Comptes Rendus Physique

Félix Perosanz

C. R. Physique 20 (2019) 171–175Contents lists available at ScienceDirect
Comptes Rendus Physique
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URSI-France 2018 Workshop: Geolocation and navigation / Journées URSI-France 2018 : Géolocalisation et navigation
GNSS: A revolution for precise geopositioning
GNSS : une révolution pour le géopositionnement précis
Félix Perosanz
Centre national d’études spatiales (CNES), GET/GRGS, 14, avenue Édouard-Belin, 31400 Toulouse, France
a r t i c l e i n f o a b s t r a c t
Keywords:
GNSS
IGS
SSR
OSR
Mots-clés :
GNSS
IGS
SSR
OSR
Global Navigation Satellite Systems (GNSS) were not initially designed to be used for 
precise scientific applications. However, a smart signal processing can provide a satellite–
receiver range measurement with millimeter accuracy. If the differential technique has 
become an essential method, the PPP mode is today an increasingly popular alternative. 
But, whatever the approach, GNSS have revolutionized the realization of space and time 
frames and the many applications requiring post-processed or real-time precise positioning.
© 2019 Published by Elsevier Masson SAS on behalf of Académie des sciences. This is an 
open access article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
r é s u m é
Les systèmes globaux de navigation par satellite (GNSS) n’avaient à l’origine pas vocation à 
répondre aux besoins de positionnement pour des applications scientifiques précises. Mais 
un usage détourné des signaux a permis d’accéder à des mesures de distance satellite–
récepteur d’une précision millimétrique. Si la technique différentielle s’est imposée comme 
une méthode incontournable, le mode PPP est aujourd’hui une alternative de plus en plus 
populaire. Mais, quelle que soit l’approche, les GNSS ont révolutionné la réalisation des 
repères d’espace et de temps ainsi que les nombreux usages nécessitant en temps différé 
ou en temps réel un positionnement précis.
© 2019 Published by Elsevier Masson SAS on behalf of Académie des sciences. This is an 
open access article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. GNSS: a geodetic technique by opportunity
Global Navigation Satellite Systems (GNSS), such as the popular US GPS operating since 1995, were not originally in-
tended to be exploited for scientific purposes. Their radio signals are based on the modulation of the phase of an L-band 
carrier wave (1–2 GHz) by a PRN code with a frequency close to 1 MHz. The demodulation of this code by a receiver makes 
it possible to measure the distance between the transmitting satellites and the user with an accuracy of a few meters. Since 
the receivers are multichannel, the user can deduct from simultaneous measurements on several satellites its own position 
by “tri-lateration” with this same precision. But quickly the idea of measuring directly the phase of the carrier wave ap-
peared. Thanks to the one thousand times higher frequency of this signal, users equipped with specific receivers have had 
E-mail address: Felix.Perosanz@cnes.fr.https://doi.org/10.1016/j.crhy.2019.05.018
1631-0705/© 2019 Published by Elsevier Masson SAS on behalf of Académie des sciences. This is an open access article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
172 F. Perosanz / C. R. Physique 20 (2019) 171–175access to measurement of millimeter precision. Scientists have since benefited greatly from these providential observations 
from an ever-increasing number of satellite constellations such as GLONASS (Russia), Galileo (Europe), or Beidou (China). 
GNSS measurements have become a precise geodetic technique and are widely exploited for many scientific purposes. At 
first, this article compares differential techniques and PPP from the point of view of parameter correlation. The essential 
contribution of GNSS to the realization of space and time references is then recalled, as well as the driving role of the 
International IGS service, which has made the GNSS technique evolve towards more precision and less delays.
2. Precise GNSS applications: a question of (de)correlation
The exploitation of the millimeter precision of the phase measurements is not immediate, because it must go through a 
very fine modeling of each of the terms that compose it:
– position of the center of mass of the transmitting satellite at the time of emission;
– center of mass vector of the phase center satellite of the transmitting antenna, which is a function of the geometry and 
the attitude (orientation in space) of the satellite;
– satellite clock bias with respect to the time scale of the constellation;
– position of the phase center of the receiving antenna at the epoch of reception;
– vector “eccentricity” between the receiver phase center and the point to be positioned;
– propagation delays in the ionosphere and the troposphere;
– relativistic terms;
– phase “wind-up” effect due to the relative rotation between the transmitter and the receiver;
– phase measurement bias corresponding to the unknown initial integer number of cycles. This bias called “ambiguity” is 
common to all phases measurements from the same pass of a satellite (between its rising and its setting);
– hardware biases at the satellite and receiver level that corrupt the integer nature of phase ambiguities.
Monitoring all these terms is the key to a “precise” use of GNSS data. The mathematical problem to be solved is generally 
oversized, that is to say that the number of observations coming from the satellites in visibility is greater than the number 
of parameters to be determined. However, a “reliable” solution will only be obtained if a sufficient level of decorrelation 
between the parameters is reached. Concretely, this means that a sufficient number of equations will have to be accumulated 
to separate the contributions of the receiver clock terms, coordinates, tropospheric biases, and phase ambiguity, which 
are “naturally” correlated (or anti-correlated) by more than 90%. Obviously, the situation is more favorable in the case 
of a post-processing where the whole system of equations can be solved globally afterwards. But for both real-time and 
non-real-time applications, two types of strategies have been adopted over time to address this problem: the differential 
approach and the PPP approach.
3. The differential approach
The basic idea is to create new observables from the difference in phase measurements from two near receivers and/or 
two satellites in simultaneous visibility. Common terms affecting the measurements are thus eliminated. The differentiation 
of GNSS phase measurements is a form of “ultimate” decorrelation. Indeed, several terms of the measurement model such as 
clock and hardware biases do not need to be solved any more. On this principle, dense networks of reference GNSS stations 
(known position) have been deployed in many countries to provide a service of “differential corrections” for users requiring 
centimeter precision (surveyors, topographers, farmers...). In France, Teria, Orpheon, or Satinfo, for example, provide this type 
of service. In this case, we speak of an OSR (Observation State Representation), for which a single term corresponding to 
the sum of the corrections to be applied to the observations is transmitted to the users. In the case of post-processing 
and “static” receivers, the ratio of the number of observations to the number of unknowns becomes very favorable, and 
the differential technique makes it possible to reach millimeter accuracies. It became in the 1990s an essential method for 
many precise applications of GPS.
4. The PPP mode
An alternative approach to the differential technique consists in modeling or estimating each term composing the phase 
measurements rather than trying to eliminate them. In this case, we speak of SSR representation (State Space Represen-
tation). The PPP (Precise Point Positioning) of a GNSS receiver without the need for a reference receiver nearby becomes 
possible. However, access to a source of precise corrections of satellite orbit and clock, for example, is necessary. Moreover, 
from a correlation point of view, the situation is less favorable because the number of parameters to be estimated (a clock 
bias per measurement period, for example) is much larger. Thus, the positioning of a mobile in real time will require a 
longer convergence time than in the case of a differentiated approach. References [1] and [2] detail the advantages and 
disadvantages of differential and PPP approaches as well as of OSR and SSR representations.
F. Perosanz / C. R. Physique 20 (2019) 171–175 1735. Phase-measurement ambiguity fixing
The ultimate exploitation of GNSS phase measurements involves estimating the integer ambiguity bias. The GNSS mea-
surement becomes accurate and precise, the number of parameters in the problem decreases, and the remaining ones are 
better de-correlated. Since the satellite and receiver hardware biases make phase ambiguities lose their “integer” nature, the 
only solution considered for many years was to eliminate them by double-differentiation. In 2007, Laurichesse and Mercier 
[3] observed that the satellite bias is stable (constant over a day), so they can be de-correlated using a receiver that is 
simultaneously tracking a sufficient number of satellites. The resolution of integer ambiguities in PPP mode then becomes 
possible. This mode of processing, called “Integer-PPP” (IPPP) or “PPP–AR” makes possible the positioning of “isolated” GNSS 
receivers with improved precision, and is becoming a competing technique with the differential mode. The idea that Galileo
could broadcast free SSR corrections of its own signals is under study.
6. The international GNSS service
The decision of the International Association of Geodesy to create in 1994 the International GNSS Service (www.igs .org) 
is a founding act. This service is based on an international effort to deploy a network of permanent geodetic stations. 
The French contribution via the REGINA network [4] comprising of forty CNES and IGN stations globally distributed meets 
this need as well as the United Nations Recommendation 69/L.53 on “A global geodetic reference frame for sustainable 
development”. The IGS also includes data archiving and processing centers that for example calculate the precise orbit of 
the GNSS satellite. More than 200 volunteer organizations contribute to the IGS with the aim of freely providing the most 
accurate GNSS products (IGS 2017). Thanks to the “friendly competition” between the different analysis centers (e.g., NASA, 
ESA, CODE, CNES. . .) and the dynamism of its Working Groups, the IGS has progressively pushed GNSS as a major geodetic 
technique by providing more and more precise products, distributing software packages (e.g., GAMIT, Bernese, GIPSY, GINS...), 
by imposing standards (RINEX, SINEX, RTCM...), by publishing hundreds of articles. If the first objective was and remains to 
contribute to the improvement of the realization of the space and time references (see next paragraph) and to measure the 
Earth kinematics (see article by Pierre Briole in this issue), the heritage of the IGS is considerable. The precise uses of GNSS 
have extended to areas as diverse as oceanography, hydrology, terrestrial and space meteorology, for example. Since 2010, 
as part of a pilot project that aims to become an “operational” service, products are calculated and delivered in real time. 
Thus, IGS has been the breeding ground of numerous innovations and developments that have significantly improved the 
processing quality and opened the field of application of precise GNSS.
7. The key role of GNSS for space and time reference realization
The International Terrestrial Reference Frame (ITRF) 2014 is today the standard for expressing coordinates of any point 
on the Earth. It is defined by a set of coordinates and velocities of a network of reference geodetic stations that “materialize” 
the frame. Regular updates of the ITRF are needed as the extrapolation of the station coordinates is affected by the error 
propagation of velocities. The solution is based on the analysis of more than 20 years of geodetic observations from more 
than 1000 sites. The GNSS technique (more economical and easier to implement compared to SLR, DORIS or VLBI techniques) 
represents the vast majority of these geodetic stations (Fig. 1).
Fig. 1. ITRF2014 horizontal velocity field [5].
174 F. Perosanz / C. R. Physique 20 (2019) 171–175The transition from the celestial reference system (in which the orbits of the satellites are calculated) to the terrestrial 
reference (in which the coordinates of the stations are expressed) is parameterized by five quantities: the precession and 
nutation angles (from models), the Xp and Yp coordinates of the pole and the UT1–UTC offset. The latter (which represents 
the irregularities of the Earth rotation velocity) can be directly observed only by the VLBI technique, which targets celestial 
objects (quasars) instead of satellites. The Xp and Yp parameters are estimated by inverse method. Any deviation from XP
and YP produces a daily oscillation of the coordinates of stations whose amplitude and phase depend on the position of 
the station. Thus, GNSS geodetic stations, thanks to their density on the Earth, allow us to measure Xp and Yp with a 
remarkable precision of 0.2 milliarcsecond.
The realization of time scales requires the comparison and combination of observations from a global network of more 
than 200 atomic clocks (https://www.bipm .org /en /bipm /tai/). This fundamental task nowadays essentially relies on the GNSS 
technique because it allows us to estimate with great precision the offset of an atomic clock connected to a GNSS receiver 
whose coordinates are known. The PPP technique, which does not even require these “time-receivers” to be in common view 
of satellites, is widely used by laboratories contributing to the realization of time scales. Recently, Petit et al. [6] showed that 
IPPP solutions, by ensuring the continuity of integer phase measurement ambiguities between successive satellite passes, 
allows a significant gain in accuracy. Whether for the realization of space and time references or the determination of the 
movement of the pole, GNSS have allowed considerable progress and have become unavoidable.
8. From geodesy to centimeter navigation
If, at the creation of the IGS, three orders of magnitude of precision separated the world of geosciences (post-
processing static positioning) from the world of navigation (real-time positioning), this situation has since then con-
siderably evolved. The densification of the networks, the modernizations of both the systems themselves, the equip-
ment and the means of communication and calculation, made the delays for positioning a GNSS receiver reduced 
and the accuracy improved. The GNSS coordinates of the geodetic stations were determined weekly for the realiza-
tion of the ITRF2008, for example. Today the sampling is daily and various studies are conducted on the model-
ing and measurement of sub-diurnal movements of the Earth. Melachroinos et al. [7] and Lescarmontier et al. [8], 
for example, have been able to observe high-frequency oceanic load deformations and glacier vibration modes, re-
spectively, thanks to the accurate positioning of GPS stations over the course of a day. For the precise orbit calcula-
tion of satellites carrying a GNSS receiver, the differentiated approach is not suitable, because the common view be-
tween a terrestrial station and a satellite in low orbit is very limited. Laurichesse [9] demonstrated the interest of 
the IPPP technique for this type of problem by determining with centimeter accuracy the trajectory of the GRACE 
and JASON-1 satellites in post-processing. Using this same technique, Fund et al. [10] have shown that the trajectory 
of an oceanographic buoy (in post-processing) can be calculated with a similar precision. At CNES, the PPP-Wizard 
project (http://www.ppp -wizard .net/) aims to demonstrate the feasibility of real-time IPPP with a centimeter accuracy. 
This service is based on the real-time calculation of both precise orbits of the GNSS satellites and SSR corrections 
(Fig. 2).
It is on this principle that, for example, the application for smartphones “PPP-Wizlite” developed by CNES [11] should 
soon allow to navigate with an accuracy 10 to 100 times higher than initially specified for GNSS.
Thus, beyond the economic, technological, or sovereign stakes, GNSS, by providing unprecedented highly accurate (post-
processed and real-time) positioning, is playing a growing scientific and societal role.
Fig. 2. Real-time (static) rover coordinate determination (http://www.ppp-wizard.net).
F. Perosanz / C. R. Physique 20 (2019) 171–175 175References
[1] G. Wubbena, M. Schmitz, A. Bagge, PPP-RTK Precise point positioning using state-space representation in RTK networks, in: Proc. ION GNSS, 18th 
International Technical Meeting of the Satellite Division, 13–16 September 2005, Long Beach, CA, USA.
[2] S. Choy, S. Bisnath, C. Rizos, Uncovering common misconceptions in GNSS precise point positioning and its future prospect, international federation of 
surveyors, Article of the Month – September 2016.
[3] D. Laurichesse, F. Mercier, Integer ambiguity resolution on undifferenced GPS phase measurements and its, application to PPP, in: Proc. ION GNSS 2007, 
20th International Technical Meeting of the Satellite Division, 25–28 September 2007, Fort Worth, TX, USA.
[4] C. Velut, L. Jolivet, B. Garayt, T. Donal, J.-P. Cardaliaguet, Regina a CNES/IGN worldwide GNSS receivers network for IGS and navigation: overview and 
perspectives, in: 6th International Colloquium – Scientific and Fundamental Aspects of the Galileo Programme, Technical University of Valencia, Spain, 
25–27 October 2017.
[5] Z. Altamimi, P. Rebischung, L. Métivier, X. Collilieux, ITRF2014: a new release of the International Terrestrial Reference Frame modeling nonlinear 
station motions, J. Geophys. Res., Solid Earth 121 (2016) 6109–6131, https://doi .org /10 .1002 /2016JB013098.
[6] G. Petit, A. Kanj, S. Loyer, J. Delporte, F. Mercier, F. Perosanz, 1 × 10−16 frequency transfer by GPS PPP with integer ambiguity resolution, Metrologia 52 
(2015) 301–309, https://doi .org /10 .1088 /0026 -1394 /52 /2 /301.
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displacements from global and local grids: comparisons to GPS estimates over the shelf of Brittany, France, J. Geod. 82 (2007) 357–371, https://
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[8] L. Lescarmontier, B. Legresy, R. Coleman, F. Perosanz, C. Mayet, L. Testut, Vibrations of Mertz Glacier ice tongue, East Antarctica, J. Glaciol. 58 (210) 
(2012) 665–676.
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51 (8) (2013) 1311–1322.
[11] D. Laurichesse, C. Rouch, F.-X. Marmet, M. Pascaud, Smartphone applications for precise point positionning, in: ION GNSS+, 24–28 September 2018, 
Miami, FL, USA.


GNSS: A revolution for precise geopositioning

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