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Galileo Millimeter-Level Kinematic Precise Point Positioning With 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 satellites were put into service, approaching the completion of the Euro- pean global navigation satellite 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 orbit 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 orbits 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 Toulouse, France Full list of author information is available at the end of the article can be identifed. Tis so-called undiferenced ambiguity © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creat iveco mmons .org/licen ses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Katsigianni et al. Earth, Planets and Space (2019) 71:76 Page 2 of 6 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.
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