# Modeling and Assessment of GPS/Galileo/BDS Precise Point Positioning with Ambiguity Resolution

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

## 3. Data and Processing Strategy

## 4. FCB Estimation

#### 4.1. GPS FCB

#### 4.2. Galileo FCB

#### 4.3. BDS FCB

## 5. PPP AR Results and Analysis

#### 5.1. Evaluation of Satellite Availability and PDOP

#### 5.2. Performance of PPP AR

## 6. Discussions

## 7. Conclusions

## Author Contributions

## Funding

## 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] - Kouba, J.; Héroux, P. Precise point positioning using IGS orbit and clock products. GPS Solut.
**2001**, 5, 12–28. [Google Scholar] [CrossRef] - Li, X.; Dick, G.; Ge, M.; Helse, S.; Wickert, J.; Bender, M. Real-time GPS sensing of atmospheric water vapor: Precise point positioning with orbit, clock, and phase delay corrections. Geophys. Res. Lett.
**2014**, 41, 3615–3621. [Google Scholar] [CrossRef] - Geng, J.; Guo, J.; Chang, H.; Li, X. Toward global instantaneous decimeter-level positioning using tightly coupled multi-constellation and multi-frequency GNSS. J. Geod.
**2019**, 93, 977–991. [Google Scholar] [CrossRef] - Gao, Y.; Chen, K. Performance analysis of precise point positioning using Real-time orbit and clock products. J. Glob. Position. Syst.
**2004**, 3, 95–100. [Google Scholar] [CrossRef] - Le, A.Q.; Tiberius, C. Single-frequency precise point positioning with optimal filtering. GPS Solut.
**2007**, 11, 61–69. [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, 25–28 September 2007; pp. 858–865. [Google Scholar]
- Melgard, T.; Vigen, E.; Jong, K.D.; Lapucha, D.; Visser, H.; Oerpen, O. G2-The first real-time GPS and GLONASS precise orbit and clock service. In Proceedings of the International Technical Meeting of the Satellite Division of the Institute of Navigation, Savannah, GA, USA, 9 September 2001; Volume 5538, pp. 1885–1891. [Google Scholar]
- Li, X.; Zhang, X.; Guo, F. Study on precise point positioning based on combined GPS and GLONASS. In Proceedings of the ION GNSS, Savannah, GA, USA, 22–25 September 2009; pp. 2449–2459. [Google Scholar]
- Li, P.; Zhang, X. Modeling and Performance Analysis of GPS/GLONASS/BDS Precise Point Positioning. In Proceedings of the China Satellite Navigation Conference, Nanjing, China, 21–23 May 2014; pp. 251–263. [Google Scholar]
- Li, W.; Teunissen, P.J.G.; Zhang, B.; Verhagen, S. Precise point positioning using GPS and COMPASS observations. In Proceedings of the China Satellite Navigation Conference, Wuhan, China, 15–17 May 2013; pp. 367–378. [Google Scholar]
- Shen, X.; Gao, Y. Analyzing the impacts of Galileo and modernized GPS on precise point positioning. In Proceedings of the ION GPS, Portland, OR, USA; 2006; Volume 49, pp. 1532–1539. [Google Scholar]
- Cao, W.; Hauschild, A.; Steigenberger, P.; Langley, R.B.; Urquhart, L.; Santos, M. Performance evaluation of integrated GPS/GIOVE precise point positioning. In Proceedings of the ION NTM, San Diego, CA, USA, March 2010; pp. 540–552. [Google Scholar]
- Cai, C.; Gao, Y.; Pan, L.; Zhu, J. Precise point positioning with quad-constellations: GPS, BeiDou, GLONASS and Galileo. Adv. Space Res.
**2015**, 56, 133–143. [Google Scholar] [CrossRef] - Teunissen, P.J.G.; Kleusberg, A. GPS Observation Equations and Positioning Concepts. In Lecture Notes in Earth Sciences: GPS for Geodesy; Springer: Berlin/Heidelberg, Germany, 1996; Volume 60, pp. 175–217. [Google Scholar]
- Gabor, M.J.; Nerem, R.S. GPS Carrier Phase Ambiguity Resolution Using Satellite-Satellite Single Differences. In Proceedings of the ION GPS 1999, Nashville, TN, USA, 14–17 September 1999; pp. 1569–1578. [Google Scholar]
- Gabor, M.J.; Nerem, R.S. Characteristics of Satellite-Satellite Single Difference Widelane Fractional Carrier Phase Biases. In Proceedings of the ION GPS 2000, Salt Lake City, UT, USA, 19–22 September 2000; pp. 396–406. [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. Geod.
**2008**, 82, 389–399. [Google Scholar] [CrossRef] - Collins, P.; Lahaye, F.; Herous, P.; Bisnath, S. Precise point positioning with AR using the decoupled clock model. In Proceedings of the ION GNSS. Institute of Navigation, Savannah, GA, USA, 16–19 September 2008; pp. 1315–1322. [Google Scholar]
- Geng, J.; Teferle, F.N.; Shi, C.; Meng, X.; Dodson, A.H.; Liu, J. Ambiguity resolution in precise point positioning with hourly data. GPS Solut.
**2009**, 13, 263–270. [Google Scholar] [CrossRef] - Geng, J.; Meng, X.; Alan, H.D.; Teferle, F.N. Integer ambiguity resolution in precise point positioning: Method comparison. J. Geod.
**2010**, 84, 569–581. [Google Scholar] [CrossRef] - 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] - Liu, Y.; Song, W.; Lou, Y.; Ye, S.; Zhang, R. GLONASS phase bias estimation and its PPP ambiguity resolution using homogeneous receivers. GPS Solut.
**2017**, 21, 427–437. [Google Scholar] [CrossRef] - Liu, Y.; Ye, S.; Song, W.; Lou, Y.; Chen, D. Integrating GPS and BDS to shorten the initialization time for ambiguity-fixed PPP. GPS Solut.
**2017**, 21, 333–343. [Google Scholar] [CrossRef] - Li, P.; Zhang, X.; Guo, F. Ambiguity resolved precise point positioning with GPS and BeiDou. J. Geod.
**2017**, 91, 25–40. [Google Scholar] - Li, X.; Li, X.; Yuan, Y.; Zhang, K.; Zhang, X.; Wickert, J. Multi-GNSS phase delay estimation and PPP ambiguity resolution: GPS, BDS, GLONASS, Galileo. J. Geod.
**2017**, 92, 579–608. [Google Scholar] [CrossRef] - Liu, X.; Jiang, W.; Li, Z.; Chen, H.; Zhao, W. Comparison of convergence time and positioning accuracy among BDS, GPS and BDS/GPS precise point positioning with ambiguity resolution. Adv. Space Res.
**2019**, 63, 3489–3504. [Google Scholar] [CrossRef] - Melbourne, W.G. The case for ranging in GP S-based geodetic systems. In Proceedings of the First International Symposium on Precise Positioning with the Global Positioning System, Rockville, MD, USA, 15–19 April 1985. [Google Scholar]
- Wübbena, G. Software developments for geodetic positioning with GPS using TI-4100 code and carrier measurements. In Proceedings of the First International Symposium on Precise Positioning with the Global Positioning System, Rockville, MD, USA, 15–19 April 1985. [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. [Google Scholar] - Blewitt, G. An automatic editing algorithm for GPS data. Geophys. Res. Lett.
**1990**, 17, 199–202. [Google Scholar] [CrossRef] - Liu, X.; Jiang, W.; Chen, H.; Zhao, W.; Huo, L.; Huang, L.; Chen, Q. An analysis of inter-system biases in BDS/GPS precise point positioning. GPS Solut.
**2019**, 23, 116. [Google Scholar] [CrossRef] - Kouba, J. A Guide to Using International GNSS Service (IGS) Products. 2009. Available online: http://igscb.jpl.nasa.gov/igscb/resource/pubs/UsingIGSProductsVer21.pdf (accessed on 15 January 2019).
- Hauschild, A.; Montenbruck, O.; Sleewaegen, J.M.; Huisman, L.; Teunissen, P. Characterization of Compass M-1 signals. GPS Solut.
**2012**, 16, 117–126. [Google Scholar] [CrossRef] - Perello Gisbert, J.V.; Batzilis, N.; Risueno, G.L.; Rubio, J.A. GNSS payload and signal characterization using a 3 m dish antenna. In Proceedings of the ION GNSS, Nashville, TN, USA, 9 December 2012; pp. 347–356. [Google Scholar]
- Montenbruck, O.; Hauschild, A.; Steigenberger, P.; Hugentobler, U.; Riley, S. A COMPASS for Asia: First experience with the BeiDou-2 regional navigation system. In Proceedings of the Poster at IGS Workshop, Olsztyn, Poland, 23–27 July 2012. [Google Scholar]
- Montenbruck, O.; Rizos, C.; Weber, R.; Weber, G.; Neilan, R.; Hugentobler, U. Getting a grip on multi-GNSS—the international GNSS service MGEX campaign. GPS World
**2013**, 24, 44–49. [Google Scholar] - Wanninger, L.; Beer, S. BeiDou satellite-induced code pseudorange variations: Diagnosis and therapy. GPS Solut.
**2015**, 19, 639–648. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Geographic distribution of the reference network. Red triangles denote the 160 stations used for GPS/Galileo/BDS FCB estimation, while yellow stars denote the eight stations used to evaluate the performance of the combined systems.

**Figure 6.**BDS WL FCB from DOY 321 to 350, 2018. Top panel: BDS GEO. Bottom panel: BDS non-GEO. C02 and C06 are taken as the reference for BDS GEO and non-GEO respectively.

**Figure 7.**BDS NL FCB on DOY 328, 2018. Top panel: BDS GEO. Bottom panel: BDS non-GEO. C02 and C06 are taken as the reference for BDS GEO and non-GEO respectively.

**Figure 8.**Global distribution of the visible satellite number for seven different constellation combinations on DOY 321, 2018.

**Figure 9.**Global distribution of the satellite PDOP values for seven different constellation combinations on DOY 321, 2018.

**Figure 10.**Comparison of the float and fixed PPP results from single-system and combined solutions in the E, N, and U components, respectively, at station KAT1 on DOY 324, 2018.

**Figure 11.**Comparison of the fixed results for the seven systems in the E, N, and U components, respectively, at station KAT1 on DOY 324, 2018.

**Figure 14.**The average RMS of float and fixed PPP solution for seven systems from DOY 321 to 350, 2018.

System | Efloat | Nfloat | Ufloat | Efix | Nfix | Ufix |
---|---|---|---|---|---|---|

G | 1.52 | 0.60 | 1.44 | 0.88 | 0.56 | 1.27 |

E | 1.08 | 0.63 | 4.58 | 0.76 | 0.55 | 4.33 |

C | 1.74 | 0.98 | 5.19 | 1.12 | 0.68 | 4.65 |

GE | 0.86 | 0.53 | 1.98 | 0.51 | 0.50 | 1.83 |

GC | 1.46 | 0.57 | 1.93 | 0.72 | 0.49 | 1.75 |

EC | 0.95 | 0.58 | 4.61 | 0.60 | 0.45 | 4.36 |

GEC | 0.92 | 0.52 | 2.21 | 0.50 | 0.46 | 1.96 |

© 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/).

## Share and Cite

**MDPI and ACS Style**

Liu, X.; Chen, H.; Jiang, W.; Xi, R.; Zhao, W.; Song, C.; Zhou, X.
Modeling and Assessment of GPS/Galileo/BDS Precise Point Positioning with Ambiguity Resolution. *Remote Sens.* **2019**, *11*, 2693.
https://doi.org/10.3390/rs11222693

**AMA Style**

Liu X, Chen H, Jiang W, Xi R, Zhao W, Song C, Zhou X.
Modeling and Assessment of GPS/Galileo/BDS Precise Point Positioning with Ambiguity Resolution. *Remote Sensing*. 2019; 11(22):2693.
https://doi.org/10.3390/rs11222693

**Chicago/Turabian Style**

Liu, Xuexi, Hua Chen, Weiping Jiang, Ruijie Xi, Wen Zhao, Chuanfeng Song, and Xingyu Zhou.
2019. "Modeling and Assessment of GPS/Galileo/BDS Precise Point Positioning with Ambiguity Resolution" *Remote Sensing* 11, no. 22: 2693.
https://doi.org/10.3390/rs11222693