An Assessment of the Precse Products on Statc Precse Pont Postonng usng Mult-Constellaton GNSS Jareer Mohammed 1,2 1 College of Engneerng, Unversty of Wast Wast, Iraq jareermohammed@uowast.edu.q Rchard M. Bngley 3 3 NERC Brtsh Isles Contnuous GNSS Faclty (BIGF), Nottngham Geospatal Insttute, The Unversty of Nottngham, UK Rchard.Bngley@nottngham.ac.uk Abstract Precse pont postonng (PPP) s hghly dependent on the precse ephemerdes and satellte clock products that are used. Dfferent ephemers and clock products are avalable from a varety of dfferent organzatons. The am of ths paper s to assess the achevable statc postonng accuracy and precson when usng dfferent precse ephemerdes from three analyss centres Natural Resources Canada (EMX), European Space Agency (ESA) and GeoForschungsZentrum (GFZ), usng GPS alone, GLONASS alone, and GPS and GLONASS combned. It wll be shown n ths paper that the precse products are sgnfcantly affected by the tme-base of the reference statons, and that ths s propagated through to all the estmated satellte clocks. In order to overcome the combned bases n the estmated satellte clock, n the PPP processng, these clocks errors need to be handled wth an approprate varaton n the estmated recever clock. It wll also be shown that the precse coordnates of the satelltes dffer between the analyss centres, and ths affects the PPP poston estmaton at the mllmetre level. However, all those products wll be shown to result n the same level of precson for all coordnate components and are equvalent to the horzontal precson from a Global Double Dfference (GDD) soluton. For the horzontal coordnate component, the level of agreement between the PPP solutons, and wth the GDD soluton, s at the mllmetre level. There s a notable, but small, bas n the north coordnate components of the PPP solutons, from the correspondng north component of the GDD solutons. It s shown that ths dfference s due to the dfferent strategy adopted for the GDD and PPP solutons, wth PPP beng more affected by the changng satellte systems. The precson of the heghts of the recever stes wll be shown to be almost the same across all the PPP scenaros, wth all three products. Fnally, t wll be concluded that accuracy of the heght component s system dependent and s related to the behavour of antenna phase centre wth the dfferent constellaton type. Keywords; GNSS, GPS, GLONASS, Precse Pont Postonng; I. INTRODUCTION The Precse Pont Postonng (PPP) technque [1] has now developed to the level of maturty to allow t to provde daly Terry Moore 2, Chrs Hll 2 2 Nottngham Geospatal Insttute (NGI), the Unversty of Nottngham Nottngham, Unted Kngdom Terry.Moore@nottngham.ac.uk soluton poston estmates wth mllmetrc level repeatablty and accuracy for statc ponts [2], and has been shown to be a vable alternatve method to the conventonal doubledfference (DD) technque. However, the coordnates of postons determned by PPP are hghly dependent on the chosen precse ephemers and satellte clock products. Ths represents a key factor when comparng dfferent PPP solutons. Gao and Chen [3] assessed the performance of PPP GPS usng real-tme precse orbt and clock correctons; they compare the recever clock offsets wth the reference clock at AMC2 statons. However, they dd not nvestgate the effect of the system tme offsets on the satelltes clocks nor the mpact these had on the PPP solutons. Ca and Gao [4] nvestgated the tme offsets between GPS and GLONASS n PPP solutons wth a suggeston that the dfference between the recever clock offsets for GPS and GLONASS represents the tme dfference between the two constellatons. Reussner and Wannnger [5] used European Space Operatons Centre (ESOC) products for assessng PPP wth the assessment of nter-frequency bases, wthout an nvestgaton to the dfferent products. In addton, even though Ca and Gao [6] analyzed the effect of usng Informaton Analytcal Center(IAC) and ESA/ESOC products on the poston estmaton, usng a 4 hour dataset from only one staton OHI3, ths s a very short sample from whch to attempt to evaluate the effect of products on poston estmaton. They also dd not dscuss the dfference between the satellte orbts or precse clock products from the two analyss centres. Guo, et al. [7] made a qualty assessment of the precse orbt and clock products for the emergng Galleo, BeDou and QZSS system provded by the Mult-GNSS Experment(MGEX) over two years. However, ther focus was on the upcomng constellatons wthout an evaluaton to the avalable fully operatonal constellatons (GPS and GLONASS); and furthermore, they dd not menton the effects of reference staton tme-base. It s notable that there s no comparson of the effect on the tme reference on the products and the resultant effect on the precse satelltes orbt, and ther effect on the estmated coordnate components from PPP. Hence, ths paper has four key ams:
Investgate the effect of the tme-base of the reference statons on the satellte clock products and how ths can be handled n the PPP processng strategy. Investgate the correspondng effect on the fnal precse orbts, from dfferent Analyss Centres (AC) (Natural Resources Canada (EMX), European Space Agency (ESA) and GeoForschungsZentrum (GFZ)), and the subsequent effect on the estmated PPP poston components. Assess the achevable accuracy and precson, from statc PPP processng, when usng dfferent precse ephemerdes from the three ACs, usng GPS only (PPP GPS) GLONASS only (PPP GLO) and GPS plus GLONASS (PPP GPS+GLO). Analyses the evdent bases between the PPP solutons when compared to Global Double Dfference (GDD) solutons. II. METHODOLOGY A. PPP Daly Soluton Methodology All of the PPP daly solutons presented n ths paper were processed usng the POINT software, whch was developed as part of the Nsght project (www.nsght-gnss.org)[8]. The POINT software s programmed n C++, and ts core s the extended Kalman flter (EKF), as presented n Feng, et al. [9]. Undfferenced observatons were used for each PPP daly soluton usng general observaton equatons for the code and phase as follows: +M PF P F = e + cδ rcode cδ + I f F 2 + S f F 3 + T + Q PF For the carrer phase (m): L F + bas P,F bas P,F (1) = e + cδ rphase cδ I f F 2 S f F 3 + T +m F + q F + λ F (N F + B F B F ) (2) where s the satellte ndex and F represents the ndex of the GNSS frequency. For GPS satelltes, F = 1 (GPS L 1) and F = 2 (GPS L 2). For GLO satelltes F = 1 (GLO L 1) and F = 2 (GLO L 2) wth f k L1 = f 0L1 + k f L1 (3) f k L2 = f 0L2 + k f L2 (4) Here, k represents the frequency channel: f 0L1 = 1602 MHz for GLONASS L 1 band, f L1 = 562.5 khz frequency separaton between the GLONASS carrers n the L1 band, f 0L2 = 1246 MHz for GLONASS L 2 band, and f L2 = 437.5 khz frequency separaton between the GLONASS carrers n the L 2 band. In the above, e represents the geometrc dstance from the recever to the satellte, cδ r code s the recever clock offset for code, cδ r phase s the recever clock offset for phase, cδ s the satellte clock offset, I s the frst-order onospherc bas term, S s the second-order onospherc bas term, f F s the GNSS frequency, T s the tropospherc bas. M F s the multpath error for pseudorange, m F s the multpath error for carrer-phase, Q F s the nose for the pseudorange, q F s the nose for the carrer-phase. bas P,F s the recever code bas for pseudorange, bas P,F s the satellte code bas for pseudorange, λ F s the wavelength, N F s the carrer phase ambguty term, B F s the recever fractonal cycle bas (FCB), and B F s the satellte FCB. For all the PPP daly solutons, a decoupled recever clock (separate clocks for code and carrer) s appled for both GPS and GLO [10], and the onosphere-free observable s used wthout applyng any second-order onospherc bas correctons. The onospherc-free combnatons for the code and phase observables follow the process descrbed by Dach, et al. [11]. The processng settngs for the PPP solutons are summarzed as follows. In terms of the troposphere, the hydrostatc component of the zenth total delay s modelled usng Saastamonen [12] and the wet component of the zenth total delay s estmated as a state n the Kalman flter for every observatonal epoch,.e. at 30 second ntervals. In order to descrbe how the slant tropospherc delay vares wth respect to the recever-tosatellte elevaton angle, the Nell Mappng functon [13] or NMF s used. The azmuthal nhomogenety of the troposphere s also taken nto account by estmatng two states for the tropospherc gradent (E, N) usng the Chen model [14] and the Chen mappng functon [15] to map the tropospherc gradent nto the range doman. The Dfferental Code Bas (DCB) between C 1 and P 1, are corrected usng the products from the Centre for Orbt Determnaton n European (CODE) [11]. In order to nvestgate the actual performance of the ndvdual satellte systems, as well as the effect of dfferent products, no weghtng functons are appled to the observatons, except for the measurement nose standard devatons that are needed for the EKF. These are set to 2.0 m for pseudo-range measurements, and 0.01 m for carrer phase measurements, for both GPS and GLONASS. In addton, for all of the PPP daly solutons: the EMX, ESA and GFZ fnal precse ephemers products are used as the nput of the satellte coordnates and the satellte clock correctons. Satellte and recever antenna phase centre offsets and varatons are corrected usng an Antenna Exchange Format (ANTEX) [16] fle from the IGS,.e. the I08.ATX fle whch s consstent wth what was used n the creaton of the precse ephemerdes. Perodc deformatons of the Earth s crust as sold Earth tdes and ocean tdal loadng are taken nto account followng Kouba [16]. The phase wnd up correcton s also appled n accordance wth Wu, et al. [17]. Sub-daly pole and nutaton motons are corrected, accordng to the IERS conventons [18]. And lastly, for all of the PPP daly solutons the carrer phase ambgutes were not fxed to ntegers, but kept as float, and the cycle slp detecton method that has been mplemented follows Lu [19].
B. Global DD GPS Daly Soluton Methodology For the UK statons, the processng strategy for the global DD GPS daly solutons s summarzed n Table 3. Approxmately 150 contnuous GNSS statons (CGNSS) n the Brtsh Isles, ncludng 100+ that are part of the Ordnance Survey of Great Brtan (OSGB) natonal network, were ncluded n the processng along wth some 200+ IGS statons. of the precse ephemers products t was necessary to process a reasonably long-term data set. For the purposes of ths study, a data set focussng on the 100+ OSGB CGNSS statons that have daly RINEX observaton data fles archved as part of BIGF, and were ncluded n the global DD GPS daly solutons created by BIGF, was chosen, wth the CGNSS staton locatons llustrated n Fg. 2. Table 1 The processng parameters for Double Dfference solutons. Software Products (precse satellte coordnates and satellte clock offsets) Satellte and recever antenna phase center offsets and varatons Troposphere Ionosphere Sold earth tdes, Ocean tdal loadng, and Atmospherc tdal loadng Carrer phase ambgutes Bernese GNSS Software verson 5.2 [11] C13 (CODE repro2/repro_2013) re-analyzed satellte orbt and earth orentaton parameter products I08.ATX models for antenna phase center varatons a-pror modelng of troposphere effects usng VMF1G and estmaton usng zenth path delay and gradent parameters. mtgaton of the frst- and hgher-order (second- and thrdorder and ray bendng) onospherc effects Appled Fxed ambguty. A total of approxmately 150 contnuous GNSS statons (CGNSS) n the Brtsh Isles, ncludng 100+ that are part of the Ordnance Survey of Great Brtan (OSGB) natonal network, were ncluded n the processng along wth some 200+ IGS statons, as llustrated n Fg. 1. Fg. 2 The 100+ OSGB CGNSS statons ncluded n BIGF that were used for the assessment of PPP n ths study An nvestgaton was carred out based on all 100+ OSGB CGNSS statons (see Fg. 2) over a 7-week perod, as detaled n Table 1. In ths nvestgaton, only OSGB CGNSS statons that were contnuous for a specfc GPS week, had optmal 24 hour observatons recorded each day, and were also present n the global DD daly solutons were ncluded, whch led to data sets wth between 56 and 85 OSGB CGNSS statons per week beng avalable for analyss, as also detaled n Table 2. It s also worth notng that the 56 statons avalable n GPS week 1775 were also ncluded n all the 7 weeks. Table 2 GPS week and the number of OSGB CGNSS statons consdered n the analyss for each week GPS Week No. of CGNSS Statons 1775 1776 1777 1778 1783 1784 1785 56 85 79 74 74 76 79 Fg. 1 The network used for the global DD GPS daly soluton on 12/01/2014. III. EXPERIMENTAL RESULTS To allow a rgorous testng of the PPP daly solutons, the POINT software, and a thorough nvestgaton of the stablty 1) Reference staton tme-base PPP tme s relyng on the satelltes clock offset. However, a tme component that s the estmated recever offsets have to be estmated for the recever part, many unmodeled errors or offsets wll be absorbed by the estmated recever clock offsets. Startng wth the satellte clock, and more specfc wth GPS constellaton, all the ACs produced GPS precse ephemers. To look at the actual estmated satelltes clocks offset by dfferent AC, Fg. 3 (upper) s an example for GPS
PRN no. 5 and 7 on DOY 12, 2014 from the three ACs (EMX, ESA and GFZ). It represents the dfferences from the mean as well as the dfferences from the mean of the estmated recever clock offset of ALDB staton. s not the same for the GLO constellaton usng the same organzaton GLO products. Fg. 4 shows an example for GLO satelltes no. 1 and 2 for DOY 12, 2014 and the recever clock offsets from PPP GLO soluton for the same staton (ALDB) that had been used for PPP GPS. Fg. 3 GPS satelltes clock offset dfferences between EMX, ESA and GFZ(upper), recever clock offsets dfferences from the mean for ALDB staton (lower), DOY 12, 2014 It s clear from Fg. 3 that there s an offset between the precse satelltes clocks from dfferent ACs. Ths dfference s n nanosecond, where every nanosecond multpled by the speed of lght wll represent around 30 cm n the range. Those ACs have dfferent strategy for producng ther products. However, all those agences are followng the same part of strategy for the tme referencng staton, meanng that one reference staton from the chosen network (or the IGS network) for that day wll be chosen and the base tme network wll be fxed relatve to a specfc epoch of the chosen reference staton. Even though ths reference staton has an external frequency nstruments, t could have a drft or offsets from the GPS tme as can be seen from Fg. 3. Ths effect wll be propagated to the estmated satelltes clocks, whch s notced that ths offset s almost the same for all satelltes. The propagated tme offset nto the satelltes clock offset wll affect the PPP soluton. More specfcally, t wll affect the responsble parameter for balancng the tme offset. Ths parameter s the recever clock offset. It wll absorb the combnaton of the propagated tme offset from all satelltes tme offset on that specfc epoch. In addton, t wll absorb the offset propagated n all satelltes to be represented as an AC tme offset from the truth GPS tme. However, t wll be absorbed for makng the needed balance f t was modelled correctly. Ths means that f a constraned was made on the recever clock offset(s), then t wll lose the ablty to overcome that offsets whch wll results as an effect on other estmated parameters from PPP. As was showng n Fg. 3 whch s an example of the dfferences from the mean between the estmated recever clock offsets for both the code and carrer recever clock offset whch clearly showed that the recever clock offset absorbed the offset caused by the staton reference tme based. It s worth mentoned that, the resulted offsets from the reference staton tme based on the GLO satelltes clock offset Fg. 4 GLO satelltes clock offset dfferences from the mean between EMX, ESA and GFZ, b) recever clock offsets dfferences from the mean for ALDB staton, DOY 12, 2014 The reference staton offset s much hgher for the GLO than GPS constellaton. Ca and Gao [4] clamed that the dfference between the recever clock offsets for GPS and GLO represents the tme dfference between the two constellatons. Ths assumpton s not entrely accurate. To see why, there s a need to look at the dfference between the recever clock offsets for the same staton. In the presented strategy, two dfferent clocks, one carrer and the second s the code clock for every constellaton, were estmated. Fg. 5 represents the dfference between the estmated recever clocks offset between GPS and GLO, usng all three products (EMX, ESA and GFZ). Fg. 5 Recever clock offset dfferences between PPP GPS and PPP GLO for EMX, ESA and GFZ for ALDB staton DOY 12, 2014 If the assumpton from Ca and Gao [4] that the dfference between the recever clock offsets represents the tme dfference between GPS and GLO s correct then those dfference have to be smlar for all products type. The
dfference between the estmated recever clock offsets wll be contamnated by the ACs reference staton bas as well as the system tme dfference. It s also evdent that the code clock have hgher varaton and ths because of the nose n the code observable, more specfcally GLO code. 2) Precse Satelltes orbt effect on PPP poston estmaton Each AC uses dfferent strategy for estmatng the fnal satelltes coordnates, e.g. tropospherc models, tropospherc strategy, as well as dfferent versons of IERS that they used. Therefore, t s mportant to nvestgate the level of those dfferences from the estmated coordnates of satelltes. Fg. 6 represents the dfference from the mean between the three organzatons EMX, ESA and GFZ for the three satelltes Cartesan coordnates, on DOY 12, 2014. centmetres level, and ths wll affect the recever poston components at the mllmetres level. Ths s because of the adjustment that has to be done usng the EKF n ths research and the poston s n statc mode. Consequently, the effect of usng dfferent products from dfferent ACs on the recever poston components can be seen from Fg. 7, whch represents the dfferences between the estmated recever Cartesan coordnates usng the three ACs products and the mean soluton for PPP GPS and PPP GLO of ALDB staton on DOY 12, 2014. Fg. 7 The effect of usng dfferent Products on the Poston estmaton from PPP GPS Fg. 6 Dfferences from the mean between satelltes precse coordnates for (EMX, ESA and GFZ) from ther mean for DOY 12, 2014 The SP3 fles (satelltes coordnates) are representng the fundamental parameters for PPP soluton because t s the responsble parameters for defnng the system coordnates of PPP. The precse coordnates have to be mplemented n the desgn matrx wth respect to the recever coordnates component as known values. Therefore, any dfferences or small error between the used coordnates and the truth value wll theoretcally be propagated nto the recever poston components, as n: ((X ± error) s X r ), ρ ((Y ± error) s Y r ) ρ, ((Z ± error)s Z r ) ρ The use of the SP3 fles from a specfc AC, wll gve a dfferent soluton because even though the dfference between the satellte coordnates from dfferent ACs are wthn Whle the processng strategy s the same for all PPP scenaros except the products type, t s clear that the dfferences between these solutons are come from the products type effect, more specfcally, from the dfferent satelltes coordnates. 3) Products Effect on the accuracy and precson of PPP The analyss n terms of repeatablty consdered weekly soluton coordnate estmates as opposed to daly soluton coordnate estmates for the statons mentoned n Table 2 wth ther relevant GPS week. In these nstances, for each of the three PPP daly solutons (GPS, GLO and GPS+GLO) and the global DD GPS daly soluton, the mean of the daly soluton coordnate estmates for seven weeks were calculated. The weekly soluton coordnate estmates for each week were then subtracted from the mean to create weekly coordnate dfferences n terms of Eastng, Northng and Up components. Followng ths, t was possble to use the weekly coordnate dfferences n order to calculate the repeatablty of the weekly soluton coordnate estmates n each case n terms of Eastng, Northng and Up components. Ths was done for all the three products (EMX, ESA and GFZ). Bar charts representng the RMS of the repeatabltes of the weekly soluton coordnate estmates from PPP (GPS, GLO and
GPS+GLO) and global DD GPS as ndvdual coordnate components (Plan, Eastng, Northng, and Up) for all of the CGNSS statons consdered as well as the three products type (EMX, ESA and GFZ) are presented n Fg. 8. Fg. 9 RMS of the dfferences between the weekly soluton coordnate estmates from PPP (GPS, GLO and GPS+GLO) Fg. 8 RMS of the repeatabltes of the weekly soluton coordnate estmates from PPP (GPS, GLO and GPS+GLO) and global DD GPS for all CGNSS statons consdered usng three products(emx, ESA and GFZ) Lookng at the ndvdual component, the two components that have smlar performance for the Northng and Eastng are ESA and GFZ. The Northng component n ESA and GFZ has almost smlar value and smlar stablty over tme. Whle the Eastng component has a lower performance to beng twce the northng values whch s the effect of the ambguty. Regardng the heght component, the precson values almost the same for all PPP scenaros as well as all the used products except the PPP GLO when usng GFZ products, see Fg. 6. Ths means that the GFZ products (0.8 mm worse than ESA and 1.3 mm worse than EMX). In addton to repeatablty, t s also possble to estmate any dfferences between the weekly soluton coordnate estmates from PPP (GPS, GLO and GPS+GLO) and the weekly soluton coordnate estmates from global DD GPS. In ths regard, measures of accuracy are obtaned f the weekly soluton coordnate estmates from global DD GPS, whch are ndependent of the weekly soluton coordnate estmates from PPP, are assumed to represent the most probable values. Bar charts representng the RMS of the dfferences between the weekly soluton coordnate estmates from PPP (GPS, GLO and GPS+GLO) and the weekly soluton coordnate estmates from global DD GPS as ndvdual coordnate components (Eastng, Northng, and Up) for all of the CGNSS statons consdered as well as the three products type (EMX, ESA and GFZ) are presented n Fg. 9. To gve a comprehensve explanaton of any bases present, bar charts representng the mean of the dfferences, or the bases, between the daly soluton coordnate estmates from PPP (GPS, GLO and GPS+GLO) and the weekly soluton coordnate estmates from global DD GPS as ndvdual coordnate components (Eastng, Northng, and Up) for all of the CGNSS statons consdered as well as the three products type (EMX, ESA and GFZ) are presented n Fg. 10. Fg. 10 Mean of the dfferences, or the bases, between the weekly soluton coordnate estmates from PPP (GPS, GLO and GPS+GLO) and the weekly soluton coordnate estmates from global DD GPS for all CGNSS statons consdered
It s clear from Fg. 10 that the mean of the dfferences, or the bases, between the daly soluton coordnate estmates from PPP (GPS, GLO and GPS+GLO) and the daly soluton coordnate estmates from global DD GPS s a constellaton type dependent. In addton, there s a consstently larger bas n the Northng component than n the Eastng component, wth the Northng component from PPP (GPS, GLO and GPS+GLO) beng to the north of the Northng component from global DD GPS. One reason for ths could be a reference frame ssue, as whle the PPP technque reles only on the precse ephemers products, the DD technque reles on these but s also affected by the network of global CGNSS statons that were used. Re-consderng Fg. 1, whch gves an example of the network that was used for the global DD GPS soluton on 2014/01/12 (DOY 012 of 2014), the global network contans 97 CGNSS statons to the south of the lowest lattude OSGB CGNSS staton (SCIL, lat = 49.9) but only 19 CGNSS statons to the north of the hghest lattude OSGB CGNSS staton (KIRW, lat = 58.9). Furthermore, the subtle dfferences n the bases for the Northng coordnate component for PPP GLO and PPP GPS could be a constellaton ssue related to the hgher nclnaton of the GLONASS satelltes when compared to GPS, whch results n a sgnfcantly dfferent pattern for the GLONASS and GPS constellatons as shown n Fg. 11. Fg. 11 North bases relatve to the GDD Soluton for 85 statons n GPS week 1776. Lastly, consderng the bases n the Up coordnate component (Fg. 10), t s clear that n the case of PPP GPS+GLO there s effectvely a balancng of the errors present n PPP GPS and PPP GLO. Ths clearly results n an mprovement n the Up component for PPP GPS+GLO over PPP GLO, as the latter may be more affected by any mperfectons n the models for GLONASS antenna phase centre varatons. Fg. 10 Representatve satellte constellaton avalablty (Left: GPS, Rght: GLONASS) for ALDB staton on DOY 12, 2014. To support that dea, the dfferences between the mean weekly soluton of PPP GPS, PPP GLO and PPP GPS+GLO were subtracted from the mean weekly soluton from the global DD GPS; see Fg. 12 for 85 statons n GPS week 1776 for all the three products (EMX, ESA and GFZ). It s clear from the Fg. 12, that all PPP scenaros Northng dfferences have almost the same shape and ncreasng dfferences wth the ncreasng of the staton lattude. These ncreasng dfferences ndcate the effect of the reduced CGNSS statons to the north for global DD GPS soluton. In addton, whle PPP GLO has avalable satelltes to the north, t has larger dfferences than PPP GPS because of the reduced avalablty of the GPS constellaton wth the ncreasng of the staton lattude. Whle PPP GPS+GLO wll has the balanced dfferences between both constellatons as was shown n Fg. 12. IV. CONCLUSIONS In ths paper, the effect of the reference staton tme-base on the precse products has been assessed. It s shown that estmated precse satellte clock are beng affected by the chosen reference staton dependng on the AC. It s also shown that the tme-base s beng balanced by the recever clock offsets to be as AC offset type. Further, the effect of the satelltes coordnates on the PPP poston component has been assessed whch s beng found to be n the level of mllmeters. Furthermore, the effect of these products on the precson and accuracy has been assessed. It s found that the all these products have the same level of precson n the horzontal component because the ACs followed the same strategy over days. It s also found that the Eastng component beng worse that the Northng component for all products. Whle for the accuracy part t s found that the products have dfferent behavor especally for the up components. It s concluded that the notceable bas n the north component s constellaton type and lattude dependent. Furthermore, an mprovement s found n the Up component for PPP GPS+GLO over PPP GLO, as the latter may be more affected by any mperfectons n the models for GLONASS antenna phase centre varatons. ACKNOWLEDGMENT The servces of the Natural Envronment Research Councl (NERC) Brtsh Isles contnuous GNSS Faclty (BIGF), www.bgf.ac.uk, n provdng archved GNSS data and products to ths study, are gratefully acknowledged. Also,
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