# PPP and PPP-AR Kinematic Post-Processed Performance of GPS-Only, Galileo-Only and Multi-GNSS

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- ${P}_{r,i}^{s}$, ${P}_{r,j}^{s}$ are the code measurement at receiver $r$ from satellite $s$ on frequency $i$ or $j$ (m)
- ${L}_{r,i}^{s}$, ${L}_{r,j}^{s}$ are the phase measurement at receiver $r$ from satellite $s$ on frequency $i$ or $j$ (m)
- ${\rho}_{r}^{s}$ is the geometric distance between receiver and satellite (m)
- $\Delta t$ ($\Delta t=\delta {t}_{r}-\delta {t}^{s}$) is the clock correction related to the satellite ($\delta {t}^{s}$) and the receiver ($\delta {t}_{r}$) with respect to the synchronization to the GPS time (s)
- ${T}_{r}^{s}$ is the troposphere delay (m)
- ${I}_{r}^{s}$ is the ionosphere delay (m)
- ${E}_{r,i}^{s}$, ${E}_{r,j}^{s}$ are the code measurement errors at receiver $r$ from satellite $s$ on frequency $i$ or $j$ (m) including all sources of code errors: multipath and noise.
- ${f}_{i}$, ${f}_{j}$ are the carrier frequency $i$ or $j$ (Hz)
- $c$ is the speed of light in vacuum (m/s)
- ${\lambda}_{i}$, ${\lambda}_{j}$ are the nominal wavelength of the carrier frequency $i$ or $j$ (m)
- ${\phi}_{r,i}^{s}$, ${\phi}_{r,j}^{s}$ are the carrier phase measurement at receiver $r$ from satellite $s$ on frequency $i$ or $j$ (cycles)
- ${N}_{r,i}^{s}$, ${N}_{r,j}^{s}$ are the integer carrier phase ambiguity at receiver $r$ from satellite $s$ on frequency $i$ or $j$
- ${W}_{r}^{s}$ is the carrier phase wind up effect (cycles)
- ${b}^{s}$, ${b}_{r}$ are the code phase biases of satellite and receiver (m)
- ${\beta}^{s}$, ${\beta}_{r}$ are the carrier phase biases of satellite and receiver (m)
- ${\epsilon}_{r,i}^{s}$, ${\epsilon}_{r,j}^{s}$ are the carrier phase measurement error at receiver $r$ from satellite $s$ on frequency $i$ or $j$ (m) including all sources of phase errors, remaining uncorrected phase center offset and phase center variation, multipath and noise.

- $M{W}_{r}^{s}$ is the Melbourne-Wübbena linear combination at receiver $r$ from satellite $s$ (m)
- ${\lambda}_{wl}$ (${\lambda}_{wl}=c/\left({f}_{i}-{f}_{j}\right)={\lambda}_{i}{\lambda}_{j}/({\lambda}_{j}-{\lambda}_{i})$) is the wide-lane (WL) wavelength (m)
- ${N}_{wl,r}^{s}$ (${N}_{wl,r}^{s}={N}_{r,i}^{s}-{N}_{r,j}^{s}$) is the WL ambiguity at receiver $r$ from satellite $s$
- ${\mu}^{s}$ is the delay coming from the satellite (also known in the bibliography as WL satellite bias (WSB))
- ${\mu}_{r}\left(t\right)$ is the delay coming from the receiver (also known in the bibliography as WL receiver bias (WRB))

- ${P}_{r,IF}^{s}$ is the ionosphere-free code measurement at receiver $r$ from satellite $s$ (m)
- ${E}_{r,IF}^{s}$ is the ionosphere-free code measurement error at receiver $r$ from satellite $s$ (m)
- ${L}_{r,IF}^{s}$ is the ionosphere-free carrier measurement at receiver $r$ from satellite $s$ (m)
- ${\epsilon}_{r,IF}^{s}$ is the ionosphere-free carrier measurement error at receiver $r$ from satellite $s$ (m)
- ${\lambda}_{nl}$ (${\lambda}_{nl}=c/\left({f}_{i}+{f}_{j}\right)={\lambda}_{i}{\lambda}_{j}/\left({\lambda}_{i}+{\lambda}_{j}\right)$) is the narrow-lane (NL) wavelength (m)

## 3. Results

#### 3.1. Some Station Examples

#### 3.2. Global Network of Stations

- The PPP-AR mode gives better repeatability for the timeseries than the PPP mode.
- Galileo only solution gives similar level of 1-σ values repeatability than the GPS only solution.
- The use of Galileo can improve the current precise positioning situation of GPS when used in a Multi-GNSS combination in a PPP-AR mode.

## 4. Discussion and Conclusions

## 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.
**1997**, 102, 5005–5017. [Google Scholar] [CrossRef] [Green Version] - Lescarmontier, L.; Legrésy, B.; Coleman, R.; Perosanz, F.; Mayet, C.; Testut, L. Vibrations of Mertz Glacier ice tongue, East Antarctica. J. Glaciol.
**2012**, 58, 665–676. [Google Scholar] [CrossRef] - Fund, F.; Perosanz, F.; Testut, L.; Loyer, S. An Integer Precise Point Positioning technique for sea surface observations using a GPS buoy. Adv. Space Res.
**2013**, 51, 1311–1322. [Google Scholar] [CrossRef] - Petit, G.; Kanj, A.; Loyer, S.; Delporte, J.; Mercier, F.; Perosanz, F. 1 × 10
^{−16}frequency transfer by GPS PPP with integer ambiguity resolution. Metrologia**2015**, 52, 301–309. [Google Scholar] [CrossRef] - Laurichesse, D.; Mercier, F.; Berthias, J.; Broca, P.; Cerri, L. Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP and satellite precise orbit determination. Navig. J. Inst. Navig.
**2009**, 2, 135–149. [Google Scholar] [CrossRef] - Katsigianni, G.; Loyer, S.; Perosanz, F.; Mercier, F.; Zajdel, R.; Sośnica, K. Improving Galileo orbit determination using zero-differenceambiguity fixing in a Multi-GNSS processing. Adv. Space Res.
**2019**, 63, 2952–2963. [Google Scholar] [CrossRef] - 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] - Loyer, S.; Perosanz, F.; Mercier, F.; Capdeville, H.; Marty, J. Zero-difference GPS ambiguity resolution at CNES-CLS IGS analysis center. J. Geod.
**2012**, 991–1003. [Google Scholar] [CrossRef] - Hadas, T.; Kazmierski, K.; Sośnica, K. Performance of Galileo-only dual-frequency absolute positioning using the fully serviceable Galileo constellation. GPS Solut.
**2019**, 23, 12. [Google Scholar] [CrossRef] - Katsigianni, G.; Perosanz, F.; Loyer, S.; Gupta, M. Galileo millimeter-level kinematic precise point positioning with ambiguity resolution. Earth Planets Space
**2019**, 71–76. [Google Scholar] [CrossRef] - GSA, Constellation Information. Available online: https://www.gsc-europa.eu/system-service-status/constellation-information (accessed on 4 October 2019).
- ESA, Four New Galileos Join Europe’s Largest Satellite Constellation. Available online: https://www.esa.int/Our_Activities/Navigation/Four_new_Galileos_join_Europe_s_largest_satellite_constellation (accessed on 4 October 2019).
- Laurichesse, D.; Mercier, F. Integer ambiguity resolution on undifferenced GPS phase measurements and its application to PPP. In Proceedings of the ION GNSS 2007 20th International Technical Meeting of the Satellite Division, Fort Worth, TX, USA, 25–28 September 2007. [Google Scholar]
- Melbourne, W. The case for ranging in GPS based geodetic system. In Proceedings of the 1st International Symposium on Precise Positioning With the Global Positioning System. U.S. Department of Commerce, 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 1st International Symposium on Precise Positioning With the Global Positioning System. U.S. Department of Commerce, Rockville, MD, USA, 15–19 April 1985. [Google Scholar]
- Mercier, F.; Laurichesse, D. Receiver/Payload hardware biases stability requirements for undifferenced Widelane ambiguity blocking. In Proceedings of the Scientific and Fundamental Aspects of the Galileo Program, Toulouse, France, 1–4 October 2007. [Google Scholar]
- Verhagen, S. The GNSS Integer Ambiguities: Estimation and Validation; Publications on Geodesy: Delft, The Netherlands, 2004; pp. 27–32. [Google Scholar]
- Teunissen, P. Success probability of integer GPS ambiguity rounding and bootstrapping. J. Geod.
**1998**, 72, 606–612. [Google Scholar] [CrossRef] [Green Version] - Hofmann-Wellenhof, B.; Lichtenegger, H.; Wasle, E. GNSS-Global Navigation Satellite Systems GPS, GLONASS, Galileo and More; Springer: Vienna, Austria, 2008; p. 59. [Google Scholar]
- Kouba, J. A Guide to Using International GNSS Service (IGS) Products. Available online: http://acc.igs.org/UsingIGSProductsVer21.pdf (accessed on 4 October 2019).
- Marty, J.C. Algorithmic Documentation of the GINS Software. Available online: https://www5.obs-mip.fr/wp-content-omp/uploads/sites/28/2017/11/GINS_Algo_2013.pdf (accessed on 4 October 2019).
- CNES/CLS Analysis Center for IGS. Available online: https://igsac-cnes.cls.fr/ (accessed on 4 October 2019).
- GSA, Galileo Satellite Metadata. Available online: https://www.gsc-europa.eu/support-to-developers/galileo-satellite-metadata (accessed on 4 October 2019).
- Böhm, J.; Möller, G.; Schindelegger, M.; Pain, G.; Weber, R. Development of an improved empirical model for slant delays in the troposphere (GPT2w). GPS Solut.
**2015**, 19, 433–441. [Google Scholar] [CrossRef] - Lagler, K.; Schindelegger, M.; Böhm, J.; Krásná, H.; Nilsson, T. GPT2: Empirical slant delay model for radio space geodetic techniques. Geophys. Res. Lett.
**2013**, 40, 1069–1073. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hernández-Pajares, M.; Juan, J.M.; Sanz, J.; Orús, R. Second-order ionospheric term in GPS: Implementation and impact on geodetic estimates. J. Geophys. Res.
**2007**, 112. [Google Scholar] [CrossRef] - Altamimi, Z.; Rebischung, P.; Métivier, L.; Collilieux, X. ITRF2014: A new release of the International Terrestrial Reference Frame modeling nonlinear station motions. J. Geophys. Res. Solid Earth
**2016**, 12, 6109–6131. [Google Scholar] [CrossRef] - Kouba, J. A simplified yaw-attitude model for eclipsing GPS satellites. GPS Solut.
**2009**, 13, 1–12. [Google Scholar] [CrossRef] - Carrère, L.; Lyard, M.; Cancet, M.; Guillot, A.; Roblou, L. FES2012: A new global tidal model taking advantage of nearly 20 years of altimetry. In Proceedings of the 20 Years of Progress in Radar Altimetry Symposium, Venice, Italy, 24–29 September 2012. [Google Scholar]
- Petit, G.; Luzum, B. IERS Conventions; Verlag des Bundesamts für Kartographie und Geodäsie: Frankfurt am Main, Germany, 2010; Volume 36, p. 179. [Google Scholar]
- Bizouard, C.; Lambert, S.; Gattano, C.; Becker, O.; Richard, J.-Y. The IERS EOP 14C04 solution for Earth orientation parameters consistent with ITRF 2014. J. Geod.
**2019**, 93, 621–633. [Google Scholar] [CrossRef] - Chen, G.; Herring, T.A. Effects of atmospheric azimuthal asymmetry on the analysis of space geodetic data. J. Geophys. Res.
**1997**, 102, 20489–20502. [Google Scholar] [CrossRef] - IGS, Antenna Working Group Charter and Members. Available online: https://kb.igs.org/hc/en-us/articles/202023633-Antenna-Working-Group-Charter-and-Members (accessed on 4 October 2019).

**Figure 1.**Steps of the procedure to perform precise point positioning (PPP) and PPP with phase ambiguity resolution (PPP-AR) of a combined Multi-GNSS solution (GPS + Galileo).

**Figure 2.**PPP and PPP-AR solutions for BRUX station for Galileo-only, GPS-only and Multi-GNSS for the period 11–19 February 2019, DOY: 42–49/2019. For Galileo-only and GPS + Galileo, additional biases of +0.05 m and −0.05 m have been added respectively for better representation in the graph.

**Figure 3.**GPS PPP-AR solutions for the network of IGS stations in East, North and Up components and their global RMS (mm).

**Figure 4.**GPS + Galileo PPP-AR solutions for the network of IGS stations in East, North and Up components and their global RMS (mm).

GNSS Frequency | ${\mathit{\lambda}}_{\mathit{w}\mathit{l}}\left(\mathbf{m}\right)$ | ${\mathit{\lambda}}_{\mathit{n}\mathit{l}}\left(\mathbf{m}\right)$ |
---|---|---|

GPS ($L1$, $L2$) | 0.862 | 0.107 |

Galileo ($E1$, $E5a$) | 0.751 | 0.109 |

Processing Strategy | |
---|---|

Software | GINS, DYNAMO, EXE_PPP [21] |

Strategy | PPP, PPP-AR zero-difference |

Estimation | Static with Kalman, 300 s sampling |

Orbit, Clocks and Satellites Biaises | |

Orbits and clocks | CNES-CLS orbits (‘grg’) [8] |

Satellite biases | CNES-CLS wide-lane satellite biases [22] |

GNSS relative weighting | Equal weighting for GPS and Galileo |

GNSS measurement sigmas (at 0° of elevation) | Code: 60 cm; Phase: 3.5 mm |

Elevation cut-off | 8 deg |

Elevation weighting function, where $\vartheta $ is the elevation angle | $\sigma \left(\vartheta \right)=\frac{0.0035}{0.15+0.85\mathrm{sin}\vartheta}$ |

Models for Processing | |

Antenna phase center corrections | ANTEX14 PCO/PCV [23] |

Troposphere model | VMF1 [24] + GPT2 [25] (A priori local meteorological parameters (pressure, temperature, and wet mapping function coefficients) of GPT2 model are used to compute hydrostatic delays and for the wet mapping function VMF1. We then adjust 1 zenithal tropospheric delay per two hours in factor of the wet mapping function). |

Ionosphere model | Ionosphere-free combination and second ordercorrections [26] |

Reference frame | ITRF 2014 [27] |

Attitude model | Kouba [28] for GPS and GSA [23] for Galileo |

Ocean loading effects | FES2012 [29] |

Earth orientation modelling | IERS Conventions 2010 [30] |

Earth orientation parameters | EOP C04 [31] |

Phase windup | Models used by Kouba [28] |

Estimated Parameters | |

Troposphere | 1 ZTD/2 h, 1 pair of gradients (E, N)/day (1 couple of gradients in north and east direction are also adjusted per day following [31,32] |

Observation sampling | 300 s |

Inter-system biases (phase obs.) | 1 per station (zero mean condition) |

Station coordinates estimates | X, Y, Z transformed to East, North, Up |

BRUX AR (%) | 042 | 043 | 044 | 045 | 046 | 047 | 048 |
---|---|---|---|---|---|---|---|

Galileo | 95.24 | 100 | 100 | 97.67 | 100 | 100 | 95.45 |

GPS | 98.63 | 91.67 | 91.30 | 98.44 | 100 | 98.48 | 94.03 |

BRUX | Mode | East (mm) | North (mm) | Up (mm) |
---|---|---|---|---|

Galileo | PPP | 4.7 | 4.6 | 11.7 |

PPP-AR | 2.6 | 2.9 | 10.3 | |

GPS | PPP | 4.7 | 4.1 | 9.2 |

PPP-AR | 2.4 | 3.4 | 8.5 | |

GPS + Galileo | PPP | 3.4 | 2.7 | 9.1 |

PPP-AR | 2.1 | 2.4 | 7.3 |

CAS1 | Mode | East (mm) | North (mm) | Up (mm) |
---|---|---|---|---|

Galileo | PPP | 7.1 | 6.8 | 16.6 |

PPP-AR | 4.2 | 5.2 | 15.6 | |

GPS | PPP | 6.4 | 6.8 | 15.2 |

PPP-AR | 3.8 | 5.2 | 14.3 | |

GPS + Galileo | PPP | 4.6 | 4.5 | 11.3 |

PPP-AR | 3.1 | 3.7 | 10.3 |

NYA2 | Mode | East (mm) | North (mm) | Up (mm) |
---|---|---|---|---|

Galileo | PPP | 4.9 | 5.0 | 13.9 |

PPP-AR | 2.8 | 2.9 | 15.5 | |

GPS | PPP | 4.2 | 4.1 | 16.0 |

PPP-AR | 2.4 | 2.2 | 11.7 | |

GPS + Galileo | PPP | 3.3 | 3.1 | 10.3 |

PPP-AR | 2.5 | 2.1 | 9.8 |

Network AR (%) | 042 | 043 | 044 | 045 | 046 | 047 | 048 | RMS |
---|---|---|---|---|---|---|---|---|

Galileo | 90.71 | 95.38 | 95.39 | 95.56 | 96.16 | 95.67 | 89.39 | 94.07 |

GPS | 93.55 | 92.25 | 89.85 | 93.90 | 94.09 | 94.54 | 89.62 | 92.56 |

Global | Mode | East (mm) | North (mm) | Up (mm) |
---|---|---|---|---|

Galileo | PPP | 17.0 | 14.6 | 33.1 |

PPP-AR | 13.7 | 12.2 | 30.8 | |

GPS | PPP | 11.8 | 9.4 | 26.0 |

PPP-AR | 9.3 | 8.3 | 24.0 | |

GPS + Galileo | PPP | 7.9 | 6.1 | 17.2 |

PPP-AR | 6.7 | 5.6 | 16.8 |

© 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**

Katsigianni, G.; Loyer, S.; Perosanz, F.
PPP and PPP-AR Kinematic Post-Processed Performance of GPS-Only, Galileo-Only and Multi-GNSS. *Remote Sens.* **2019**, *11*, 2477.
https://doi.org/10.3390/rs11212477

**AMA Style**

Katsigianni G, Loyer S, Perosanz F.
PPP and PPP-AR Kinematic Post-Processed Performance of GPS-Only, Galileo-Only and Multi-GNSS. *Remote Sensing*. 2019; 11(21):2477.
https://doi.org/10.3390/rs11212477

**Chicago/Turabian Style**

Katsigianni, Georgia, Sylvain Loyer, and Felix Perosanz.
2019. "PPP and PPP-AR Kinematic Post-Processed Performance of GPS-Only, Galileo-Only and Multi-GNSS" *Remote Sensing* 11, no. 21: 2477.
https://doi.org/10.3390/rs11212477