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Acta Geodyn. Geomater., Vol. 17, No. 4 (200), 485–499, 2020DOI: 10.13168/AGG.2020.0035journal homepage: https://www.irsm.cas.cz/actaORIGINAL PAPERANALYSIS OF POSITION COORDINATE ACCURACY OF TRIPLE GNSS SYSTEM BYPOST-PROCESSING DUAL FREQUENCY OBSERVATIONS USING OPEN SOURCEGAMP: A CASE STUDYJabir Shabbir MALIK 1) *, Zhang JINGRUI 1) and Zahid Younas KHAN 2, 3)1)School of Aerospace Engineering, Beijing Institute of Technology, 100081 Beijing, ChinaSchool of Computer Science and Technology, Beijing Institute of Technology, 100081 Beijing, China3)Department of Computer Science and Information Technology, University of Azad Jammu and Kashmir, Muzaffarabad, Pakistan2)*Corresponding author‘s e-mail: jsmalik@bit.edu.cnARTICLE INFOABSTRACTArticle history:Received 19 July 2020Accepted 1 December 2020Available online 12 December 2020Multi GNSS system increases the GNSS positioning accuracy, efficiently improve the satellitegeometry strength and further enhances precise point positioning (PPP) performance. In this study,positioning coordinate accuracy of GPS, GLONASS, Galileo and BeiDou dual frequencyobservations is estimated and comparatively analysed. Ten days of dataset from nine InternationalGNSS service sites are adopted for eight different GNSS PPP scenarios. Position in east, north andup components and convergence speed test for single system GPS, GLONASS, BeiDou andGalileo, dual system GPS/GLONASS and Galileo/BeiDou, combined triple systemGPS/GLONASS/BeiDou and GPS/GLONASS/Galileo is investigated. Results demonstrate thatPPP solutions of GPS show an improvement in east, north and up components over GLONASS,BeiDou and Galileo PPP solutions. GPS PPP solutions reach to 2.88, 2.32 and 6.10 cm in eastnorth and up components, respectively. Difference of standard deviation (STD) values betweenGPS and GLONASS PPP results is 4, 3 and 2 cm, in east, north and up direction, respectively.Moreover, difference of STD between GPS and Galileo PPP is 1cm in all three components.Furthermore, BeiDou only PPP results reach to 15, 10 and 20 cm in east, north and up direction inAsia Pacific, respectively. Horizontal component for combine Galileo/BeiDou PPP andGPS/GLONASS PPP solutions reach to 3.24 and 3.02 cm, respectively. Calculation results of 3Dpositioning show that combined GPS/GLONASS/BeiDou PPP solutions improve by 5.59 % and17.72 % over GPS/GLONASS and Galileo/BeiDou PPP solutions, respectively. Furthermore,STD for 3D positioning of triple system GPS/GLONASS/Galileo shows an improvement of47.53 %, 31.56 % and 24.90 % over Galileo/BeiDou, GPS/GLONASS andGPS/GLONASS/BeiDou PPP results, respectively. Two different convergence time tests areundertaken. Results of GPS-only PPP solutions show fastest convergence speed to achieveaccuracy level of 1.0 cm over GLONASS-only, BeiDou-only, Galileo-only, and Galileo/BeiDouPPP solutions. Combine dual system GPS/GLONASS PPP convergence time show animprovement of 56.46 % over GPS-only solutions. The contribution of BeiDou to reducing theconvergence time of the combine GPS/GLONASS PPP improve by 27.53 % over combineGPS/GLONASS PPP convergence time. Moreover, GPS/GLONASS/Galileo PPP convergencespeed show an improvement of 20.06 % over convergent sessions of GPS/GLONASS/BeiDouPPP. Furthermore, to achieve accuracy level of 5.0 cm, combine three systemGPS/GLONASS/BeiDou PPP reduces the convergence time than the GPS/GLONASS/Galileoconvergent sessions length.Keywords:Multi GNSS Experiment (MGEX)Precise Point Positioning (PPP)Software package, GAMP1.INTRODUCTIONPrecise point positioning (PPP) is a most popularpositioning technique among GNSS users due to itshigh accuracy and flexibility. As a result, PPPattracted wide attention within GNSS researchcommunity. PPP employs precise satellite orbit andclock products generate by the International GNSSService (IGS) to improve the positioning accuracy(Zumberge et al., 1997; Kouba and Héroux, 2001).The improvement of positioning accuracy andinitialization time that required to converge positionaccuracy from decimeter to centimeter are two mostcritical parts in PPP (Cai and Gao, 2015). Researchersand scientists utilize GNSS data for scientific researchand GNSS applications, such as landslide monitoring(Wang, 2013; Capilla et al., 2016), crustal deformation(Tadokoro et al., 2012), meteorological applications(Li et al., 2015; Acheamponget al., 2016), GNSSreflectrometry applications (Malik et al., 2018) andsurface tomographic studies (Dong and Jin, 2018).Modernization of European satellite system (Galileo)and the evolution of Chinese navigation system(BeiDou), integration of GPS, GLONASS, Galileoand BeiDou constellation significantly improve thepositioning accuracy due to the increased number ofavailable satellites (Montenbruck et al., 2017; Liu etal., 2017; Afifi and El-Rabbany, 2016). To achievebetter positioning accuracy, error source such asionospheric delay must be mitigated. Therefore, PPPmodels such as ionospheric-free (IF) linearCite this article as: Malik JS, Jingrui Z, Khan ZY: Analysis of position coordinate accuracy of triple GNSS system by post-processing dualfrequency observations using open source GAMP: A case study. Acta Geodyn. Geomater., 17, No. 4 (200), 485–499,2020. DOI: 10.13168/AGG.2020.0035

486J. S. Malik et al.combinations to remove ionosphere first order delayor un-differenced un-combined (UDC) model by usingparameter estimation is adopted to mitigate theionospheric delay (Zhou et al., 2018a). UDC model isconsidered as a multi-frequency PPP model that keepsall the basic information of the observation and avoidnoise amplification (Liu et al., 2017; Liu et al., 2019).Next generation GPS III block system has successfullycompleted the in-orbit check after August 2019(http://www.gps.gov). GLONASS system recentlyintroduced the Code Division Multiple Access(CDMA) signals, while keeping the FrequencyDivision Multiple Access (FDMA) signals and theimprovement of the on-board clock stability(http://www.glonass-iac.ru). At the end of 2020 orbeginning of 2021, Galileo system will be upgradedthe constellation from 24 to 26 operational satellites(also included In-Orbit Validation (IOV) threesatellites). Old commercial service will be replaced bya High-Accuracy Service (HAS) and a CommercialAuthentication Service (CAS). Currently, Galileosystem is transmitting signals on five frequencies, i.e.E1 (1575.42 MHz), E5a (1176.45 MHz), E5b(1207.14 MHz), E5 (1191.795 MHz) and E6 (1278.75MHz) for several public services (Liu et al., 2019).Recently, 30th BD-3 satellite was launched intogeosynchronous orbit and currently BeiDous systemcomprises total of 55 satellites in orbit(www.en.beidou.gov.cn). BeiDous satellite basedaugmentation system (BDSBAS) provides services,among others, in aerospace, maritime affairs,transportation, and agriculture industry (Li et al.,2020; Hein, 2020).Several PPP software packages have beendeveloped by different research and academicorganizations. Bernese is a commercial softwaredeveloped at Astronomical Institute of the Universityof Bern (AIUB) (Dach et al., 2009). Bernese softwarehandles single and dual frequency GPS andGLONASS observations. GIPSY/OASIS (GOA II)designed and developed by National Aeronautical andAstronautical Jet Propulsion Laboratory (NASA, php),process GPS dual frequency observations andprovides station coordinates, clock offsets andestimates of atmospheric products. The ‘‘GPSToolkit’’ (GPSTk) is an open source projectdeveloped by the Applied Research Laboratories ofthe University of Texas (ARL, UT) (Salazar et al.,2010). GPSTk consists of core library, mathematicalfunctions, and source codes for GNSS community.GAMIT/GLOBK developed by MassachusettsInstitute of technology (MIT), which isa comprehensive analysis packages for GPSobservations.OutputofGAMITcontains3- dimensional relative positioning and earth-rotationparameters (Herring et al., 2015). GNSS-Lab (gLAB)is developed by Astronomy and Research Group atUniversitat Politecnica de Catalunya (UPC) isa multipurpose programming tool suit to processsingle and dual frequency of GPS and GLONASSmeasurements (Hernandez-Pajares et al., 2010). PPPHis an open software package, built and designed ontopopular programming language MATLAB (Bahadurand Nohutcu, 2018). PPPH is implemented foranalyzing dual frequency precise point positioningsingle or combined GNSS system (GPS, GLONASS,Galileo and BeiDou). Extra visual components andtools must be installed for MATLAB 2016a or olderversions. Aforementioned software tools and packagesdesign on different programming languages. Inaddition, all of the software packages have complexdata structure and complicated modules to processGNSS measurements. Moreover, some commercialsoftware requires an official license and payment feesfor registration.The performance of the GPS-only and combinedGPS/GLONASS PPP has been widely investigated,which confirms the improvements in the accuracy andconvergence time (Martín et al., 2011; Cai and Gao,2013; Choy et al., 2013; Yigit et al., 2014; Malik,2020). In some studies performance assessment ofGPS-only and combined GPS/BeiDou PPP wasanalysed (Wang et al., 2017). Shi et al. (2012)analyzed BeiDous/GPS combined PPP solutions usingPANDA (Position and Navigation Data Analyst,developed by the GNSS Research Center at WuhanUniversity) software package. The RMS of static PPPcan reach several centimeters to even millimeters forbaseline relative positioning. Zhao et al. (2017)showed that the contribution of BeiDou observationsto the combined GPS/GLONASS PPP in Asia-Pacificregion significantly reduces mean convergence speedby an average of 49.6 % with short observations ofdata and under harsh environment. The Galileoconstellation further increases the number of visiblesatellites and enhances geometric structure in space(Xia et al., 2019). Afifi and El-Rabbany (2016)demonstrated that the combination of Galileo, BeiDouand GPS observations further increased thepositioning accuracy and shortens the convergencetime compared to the GPS static PPP solutions. Xia etal. (2019) indicated that combination of Galileo, GPSand GLONASS observations can be improved by11.03 %, 10.59 % and 11.07 % in the north, east andup components in static mode, respectively. Theaverage convergence time can be reduced by 11.04 %for GPS/GLONASS solutions by adding Galileoobservations. Liu et al. (2019) analyzed combinedGPS/Galileo/BeiDou PPP with ambiguity resolution(PPP-AR) and estimated fractional cycle biases (FCB)for GPS, Galileo and BeiDou system using PANDAsoftware. Their results show that combinedGPS/Galileo/BDS PPP results can be improved in eastand north components. For the cut-off elevation angleof 400, the use of combine three systemGPS/GLONASS/Galileo enable to obtain about 90 %of the availability of PPP solutions with a centimeterlevel accuracy (Kiliszek and Kroszczyński, 2020). InOgutcu (2020), PPP solutions are analyzed using three

ANALYSIS OF POSITION COORDINATE ACCURACY OF TRIPLE GNSS SYSTEM BY .different cut-off angles 50, 150 and 300, static PPPresults show that three-dimensional accuracy isimproved when adding Galileo to GPS/GLONASSstatic PPP, especially for short observation times andup to 50 % (12 hr) and 65 % (24 hr) improvements areobserved for horizontal and vertical components,respectively.Previous studies demonstrated that with theaddition of Galileo observations with combinedGPS/GLONASS PPP solutions provide better positionaccuracy and reduce the convergence time. Inaddition, BeiDou system has been announced globallyafter June 2020. Therefore, main motivation of thisresearch is to evaluate and comparative analyze thestatic PPP coordinates accuracy and convergencespeed test of single-, dual- and triple system. Primaryfocus of this study is the post-processing the GNSSdata observations from each of the GNSS constellation(GPS, GLONASS, BeiDou, and Galileo). In addition,this study also investigates the positioning estimatesachievable using integration of Galileo and BeiDouobservations to the combine GPS/GLONASS PPPresults using recently available open source softwareGAMP for GPS (G), GLONASS (R), BeiDou (C),Galileo (E), combined two system GPS/GLONASS(G/R), Galileo/BeiDou (E/C) and three leo (G/R/E) PPP combinations.2.MULTI GNSS PPP MODELLINGThe basic observation equations for GNSSpseudorange (P) and carrier phase (L) can beexpressed as (Zhou et al., 2018b; Lou et al., 2016);𝑃 , 𝜌 𝑔 𝛿𝑡 𝛿𝑇 𝑐 𝒹 𝒹, 𝐼, 𝓂 𝑍 𝜉(𝑃 , )𝐿,(1) 𝜌 𝑔 𝛿𝑡 𝛿𝑇 𝜆 (𝒷 𝑁 , 𝜆 𝓂 𝑍 𝜉 𝐿𝐼, 𝜒 𝐼,; 𝜒 𝜆 /𝜆,, 𝒷 ) 𝐼, (2)(3)where scripts f, r, and j shows the frequency of satellite(f 1 , 2), receiver , and satellite system respectively;𝜌 is the true geometric range between satellite and thereceiver, c is the speed of light in vacuum (m/s);𝛿𝑡 and 𝛿𝑇 are the receiver and satellite clock offsetin seconds, respectively; 𝒹 , and 𝒹 are un-calibratedcode bias (UCB) of the receiver and satellite; 𝒷 , and𝒷 are the un-calibrated phase delay (UPD) of thereceiver and satellite; 𝐼,is the ionospheric delay ofthe signal in meters; 𝑁 , is the integer carrier phaseambiguity term in cycle; 𝜆 is the carrier wavelengthof dual frequency in meters; 𝜒 is the frequencydependent multiplier factor; 𝑍 tropospheric zenithwet delay; 𝓂 is the wet mapping function; 𝜉(𝑃 , )487and 𝜉 𝐿 ,are un-modelled measurement errors(noise, multipath) in GNSS code and phaseobservations respectively. The slant troposphericdelay on the path can be split into a hydrostatic drypart (ZHD) and a non-hydrostatic wet part (ZWD).ZHD is modelled using empirical Saastamoinen model(Saastamoinen, 1972); While, ZWD is estimated asunknowns along with other parameters in PPP model.Traditionally, ionospheric free (IF) linear combinationof pseudo-range and phase observations is adopted toremove the ionospheric delay, however, in this studyuncombined pseudorange and carrier phaseobservation model is used to estimate the slantionospheric delay as unknown parameter. Therefore,linearizing Eq(1) and Eq(2), we get;𝑝𝐣 𝓾𝐫 𝓿𝐫 𝛿𝑡 𝛿𝑇 𝑐 𝒹, 𝜒 𝐼𝑙 𝓂 𝑍 𝜉(𝑃 , ),(4)𝐣 𝓾𝐫 𝓿𝐫 𝛿𝑡 𝛿𝑇 𝜆 𝒷, 𝒹, 𝑁 , 𝜆 𝜒 𝐼, 𝓂 𝑍 𝜉 𝐿 𝒷, (5),where 𝑝 , and 𝑙 , denotes observed minus computed(OMC) pseudorange and phase observables fromsatellite j to receiver r at the frequency f, with all thenecessary corrections i.e, satellite and receiver antennaphase center offsets (PCO) and variations (PCVs),relativistic effects, Sagnac effect, tidal loadings, and𝐣phase windup is already modeled and added; 𝓾𝐫 is theunit vector of the direction from receiver to satellite;𝓿𝐫 denotes the vector of the receiver positionincrements relative to a priori position forlinearization. For the multi GNSS constellation(GPS/GLONASS/Galileo/BeiDou) PPP model of thepseudorange and carrier phase can be expressed as𝑝 𝓾𝐆𝐫 𝓿𝐫 𝛿𝑡 𝛿𝑇 𝑐 𝒹 , 𝜒 𝐼 , 𝓂 𝑍 𝜉 𝑃 , 𝐑 𝑝 , 𝓾𝐫 𝓿𝐫 𝛿𝑡 𝛿𝑇 𝑐 𝒹 𝜒 𝐼 , 𝓂 𝑍 𝜉 𝑃 , 𝑝 𝑝 𝑙 𝑙, 𝓾𝐂𝐫 𝓿𝐫 𝛿𝑡 𝛿𝑇 𝑐 𝒹, 𝓾𝐄𝐫 𝓿𝐫 𝛿𝑡 𝛿𝑇 𝑐 𝒹 𝜒 𝐼 𝜒 𝐼,,, 𝑙 𝑙 𝒹 , 𝒹 , 𝒹 (6) 𝓂 𝑍 𝜉 𝑃 ,, 𝜒 𝐼,𝒷 𝓿𝐫 𝛿𝑡 𝛿𝑇 𝜆 𝒷,, 𝓾𝐄𝐫 𝓿𝐫 𝛿𝑡 𝛿𝑇 𝜆 𝒷 𝑁 , 𝜆 𝜒 𝐼,, 𝒷,, 𝓂 𝑍 𝜉 𝐿, 𝓂 𝑍 𝜉 𝐿 , 𝓂 𝑍 𝜉 𝐿 𝑁 , 𝜆 𝜒 𝐼 𝒷, 𝓂 𝑍 𝜉 𝐿 𝓾𝐑𝐫 𝓿𝐫 𝛿𝑡 𝛿𝑇 𝜆 𝓾𝐂𝐫 , 𝓾𝐆𝐫 𝓿𝐫 𝛿𝑡 𝛿𝑇 𝜆 𝒷 𝑁 , 𝜆 𝒹 𝓂 𝑍 𝜉 𝑃 , 𝑁 , 𝜆 𝜒 𝐼,, , 𝒷 (7), 𝒷 ,where superscripts G, R, C and E refer to the GPS,GLONASS, BeiDou and Galileo, respectively; 𝑅

488J. S. Malik et al.denotes the GLONASS satellite with frequency factorj that are used for the computation of the carrier phasefrequencies of the individual GLONASS satellites;𝒷 , , 𝒷 , , 𝒷 , and 𝒷 , denotes phase delays of thereceiver r for G, R, C and E, respectively; 𝒹 , , 𝒹 , ,𝒹 , and 𝒹 , refers to the UCBs of the receiver for G,R, C and E, respectively.Frequency dependent satellite differential codebias (DCB) between pseudoranges of different GNSSconstellation needs to be corrected using productsfrom Center for Orbit Determination in Europe(CODE). The receiver UCBs are identical for codedivision multiple access (CDMA) signals (i.e., GPS,BeiDous, and Galileo) for all the satellites at eachfrequency, while they are different for GLONASS dueto the frequency division multiple access (FDMA)technique, which lead to frequency-dependent biasesin the receiver (Liu et al., 2017). For the GLONASSsatellites with different frequency factors, the receivercode biases are different. These biases are referred ), these bianes will influence positioningand show up in code residuals if not considered.GLONASS code IFBs are modeled as satellitespecific or frequency-specific parameters in PPPmodel. Both the ionospheric delay and DCBs arefrequency dependent. This implies that not allparameters can be unbiasedly estimable due to rankdeficiency. Ionospheric delay and receiver DCB areperfectly correlated, and they are estimated as lumpedterms.In multi GNSS PPP approach, precise satelliteorbit and clock products provide by internationalGNSS service (IGS) multi GNSS Experiment(MGEX) are applied, resulting satellite clock offsetsabsorb satellite UCBs in pseudorange Eq(6) andcarrier phase Eq(7) ;𝑝 𝓾𝐆𝐫 𝓿𝐫 𝛿𝑡 𝑐 𝒹 , 𝜒 𝐼 , 𝓂 𝑍 𝜉 𝑃 , 𝐑 𝑝 , 𝓾𝐫 𝓿𝐫 𝛿𝑡 𝑐 𝒹 𝜒 𝐼 , 𝓂 𝑍 𝜉 𝑃 , 𝑝 𝑝 𝑙 𝑙,, 𝓾𝐂𝐫 𝓿𝐫 𝛿𝑡 𝑐 𝒹 𝜒 𝐼 𝓂 𝑍 𝜉 𝑃 , 𝓿𝐫 𝛿𝑡 𝑐 𝒹, 𝓾𝐄𝐫 𝜒 𝐼, , 𝑁 , 𝜆 𝓂 𝑍 𝜉 𝐿, 𝓿𝐫 𝛿𝑡 𝜆 𝜒 𝐼 𝒷,,𝒷,,𝒹,𝒹,𝐼 𝑍 𝑁 )𝑁 𝑁 𝒷 𝒷The vector V includes, the receiver positionincrement 𝓋 , receiver clock offset 𝛿𝑡 , zenithtropospheric wet delay 𝑍 , slant ionospheric delay 𝐼 ,phase ambiguity 𝑁 in which UPD will be absorbedby phase ambiguity term, and the frequency dependentUCBs in the receiver 𝒹 , 𝒹 , 𝒹 , relative to theGPS 𝒹 , . The estimated parameters can be smoothedthrough a forward and backward filtering in postprocessing mode. To get most strengthen PPPsolutions, priori knowledge of the ionospheric delaysincluding the temporal correlation, spatialcharacteristics and external ionospheric model is alsoutilized to constrain the estimated ionosphericparameters. These constraints, to be imposed onobservations of a single station can be expressed as𝐼, 𝐼𝜈𝐼 ,𝐼𝑓, 𝑥 , 𝑥 𝑁(0, 𝜎 ) 𝑎 𝑎 𝑑𝐿 𝑎 𝑑𝐿 𝑎 𝑑𝐵 𝑎 𝑑𝐵 , 𝜎𝐼 𝐼 ,𝜎where k is the current epoch and k–1 is the previousepoch; 𝑥 is a zero mean with variance 𝜎 ; 𝜈𝐼 is thevertical ionospheric delay with a variance 𝜎 ; 𝑓 ,is the mapping function at the ionospheric pierce point(IPP); the coefficients 𝑎 describe the trend; 𝑑𝐿 and 𝑑𝐵are the longitude and latitude difference between theIPP and the station location; 𝐼 is the ionospheric delayobtained from external ionospheric model witha variance of 𝜎 .PERFORMANCE ANALYSIS ANDMETHODOLOGY3.1. EXPERIMENT SITE ,𝑉 (𝓋 𝛿𝑡 𝒹3. , 𝓿𝐫 𝛿𝑡 𝜆 𝒷 𝑁 , 𝜆 𝜒 𝐼, , 𝓂 𝑍 𝜉 𝑃 , 𝓾𝐆𝐫 𝓾𝐑𝐫 ,An equation to estimate unknown parameters ina state space vector V can be written as (Liu et al.,2017); , 𝒷 𝓂 𝑍 𝜉 𝐿 𝑙 , 𝓾𝐂𝐫 𝓿𝐫 𝛿𝑡 𝜆 𝒷 , 𝒷 𝑁 , 𝜆 𝜒 𝐼 , 𝓂 𝑍 𝜉 𝐿 , 𝑙 𝓾𝐄 𝓿 𝛿𝑡 𝜆 𝒷 𝒷𝐫𝐫, , 𝑁 , 𝜆 𝜒 𝐼 , 𝓂 𝑍 𝜉 𝐿 , , Consecutive ten days of dataset is collected from9 IGS stations which are distributed around the Earthduring September 21 – 30, 2020. IGS sites are alsodesignated as MGEX stations which are equipped withmulti- GNSS receivers to instantaneously trackobservations from GPS, GLONASS, Galileo andBeiDou satellites. Figure 1 presents the geographiclocation of IGS stations adopted in this study. Table 1shows the IGS study sites, coordinates, receiver typeand antenna. Figure 2 shows IGS station mean numberof available GNSS satellite system and the positiondilution of precision (PDOP) values of different GNSScombinations mode, i.e., single system GPS (G-only),GLONASS (R-only), Galileo (E-only), BeiDou(C- only), combined dual system GPS/GLONASS(G/R) and Galileo/BeiDou (E/C), triple system

ANALYSIS OF POSITION COORDINATE ACCURACY OF TRIPLE GNSS SYSTEM BY .Fig. 1489Geographical distribution of IGS MGEX stations used in the study.Table 1 Information about IGS MGEX stations coordinates,

analyzing dual frequency precise point positioning single or combined GNSS system (GPS, GLONASS, Galileo and BeiDou). Extra visual components and . focus of this study is the post-processing the GNSS data observations from each of the GNSS constellation (GPS, GLONASS, BeiDou, and Galileo). In addition,

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