] [CrossRef] - Li, X.; Zhang, X.; Ge, M. Regional reference network augmented precise point positioning for instantaneous ambiguity resolution. J. Geodesy
**2011**, 85, 151–158. [Google Scholar] [CrossRef] - Geng, J.; Bock, Y. Triple-frequency GPS precise point positioning with rapid ambiguity resolution. J. Geodesy
**2013**, 87, 449–460. [Google Scholar] [CrossRef] - Li, M.; Qu, L.; Zhao, Q.; Guo, J.; Su, X.; Li, X. Precise point positioning with the BeiDou navigation satellite system. Sensors
**2014**, 14, 927–943. [Google Scholar] [CrossRef] [PubMed] - Gu, S.; Lou, Y.; Shi, C.; Liu, J. BeiDou phase bias estimation and its application in precise point positioning with triple-frequency observable. J. Geodesy
**2015**, 89, 979–992. [Google Scholar] [CrossRef] - Cai, C.; Gao, Y. Performance analysis of precise point positioning based on combined GPS and GLONASS. In Proceedings of the ION GNSS 2007, Fort Worth, TX, USA, 25–28 September 2007; pp. 858–865. [Google Scholar]
- Li, P.; Zhang, X. Integrating GPS and GLONASS to accelerate convergence and initialization times of precise point positioning. GPS Solut.
**2014**, 18, 461–471. [Google Scholar] [CrossRef] - Li, X.; Zhang, X.; Ren, X.; Fritsche, M.; Wickert, J.; Schuh, H. Precise positioning with current multi-constellation Global Navigation Satellite Systems: GPS, GLONASS, Galileo and BeiDou. Sci. Rep.
**2015**, 5, 8328. [Google Scholar] [CrossRef] [PubMed][Green Version] - Cai, C.; Gao, Y. Modeling and assessment of combined GPS/GLONASS precise point positioning. GPS Solut.
**2012**, 17, 223–236. [Google Scholar] [CrossRef] - Geng, J.; Shi, C. Rapid initialization of real-time PPP by resolving undifferenced GPS and GLONASS ambiguities simultaneously. J Geodesy
**2017**, 91, 361–374. [Google Scholar] [CrossRef] - China Satellite Navigation Office (CSNO). BeiDou Navigation Satellite System Signal in Space Interface Control Document Open Service Signal (Version 2.1); China Satellite Navigation Office: Beijing, China, 2016. [Google Scholar]
- Montenbruck, O.; Steigenberger, P.; Prange, L.; Deng, Z.; Zhao, Q.; Perosanz, F.; Romero, I.; Noll, C.; Stürze, A.; Weber, G.; et al. The Multi-GNSS Experiment (MGEX) of the International GNSS Service (IGS)—Achievements, prospects and challenges. Adv. Space Res.
**2017**, 59, 1671–1697. [Google Scholar] [CrossRef] - Li, T.; Wang, J.; Laurichesse, D. Modeling and quality control for reliable precise point positioning integer ambiguity resolution with GNSS modernization. GPS Solut.
**2014**, 18, 429–442. [Google Scholar] [CrossRef] - Li, P.; Zhang, X.; Guo, F. Ambiguity resolved precise point positioning with GPS and BeiDou. J Geodesy
**2016**, 91, 25–40. [Google Scholar] - Pan, L.; Zhang, X.; Li, X.; Li, X.; Lu, C.; Liu, J.; Wang, Q. Satellite availability and point positioning accuracy evaluation on a global scale for integration of GPS, GLONASS, BeiDou and Galileo. Adv. Space Res.
**2017**. [Google Scholar] [CrossRef] - Tegedor, J.; Øvstedal, O.; Vigen, E. Precise orbit determination and point positioning using GPS, Glonass, Galileo and BeiDou. J. Geod. Sci.
**2014**, 4, 65–73. [Google Scholar] [CrossRef] - Hanson, W.A. In Their Own Words: OneWeb’s Internet constellation as described in their FCC form 312 application. New Space
**2016**, 4, 153–167. [Google Scholar] [CrossRef] - Reid, T.G.; Neish, A.M.; Walter, T.F.; Enge, P.K. Leveraging Commercial Broadband LEO Constellations for Navigation. In Proceedings of the ION GNSS+ 2016, Portland, OR, USA, 12–16 September 2016; pp. 2300–2314. [Google Scholar]
- Liu, J.; Ge, M. PANDA software and its preliminary result of positioning and orbit determination. Wuhan Univ. J. Nat. Sci.
**2003**, 8, 603–609. [Google Scholar] - Saastamoinen, J. Atmospheric correction for the troposphere and stratosphere in radio ranging satellites. Use Artif. Satell. Geod.
**1972**, 15, 247–251. [Google Scholar] - Boehm, J.; Niell, A.; Tregoning, P.; Schuh, H. Global Mapping Function (GMF): A new empirical mapping function based on numerical weather model data. Geophys. Res. Lett.
**2006**, 33. [Google Scholar] [CrossRef][Green Version] - SMC/GP. Navstar Global Positioning System Interface Specification IS-GPS-200 (Revision D). 2004. Available online: https://www.gps.gov/technical/icwg/IS-GPS-200D.pdf (accessed on 21 June 2018).
- Enge, P.; Ferrell, B.; Bennett, J.; Whelan, D.; Gutt, G.; Lawrence, D. Orbital Diversity for Satellite Navigation. In Proceedings of the ION GNSS 2012, Nashville, TN, USA, 17–21 September 2012; pp. 3834–3845. [Google Scholar]

**Figure 5.**Satellite visibility of LEO satellites at four stations on one day. The different colors denote the different orbital planes (there are six colors here corresponding to six orbital planes).

**Figure 6.**Sky plots (azimuth vs. elevation) of GPS (blue), BDS (green), and LEO (red) for four stations over one hour.

**Figure 7.**Number of satellites and the corresponding GDOP values at four stations for different system combinations.

**Figure 9.**Histogram of convergence time in each component for GPS, G/C, G/L, and G/C/L (from top to bottom) PPP. The dashed line denotes that the convergence time of 95% of stations are smaller than the corresponding time.

**Figure 10.**Histogram of convergence time for sampling intervals of 30, 10, 5, and 1 s (from top to bottom) G/C/L PPP. The dashed line means the convergence time of 95% of the world’s stations are smaller than the corresponding time.

GNSS | LEO | ||
---|---|---|---|

Satellite part | BDS | GPS | LEO |

Angular range | GEO/IGSO: 10° | 14.3° | 65° |

MEO: 15° | |||

PCO | YES | YES | NO |

PCV | NO | YES | NO |

Clock | YES | YES | YES |

Receiver part | |||

Cut off elev. | 1° | 1° | |

PCO | YES | YES | |

PCV | YES | YES | |

Clock | YES | YES | |

Solid/Pole/Ocean tidal | YES | YES | |

Propagation path | |||

Troposphere | YES | YES | |

Ionosphere | NO | NO | |

Phase windup | YES | YES | |

General relativity | YES | YES | |

STD of noise | |||

Code | 1.0 m | 1.0 m | |

Phase | 5 mm | 5 mm |

GPS-Only | GPS/BDS | GPS/LEO | GPS/BDS/LEO | |
---|---|---|---|---|

P1 | 34.9 | 22.8 | 5.2 | 5.2 |

P2 | 36.8 | 36.8 | 30.0 | 30.0 |

P3 | 38.3 | 17.1 | 12.3 | 8.2 |

P4 | 26.0 | 14.0 | 5.3 | 5.0 |

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**MDPI and ACS Style**

Ge, H.; Li, B.; Ge, M.; Zang, N.; Nie, L.; Shen, Y.; Schuh, H. Initial Assessment of Precise Point Positioning with LEO Enhanced Global Navigation Satellite Systems (LeGNSS). *Remote Sens.* **2018**, *10*, 984.
https://doi.org/10.3390/rs10070984

**AMA Style**

Ge H, Li B, Ge M, Zang N, Nie L, Shen Y, Schuh H. Initial Assessment of Precise Point Positioning with LEO Enhanced Global Navigation Satellite Systems (LeGNSS). *Remote Sensing*. 2018; 10(7):984.
https://doi.org/10.3390/rs10070984

**Chicago/Turabian Style**

Ge, Haibo, Bofeng Li, Maorong Ge, Nan Zang, Liangwei Nie, Yunzhong Shen, and Harald Schuh. 2018. "Initial Assessment of Precise Point Positioning with LEO Enhanced Global Navigation Satellite Systems (LeGNSS)" *Remote Sensing* 10, no. 7: 984.
https://doi.org/10.3390/rs10070984