Katsigianni et al. Earth, Planets and Space (2019) 71:76 https://doi.org/10.1186/s40623-019-1055-1

EXPRESS LETTER Open Access Galileo millimeter‑level kinematic precise point positioning with ambiguity resolution Georgia Katsigianni1,2* , Felix Perosanz1, Sylvain Loyer2 and Mini Gupta3

Abstract On February 11, 2019, four additional Galileo were put into service, approaching the completion of the Euro- pean global navigation system constellation. For the frst time, the performance of Galileo system in terms of high-accuracy precise point positioning (PPP) can be evaluated. The results presented in this paper are based on one full week (February 11–17, 2019) of post-processed kinematic positioning for a set of fxed stations at a 30-s sampling. Due to the availability of precise Galileo and “integer” clock products, delivered by CNES/CLS Analysis Center of International GNSS Service, the impact of Galileo ambiguity resolution on the positioning results is also quantifed. The precision using Galileo-only measurements in the East, North and Up directions is 10 mm, 7 mm and 33 mm for PPP and 6 mm, 5 mm and 28 mm for PPP-AR (PPP with ambiguity resolution) (1 sigma), respectively. These results shall represent the future performance of the Galileo system for kinematic post-positioning. They also indicate the important future contribution of Galileo to high-accuracy multi-GNSS applications. Keywords: Galileo, Precise point positioning, Ambiguity resolution, Integer precise point positioning, Kinematic, Post-processing

Introduction segment consisted of 22 usable satellites (8 in plane A, 7 in Te International GNSS Service (IGS) gives an open plane B and 7 in plane C) and 2 satellites in elliptical access to the highest quality of GPS and GLONASS that drift relatively to the 3 nominal planes (GSA 2019). data and products (Dow et al. 2009). Te development Te satellite distribution within the constellation allows of new global navigation satellite system (GNSS), such for the frst time to evaluate the performance of the Gali- as the European Galileo, the Chinese Beidou, made it leo system that is approaching an optimal confguration. clear that the new era of multi-GNSS is forthcoming. In this study, we focus on the so-called precise point Consequently, the IGS has started a pilot project called positioning (PPP) technique (Zumberge et al. 1997). In multi-GNSS Experiment (MGEX) (IGS 2011). Since then, contrast to diferential positioning, which eliminates MGEX started delivering the best possible multi-GNSS common measurement biases between the stations and products available to the users (Montenbruck et al. 2017). the user, the PPP approach consists in considering cor- Various so-called analysis centers (AC) participate in this rections for each individual measurement bias; thus, no efort, using a global network of GNSS stations. It has control station around is needed. Te PPP technique can been demonstrated by Xia et al. (2018) and Li et al. (2018) provide positioning accuracy of sub-decimeter or even that including Galileo observations in a global multi- sub-centimeter level using the already fully deployed GPS GNSS processing is feasible for PPP-AR. and/or GLONASS systems. Te fnal accuracy depends On February 11, 2019, four additional Galileo satellites on individual terms compositing the observation model were put into service. At that moment, the Galileo space like satellite position, clock ofsets, atmospheric delays, phase center ofsets, phase center variations or phase win- dup efect (Kouba 2009). Nevertheless, the ultimate PPP *Correspondence: [email protected] performance is reached only when the integer number of 1 Centre National d’ Etudes Spatiales (CNES), 18 Avenue Edouard Belin, phase observations between a receiver and a given satellite 31400 , Full list of author information is available at the end of the article can be identifed. Tis so-called undiferenced ambiguity

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1 resolution step is challenging, but its feasibility has been where fE1 and fE5a are the Galileo frequencies E 5 demonstrated using GPS data (Laurichesse et al. 2009). (1575.420 MHz) and E a (1176.450 MHz), E1 Recently, Katsigianni et al (2018a, b) and Li et al. (2018) and E5a are the respective wavelengths (in [m]), 0.751 m have shown that such method can be applied to Galileo WL = c/ fE1 − fE5a = is the wide-lane wave- 0.109 m data. As a consequence, for the frst time and from this length, NL = c/ fE1 + fE5a = is the narrow- time onward, Galileo-only kinematic (post-processed) lane wavelength, and c represents the speed of light (in solutions using PPP and PPP with ambiguity resolution [m/s]). It has been proven (Katsigianni et al. 2018a, b) (PPP-AR) can be computed with nearly full constellation. that the following equations are valid for Galileo: Tis publication is organized in the following sec- ˜ s NWL = (NE1 − NE5a) + µr − µ tions. Firstly, the undiferenced ambiguity resolution and (2) PPP-AR processing are briefy presented. “Experimenta- N˜ WL tion and analysis of the results” section is devoted to the where is the averaged values of wide-lane ambigui- ties over one pass, N is the ambiguity term for the corre- experiments, the processing and the results. Finally, in µs “Summary, conclusions and perspectives” section, some sponding frequency, is the satellite delay (also known µr conclusions are given together with suggestions for fur- in the bibliography as WL satellite bias—WSB), and ther work and perspectives. is the receiver delay (also known as WL receiver bias— WRB) (both are in [WL wavelengths units]). Galileo PPP with ambiguity resolution It has been confrmed that µ are stable and constant for Te phase measurements transmitted by Galileo satellites Galileo over long periods. Hence, values are stable unless a change is observed (Katsigianni et al. 2018a, b). Te values give the distance to the receiver with a mm-level noise, µs but they are biased by satellite and receiver electronic of and their stability over a period of 2 years are shown in delays and by an integer number of phase cycles called Fig. 1. µr phase ambiguity. Resolving these biases is a key issue to Te can be estimated at each epoch (when at least two access the ultimate precision of the so-called IPPP (inte- satellites are visible). Te WL ambiguities are solved as real ger-PPP) or PPP-AR (PPP with ambiguity resolution) numbers, using a least squares estimation (LSE) system of technique. One possible approach called “integer recov- equations. Te foat ambiguities are fxed to integer values ery clock” consists in using a consistent and dedicated by applying a bootstrap method (Blewitt 1989; Dong and set of satellite clock ofsets and satellite hardware biases Bock 1989). (Geng et al. 2010). In October 2018, the CNES/CLS IGS Te next step is to form an ionosphere-free linear com- Analysis Centre started providing post-processed “inte- bination for code and carrier phase measurements (Loyer ger” Galileo satellite clock ofsets associated with Galileo et al. 2012): “wide-lane satellite biases” hardware delays (Katsigianni γ PE1 − PE5a γ DPE1 − DPE5a = + �hP et al. 2018a, b; Perosanz et al. 2018; Loyer et al. 2018). γ − 1 γ − 1 (3) Tese products are used in the following analysis. A direct comparison of pseudorange and phase measure- γ 1 1 − 5 5 − 5 ˜ WL ments cannot identify reliably the correct integer ambigu- E LE E aLE a E aN 1 ity bias. Te main reasons are the pseudorange noise level γ − compared to the phase wavelength and the opposite sign γ DLE1 − DLE5a = + NLW + �hL + NLNE1 of the ionosphere delays afecting the two measurements. γ − 1 Terefore, a two-step procedure based on diferent combi- (4) nations of pseudorange and phase measurements is needed. = 2 2 = 2 2 where γ E5a/ E1 fE1/fE5a , hP and hL are iono- In the frst step, the following Melbourne–Wübbena (MW) (Melbourne 1985; Wübbena 1985) equation for sphere-free phase clock diferences for code and carrier Galileo pseudorange from code ( PE1 and PE5a in [m]) and phase measurements [extensive explanation in Loyer carrier phase ( LE1 and LE5a in [m]) is used: et al. (2012)], DPE1 , DPE5a , DLE1 and DLE5a are the geo- metrical propagation distances between the satellite and fE1 fE5a the receiver for each type of measurement including MW = LE1 − LE5a fE1 − fE5a fE1 − fE5a  tropospheric elongation, relativistic efects, etc., and W is fE1 fE5a the phase windup efect (in [cycles]). − PE1 + PE5a fE1 + fE5a fE1 + fE5a  Te system of equations can be solved using the GRM (name for MGEX contribution of the CNES/CLS IGS = WL(LE1 − LE5a) − NL(PE1/ E1 + PE5a/ E5a) Analysis Center) satellite orbit and clock products. Te (1) GRM clock products are the so-called integer recovery Katsigianni et al. Earth, Planets and Space (2019) 71:76 Page 3 of 6

s Galileo µ 1 E01 E02 0.8 E03 E04 E05 0.6 E07 E08 0.4 E09 E11 E12 0.2 E13 E14 0 E15 E18 E19 -0.2 E21 E22

Fractional part [cycles] E24 -0.4 E25 E26 -0.6 E27 E30 E31 -0.8 E33 E36 -1 Jul 2016 Jan 2017 Jul 2017 Jan 2018 Jul 2018 Jan 2019 Month / Year Fig. 1 Fractional part of µs values for Galileo

clocks (IRCs) method (Geng et al. 2010) which preserves parameter satisfying covariance criteria is sequentially the integer nature of phase ambiguity biases (Loyer et al. fxed to an integer value. At this point only ionosphere- 2012). Te frst result of the LSE system of equations free ambiguity-fxed phase measurements are kept. Te gives a PPP solution in which ambiguity parameters are system of equations is again solved to give the PPP-AR resolved as real values. solution. Ten, the integer ambiguity resolution is taking place An extended overview of the entire process for PPP by applying a bootstrap method (Blewitt 1989; Dong and PPP-AR procedure is given in Fund et al. (2013), and Bock 1989). Each NE1 (integer number of NL cycles) Petit et al. (2015) and Montenbruck et al. (2018).

Table 1 Ambiguity fxing rates for every day of the year (DOY) DOY 042 043 044 045 046 047 048

BRUX (%) 90.42 100 100 100 100 100 95.12 KOUG (%) 91.67 100 100 100 96.30 100 92 AREG (%) 93.10 93.75 96.97 97.87 96.77 96.67 88.57 KIRU (%) 90.38 98.04 98.00 98.08 100 97.87 93.62

Table 2 Precision in East, North and Up directions for PPP and PPP-AR Mode PPP PPP-AR Station clock Direction East (mm) North (mm) Up (mm) East (mm) North (mm) Up (mm)

BRUX 10 7 33 6 5 28 External maser KOUG 10 10 38 9 8 36 Internal AREG 13 9 30 10 8 34 External rubidium KIRU 9 8 19 5 6 17 External cesium Katsigianni et al. Earth, Planets and Space (2019) 71:76 Page 4 of 6

Galileo PPP E Hist. E =0.00957m 0.1 0.15

0.05

y 0.1

0 [m ] 0.05 -0.05 Probabilit

-0.1 0 42 43 44 45 46 47 48 49 -0.1 -0.0500.05 0.1

N Hist. N =0.00668m 0.1 0.15

0.05

y 0.1

0 [m ] 0.05 -0.05 Probabilit

-0.1 0 42 43 44 45 46 47 48 49 -0.1 -0.0500.05 0.1

U Hist. U =0.03303m 0.2 0.06

0.1

y 0.04

0 [m ] 0.02 -0.1 Probabilit

-0.2 0 42 43 44 45 46 47 48 49 -0.1 -0.0500.05 0.1 doy [m] Fig. 2 Galileo-only PPP solutions of BRUX station in East (E), North (N) and Up (U) components (left) and their respective histograms with 1 σ values (right)

Experimentation and analysis of the results We used the one of the L2 bands instead, which may Using a fxed point and checking the repeatability of degrade the solutions by few millimeters. In addition to its independent epoch per epoch positioning solutions the receiver position estimation for every 30 s, integer is the easiest way to evaluate the data, the process- phase ambiguities, zenith tropospheric delays and hor- ing strategy (i.e., models used) and the software used. izontal gradients as well as receiver clock biases were Post-processing of the data benefts from better orbit estimated. A set of four IGS stations is used. For the corrections and from better decorrelation of the param- period of study, 1 week of data (February 11–17, 2019) eters to be resolved using a global resolution (e.g., least are chosen. During that period, 24 Galileo satellites squares) instead of a sequential flter (e.g., Kalman). (including the ecliptic E14 and E18) were processed. We processed Galileo-only PPP and PPP-AR solu- For the PPP-AR solutions, the ambiguity fxing rates tions using the state-of-the-art of models and conven- are given in Table 1. tions recommended by the IERS and the IGS. However, Te results in East, North and Up directions are given phase center variation maps of ground geodetic anten- in Table 2 for each mode. nas of the E5 signals are still not available to the users. Katsigianni et al. Earth, Planets and Space (2019) 71:76 Page 5 of 6

Galileo PPP-AR

E Hist. E =0.00575m 0.1 0.15

0.05

y 0.1

0 [m ] 0.05 -0.05 Probabilit

-0.1 0 42 43 44 45 46 47 48 49 -0.1 -0.0500.05 0.1

N Hist. N =0.00519m 0.1 0.15

0.05

y 0.1

0 [m ] 0.05 -0.05 Probabilit

-0.1 0 42 43 44 45 46 47 48 49 -0.1 -0.0500.05 0.1

U Hist. U =0.02842m 0.2 0.06

0.1

y 0.04

0 [m ] 0.02 -0.1 Probabilit

-0.2 0 42 43 44 45 46 47 48 49 -0.1 -0.0500.05 0.1 doy [m] Fig. 3 Galileo-only PPP-AR solutions of BRUX station in East (E), North (N) and Up (U) components (left) and their respective histograms with 1 σ values (right)

Figures 2 and 3 present a comparison between the In this paper, we examined the performance of the Gal- foat and fxed solutions for BRUX station. As it is ileo-only PPP and PPP-AR solutions in post-processing shown, the precision is improved signifcantly from kinematic mode. Repeatability results showed 10 mm PPP to PPP-AR solutions. for East, 7 mm for North and 33 mm for Up component when performing PPP solution. Te quality of results Summary, conclusions and perspectives increases when performing PPP-AR solution: 6 mm for With the appearance and the completion of new GNSS East, 5 mm for North and 28 mm for Up component in systems, it became clear that we move toward a multi- the example of BRUX station. GNSS era. However, it is also important to examine the Processing on other stations were also performed giv- performance of each GNSS system individually. Since the ing similar results (in the order of mm level). Results CNES/CLS AC is already providing orbit and clock prod- show that the method is applicable to any geodetic Gali- ucts to enable ambiguity resolution for Galileo (Loyer leo data receiver. et al. 2018), it is essential that these high-quality products Tis is a frst indication showing that Galileo-only solu- be used for PPP and PPP-AR performance evaluation. tions can reach unprecedented levels of precision that Katsigianni et al. Earth, Planets and Space (2019) 71:76 Page 6 of 6

can be used for the most high-accuracy demanding post- Fund F, Perosanz F, Testut L, Loyer S (2013) An integer precise point position- ing technique for sea surface observations using a GPS buoy. Adv Sp Res processing applications. 51:1311–1322. https://doi.org/10.1016/j.asr.2012.09.028​ Taking all the above benefts into consideration, it Geng J, Meng X, Dodson A, Teferle F (2010) Integer ambiguity resolution in seems obvious that eforts toward the PPP-real-time kin- precise point positioning: method comparison. J Geodesy 84:569–581. https://doi.org/10.1007/s0019​ 0-010-0399-x​ ematic (RTK) with ambiguity resolution using Galileo GSA (2019) Galileo system status—orbital and technical parameters. https://​ will be the next future demand. Tere is a big anticipa- www.gsc-europa.eu/syste​ m-statu​ s/orbit​ al-and-techn​ ical-param​ eters​ ​ tion from the GNSS community for the completion of the IGS (2011) International global navigation satellite systems service multi-GNSS experiment—call for participation. ftp://igs.org/pub/resource/pubs/​ full Galileo constellation. One thing is clear: Te Galileo IGS%20M-GEX%20VF.pdf system rests an important contribution to multi-GNSS Katsigianni G, Loyer S, Perosanz F, Mercier F (2018a) Improving Galileo orbit processing. determination using zero-diference ambiguity resolution in a multi-GNSS processing. Wuhan, China Katsigianni G, Loyer S, Perosanz F, Mercier F, Zajdel R, Sośnica K (2018) Improving Galileo orbit determination using zero-diference ambiguity Abbreviations fxing in a multi-GNSS processing. Adv Sp Res https://doi.org/10.1016/j.​ PPP: precise point positioning; GNSS: global navigation satellite system; asr.2018.08.035 PPP-AR: PPP with ambiguity resolution; IGS: International GNSS Service; IRCs: Kouba J (2009) A guide using the IGS products. https://kb.igs.org/hc/en-us/​ integer recovery clocks; MGEX: multi-GNSS experiment; AC: analysis centers; articles/20127​ 1873-A-Guide​ -to-Using​ -the-IGS-Produ​ cts​ IPPP: integer-PPP; MW: Melbourne–Wübbena; WL: wide-lane; WSB: wide-lane Laurichesse D, Mercier F, Berthias J, Broca P, Cerri L (2009) Integer ambiguity satellite bias; WRB: wide-lane receiver bias; RTK: real-time kinematic. resolution on undiferenced GPS phase measurements and its application to PPP and satellite precise orbit determination. Navigation 2:135–149 Acknowledgements Li X, Li X, Yuan Y, Zhang K, Zhang X, Wickert J (2018) Multi-GNSS phase delay Not applicable. estimation and PPP ambiguity resolution: GPS, BDS, GLONASS, Galileo. J Geodesy 92(6):579–608. https://doi.org/10.1007/s0019​ 0-017-1081-3​ Authors’ contributions Loyer S, Perosanz F, Mercier F, Capdeville H, Marty J (2012) Zero-diference GK and MG performed the processing. GK, FP and SL discussed and analyzed GPS ambiguity resolution at CNES-CLS IGS analysis center. J Geodesy the data. GK and FP edited the article. All authors read and approved the fnal 86:991–1003. https://doi.org/10.1007/s0019​ 0-012-0559-2​ manuscript. Loyer S, Perosanz F, Versini L, Katsigianni G, Mercier F, Mezerette A (2018) CNES/ CLS IGS analysis center: recent activities. Poster at IGS Workshop 2018. Funding Wuhan, China Not applicable. Melbourne W (1985) The case for ranging in GPS based geodetic system. In: 1st international symposium on precise positioning with the global position- Availability of data and materials ing system. U.S. Department of Commerce, Rockville, MD, pp 373–386 All data used in the present letter are available from the authors upon request. Montenbruck O, Steigenberger P, Prange L, Deng Z, Zhao Q, Perosanz F, Schaer S (2017) The multi-GNSS experiment (MGEX) of the international Competing interests GNSS service (IGS)–achievements, prospects and challenges. Adv Sp Res The authors declare that they have no confict of interest. 59(7):1671–1697. https://doi.org/10.1016/j.asr.2017.01.011​ Montenbruck O, Hackel S, Jäggi A (2018) Precise orbit determination of the Declarations Sentinel-3A altimetry satellite using ambiguity-fxed GPS carrier phase Not applicable. observations. J Geodesy 92(7):711–726. https://doi.org/10.1007/s0019​ ​ 0-017-1090-2 Availability of data Perosanz F, Loyer S, Katsigianni G, Mercier F, Versini L (2018) Galileo un-difer- All data used in the present paper are available from the authors upon enced integer products: method, results and perspectives: presentation at request. IGS workshop 2018. 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