GPS-only, GLONASS-only and Combined GPS+GLONASS Absolute Positioning under Different Sky View Conditions

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1 ISSN (Prit), ISSN (Olie) Prelimiary commuicatio GPS-oly, GLONASS-oly ad Combied GPS+GLONASS Absolute Positioig uder Differet Sky View Coditios Kamil MACIUK Abstract: I recet years GNSS measuremets techiques obtaied a majority role i civil egieerig ad other techical fields. A example of this is the moitorig of both atural pheomea ad mamade costructios. The mai advatages of satellite positioig, as opposite to classical surveyig techiques like levellig or total statios, are cotiuous log term observatios ad ecoomic advatage, due to the lack of measuremet crew. Curretly, apart from GPS, other satellite systems i use like GLONASS or Galileo are becomig more importat. Together with developmet of GNSS measuremets for satellite positioig i ope areas, also urba ad moutaious areas ca be measured. This kid of areas was excluded from measuremets with sigle GNSS system, due to the lack of the required miimum umber of visible satellites. Multi-GNSS (hybrid, itegrated - usage of more tha oe satellite avigatio system i measuremets) positioig, curretly providig more tha 80 active satellites, opes ew grouds for satellite measuremets. Amog measuremet methods PPP is the most developig oe sice the begiig of 2 st cetury. Mai PPP advatages are: idepedece from referece statio, lack of limitatio of use to certai areas ad global coverage with cosistet, homogeous solutios. The paper shows the results of 90-days cotiuous static observatios processed with the usage of PPP techique o simulated differet sky view coditios. Measuremets were made o poits with kow coordiates as a costructio simulatio. The data were processed i three modes: GPS-oly, GLONASS-oly ad hybrid GNSS (GPS+GLONASS) usig three differet elevatio cut-off agles. Accuracy aalyses were carried out o the basis of fial, daily EPN solutios at the observatio time. Keywords: absolute positioig; egieerig; GLONASS; GNSS; GPS; PPP INTRODUCTION I the last years due to expasio of other tha GPS (Global Positioig System) systems itegrated GNSS (Global Navigatio Satellite System) become stadard of satellite measuremets. First GPS satellite was lauched i 978 ad the system became fully operable i 995 as a first GNSS. Fully operable meas to achieve omial plaed umber of satellites active o the orbit. Curretly besides GPS, also GLONASS (trasliteratio from Russia is GLObalaya NAvigatsioaya Sputikovaya Sistema or Global Navigatio Satellite System) is fully operable, ext to them partly operable are Chiese BeiDou ad Europea Galileo. Curretly there are more tha 80 GNSS satellites available []. Greater umber of simultaeously visible satellites theoretically brigs may advatages. First of all, the usage of multiple avigatio systems helps to icrease the quality ad accuracy especially i real time positioig [2]. It helps i a proper way to weight sigals proportioally to its stregth ad quality, or eve elimiate the less accurate satellites. Greater umber of available satellites also helps to shorte the duratio of the sessio, especially for most accurate measuremets. Also it makes available areas so far uavailable for GPS-oly observatios due to the lack of ecessary umber of simultaeously trackig satellites [3] (Figs. ad 2). There are also disadvatages associated with the usage of itegrated GNSS measuremets. The mai disadvatage icludes differet referece frames, the time scales ad iter-chaels are biased [4]. There are two types of GNSS positioig techiques i use: absolute ad relative positioig. Accordig to costructio ad priciple of GNSS operatio vertical compoet accuracy is three times smaller tha horizotal oes [5]. Sice the begiig of GNSS positioig most accurate ad commo i use is relative (differetial) positioig. This method is based o iformatio from referece statio or group of referece statios with kow coordiates. By observatio s differetiatio most of errors are reduced so this method is more precise tha absolute positioig after takig ito accout referece statio s error. The best kow ad most commoly used differetial positioig method is RTK (Real Time Kiematic) techique. Static measuremets withi a millimetre accuracy ca be achieved for respectively log sessios legth ad short vectors. For extremely short baselies (<several hudred metres) i 24-hours sessio, the accuracy could be less tha a millimetre [6]. O the other had, usig sigle vector of km with oe hour observatio sessio allows us to achieve results better tha 0 cm 3D [7]. As the practice shows addig GLONASS observatios to GPS i etwork processig does ot sigificatly chage accuracy of ay coordiates. I some cases addig GLONASS sigals improves solutio s quality for others, GPS-oly solutios were slightly better [8]. Figure Satellite blockig i urba cayos [2] A relatively ew GNSS positioig techique, used for about 5 years is PPP (Precise Poit Positioig). PPP is a absolute method, idepedet from the referece statio ad errors coected with it, but this method requires a dual frequecy receiver ad the use of precise Tehički vjesik 25, 3(208),

2 products. The accuracy ad reliability of GNSS PPP have bee coducted so far by various authors. Daily observatios without horizo obstacles geerally have coordiates repeatability at 2-3 mm level for horizotal coordiates ad 5-6 mm for height [9]. GPS+GLONASS observatios i kiematic mode were coducted by [0]. The authors cocluded that accuracy of combied GPS+GLONASS measuremets is compared to GPS-oly oes ad it is clearly visible that GLONASS-oly accuracy was lower tha other results. Combied GPS, GLONASS, BeiDou ad Galileo static positioig results show o sigificat improvemet of accuracy relatig to sigle GNSS positioig, but the covergece time has bee improved []. Figure 2 The example of the visible part of sky o a urba area [5] I aother elaboratio static PPP positioig i GPS+GLONASS mode shows slightly better results comparig to GPS-oly both for horizotal ad vertical coordiates [3]. Similar proposals metio authors [4], for 24 h ad 8 h observatios all (GPS-oly, GLONASSoly ad GPS+GLONASS) results are at the same accuracy level. For shorter observatios periods GPS oly solutios provide better accuracy compared with GLONASS-oly equivalets. Nowadays satellite measuremets techiques are i use for a wide rage of applicatios like: ladslides, miig areas moitorig, crustal deformatios or costructios moitorig. Curretly the most commo use refers to relative positioig especially RTK e.g. i bridges [6] or skyscrapers [7] moitorig for short itraday observatio sessios (Fig. 3). Figure 3 GPS moitorig ateas o a skyscraper [8] ad bridge [9] For a log term stability moitorig (several days, moths or permaet moitorig) various types of static measuremets (fast/rapid static, "stop-ad-go") or RTK methods are geerally i use. So far moitorig PPP techique was used oly for atural pheomea ad there are a lot of publicatios cosiderig static ad kiematic PPP mode e.g. [20, 2]. Deformatio moitorig i simulatio platform based o kiematic PPP observatios i four differet modes, was made [22]. I the best mode RMSE (Root Mea Squared Error) of horizotal coordiates was,5 cm, ad for vertical coordiate 2,2 cm. Accuracy of daily PPP observatios with the usage i GPS-oly, BeiDou-oly ad hybrid GPS BeiDou mode were made i [23]. The least accurate were BeiDou oly observatios (3D RMSE 3,7 cm). GPS-oly ad hybrid mode had the same accuracy level (respectively,6 ad,5 cm). 2 PRECISE POINT POSITIONING Stadard market GPS receiver usig code observatios i stadaloe mode accuracy ca be up to a few meters. Idepedece from the ifluece of errors trasferred from the referece statio is oe of the best PPP advatages. It makes from PPP a great tool for research of pheomeo coected with the movemet of earth crust [24]. I modellig PPP observatios, beside the ecessity of referece statio, satellite clock correctios are ot estimated, but assumed to be kow. Satellite clock correctios are itroduced ito processig together with Earth orietatio parameters ad orbit iformatio by precise products from e.g. IGS or CODE. Therefore estimated parameters are statio clock correctios, troposphere parameters ad coordiates. PPP observatio equatios of respective code ad phase o dual-frequecy GPS/GLONASS receiver o L ad L2 is defied as [25, 26]: g g g g i = rg + + orb + g g g g + dtrop + dio/ P + d i multi / P + ε i Pi P cdt cdt d Φ g g g g g i rg cdt cdt dorb dtrop g g g g g dio/ Φ + d i multi / Φ l i i Ni + εφi = r r r r i = rr + + orb + r r r r + dtrop + dio/ P + d i multi / P + ε i Pi P cdt cdt d Φ r r g r r i rr cdt cdt dorb dtrop r r r r r dio/ Φ + d i multi / Φ l i i Ni + εφi = where subscripts g ad r refer to GPS ad GLONASS satellites respectively: P i - is the measured pseudorage o L i (m) Φ i - is the measured carrier phase o L i (m) ρ - is the true geometric rage (m) c - is the speed of light (m/s) dt - is the receiver clock error (s) dt - is the satellite clock error (s) λ i - is the wavelegth o L i (m/cycle) N i - is the iteger phase ambiguity o L i (m/cycle) ε - is the measuremet oise (m) d orb - is the satellite orbit error (m) d trop - is the tropospheric delay (m) d io/li - is the ioospheric delay o L i (m) d multi/pi - is the multipath effect i the measured pseudorage o L i (m) d multi/φi - is the multipath effect i the measured carrier phase o L i (m) () (2) (3) (4) 934 Techical Gazette 25, 3(208),

3 I Eqs. (3) ad (4) the system time differece must be also cosidered for mixed GPS/GLONASS measuremets processig [27]: dt = t t sys (5) where t sys deotes either GPS system time (t GPS ) for GPS observatios or GLONASS system time (t GLONASSS ) for GLONASS observatios. U-differeced ioosphere-free code ad carrier phase combiatio, called L3, is widely used i PPP model. It ca be writte as [28]: 2 2 ( ) L = f L f L f f2 Its liear combiatio is appropriate for PPP, because it elimiates first order ioospheric path delay. Correspodig combiatios for code measuremets are defied as: 2 2 ( ) P = f P f P f f2 After takig ito accout Eq. (5), (6), (7) ito Eq. (3) ad (4) followig [25]: 2 g 2 g fg P fg P g 2 2 g g g IF = = r 2 2 g + + trop + εp f IF g f g2 2 g 2 g fg F fg F g 2 2 g g g g IF = = 2 2 g + cdt + dtrop + NIF + FIF fg f g2 2 r 2 r fr P r -fr P 2 2 g r r IF 2 2 r sys trop PIF fr -f r2 2 r 2 r frf fr F r 2 2 g r r r IF = = 2 2 r + cdt + cdtsys + dtrop + NIF + FIF fr f r2 P cdt d F r ε P = =r +cdt +cdt +d +e F r ε (6) (7) (8) (9) (0) () where subscripts g ad r refers to GPS ad GLONASS respectively: P IF - is the ioosphere-free code combiatio (m) Φ IF - is the ioosphere-free phase combiatio (m) f i - is the frequecy of L i (Hz) N IF - is the combied ambiguity term (m) ε IF - measuremet oise, multipath as well as other residual errors (m) For processig PPP a miimum of five satellites tracked at the same time is eeded. Observatios from five satellites are used to determie three coordiates, receiver s clock error ad tropospheric delay. Research shows that, depedig o sessio legth PPP, < cm accuracy ca be achieved [29]. Problems of GPS/GLONASS combied processig were discussed i detail by e.g. [30]. 3 METHODOLOGY To observe ifrastructure settlemet, superstructure deformatio ad to detect structural deficiecies ad damage treds, moitorig should be started i the early stage, just after structure completio. I this paper, the author put through simulatio of log-term costructio moitorig i differet sky view coditios. As show i Fig. 2 curretly o urba areas especially for ot tall buildigs this kid of field coditios is becomig more ad more frequet. Processig was made at two EPN statios to compare repeatability oe to aother. Statios are located o the territory of Polad: ZYWI (Zywiec, 49 4 N, 9 2 E) ad WROC (Wrocław, 5 7 N, 7 3 E). Both statios were equipped with dual frequecy GNSS (GPS+GLONASS) receivers. Receiver Trimble NETR5, atea Trimble TRM TZGD o ZYWI ad receiver Leica GRX200GGPRO with atea LEIAT504GG LEIS o WROC statio. GPS-oly, GLONASS-oly ad combied GNSS (GPS+GLONASS) data processig was made usig Berese GNSS Software 5.2. Processig parameters were: orbits - fial IGS ioosphere model - CODE 2h troposphere model - Neil daily DCB files - CODE Earth Orietatio Parameters - CODE satellites clock correctio - 30s IGS ateas calibratio model - IGS08 ambiguities resolutio QIF (Quasi-Ioosphere Free) Research refers to the accuracy of successive 90 daily observatio sessios with 30 s samplig iterval betwee st Jauary ad 3 st March. Accuracy aalysis was made o the basis of fial daily EPN solutios, referrig to the observatio time. Cartesia coordiates were trasformed to topocetric coordiates NEU by the formula (2): N siφicosλi siφisiλi cosφi dxi E siλi cosλi 0 dy = i U cosφicosλi cosφisiλi siφi dzi (2) where dx ˆ i = Xi X, dy ˆ i = Yi Y ad dz ˆ i = Zi Z. Coordiates residuals were calculated as mea absolute differeces accordig to Eq. (3): x = i= x ˆx i ad stadard deviatios Eq. (4): i= σ x = ( x ) 2 i ˆx (3) (4) where: ˆx - referece value from EPN coordiates x - mea deviatio of x coordiate (N, E ad U) Tehički vjesik 25, 3(208),

4 x i - value of i observatio - umber of observatios (here 90 daily solutios) As research shows, miimal elevatio mask is oe of the factors that ifluece the accuracy of measuremets the most [3]. Each of GPS-oly, GLONASS-oly ad GNSS processig were made i three differet miimal elevatio cut-off agles: 0, 25 ad 30. Tab. cosists of the collatio of sky accessibility above the observer, depedig o the elevatio cut-off agle. Table Sky visibility accordig to the cut-off agle Cut-off agle Sky visibility 79,0% 52,2% 30,9% Value 0 of miimal cut-off agle is assumed as a recommedatio for the applicatio i PPP [32]. It elimiates observatios with the biggest oise, multipath effect ad miimizes cycle slips [33]. Two other miimal elevatios of cut-off agles are simulatios of urba areas with very large sky obstructios. 4 RESULTS AND DISCUSSION Icreasig elevatio of the cut-off agle reduces visibility of least accurate satellites, but decreases the umber of observatios. Fig. 4 presets tracked satellites o statio WROC of st Jauary for 0 ad 40 elevatio cut-off agles. For 0 elevatio cut-off agle for all day mea umber of visible GPS ad GLONASS ad GNSS satellites are respectively 8,5, 6,0 ad 4,5. Figure 4 Number of visible satellites, st Jauary o WROC statio For 0 cut-off agle mea umbers of GPS, GLONASS ad GNSS satellites are 5,7, 4, ad 9,8 respectively. I case of last elevatio cut-off agle (<70% sky visibility) mea umber of GPS, GLONASS ad GNSS satellites is respectively 3,6, 2,7 ad 6,3. Fig. 4 shows that at mea latitudes (ZYWI 49 4 N, WROC N) due to costructio of global avigatio satellite systems umber of visible satellites dramatically fall eve i small elevatio agles. Dimesioless DOP (Dilutio of precisio) coefficiets represets geometric cofiguratio of satellites ad it is i correlatio with possible accuracy to achieve. Theoretically, the smaller the DOPs, the better accuracy achieved. It is assumed that for precise measuremets PDOP coefficiet should ot exceed value 2-3. Fig. 5 shows PDOP (Positio 3D DOP) o WROC statio for 40 cut-off agle mea GNSS PDOP was 0,8, max exceeds 70 so it was ot illustrated. Figure 5 PDOP, st Jauary, WROC statio I case of 0 ad 25 miimum PDOP values were respectively, ad,6, maximum,7 ad 5,3 ad mea values,4 ad 2,9. It clearly idicates that precise results for daily sessios ca be achieved with usage of 0 ad 25 cut-off agles. I some cases eve 40 cut-off agles ca assure precise results but such observatio sessios must be plaed i advace or measuremet duratio has to be log eough. Fig. 6 shows North-East coordiates residuals of the aalysed statios. Clearly visible accuracy dispersio is related to magitude of cut-off agle. The most accurate results o both statios were obtaied at 0 cut-off agle. I this case residuals do ot overstep 2 cm. For 25 miimal cut-off elevatio, beside GLONASS-oly results, most residuals do ot exceed 2 cm. Similar i case of 40 cut-off agle, beside GLONASS-oly results, most results are withi 3 cm accuracy. Aalysig results, because the satellite system used the less accurate i each case, were data based o GLONASS-oly measuremets. Results with usage of GPS-oly ad GNSS results are similar oe to aother i each case with o sigificat differeces. The course of Up compoet residuals is similar to the horizotal oes the most accurate results were achieved through the usage of GPS-oly ad GNSS sigals (Fig. 7). I each case GLONASS-oly results are the worst oes, eve i the slightest sky obstructio there are sigle >0 cm error results. GPS oly ad GNSS results are very similar at each statio ad each cut-off agle, ad i this case there is o sigle accidetal coordiate deviatio. Pheomea described i this paragraph might be explaied by algorithms applied i the software for GLONASS ambiguities resolutio. It is the result of iter-frequecy biases caused by divisio multiple access techique of GLONASS sigals, which causes fixig GLONASS PPP ambiguities difficult [34]. Compared to GPS, the resolved GLONASS ambiguities are characterized by lower quality, therefore GLONASS solutios have the accuracy lower tha the GPS oes. Similar coclusios for 24 h GPS ad GPS/GLONASS observatios were reached by e.g. [35]. 936 Techical Gazette 25, 3(208),

5 Kamil MACIUK: GPS-oly, GLONASS-oly ad Combied GPS+GLONASS Absolute Positioig uder Differet Sky View Coditios Figure 6 The residuals of North-East coordiates (m) Figure 7 The residuals of Up coordiate (m) For better uderstadig of the results, Tab. 2 presets the accuracy aalysis mea, absolute residuals ad stadard deviatios of fial coordiates. Rows are divided by cut-off agles (0, 25, 40 ) ad system i use (GPS, GLO - GLONASS, GNSS - GPS+GLONASS). Colums are divided by statios (WROC, ZYWI) ad coordiates (x, y, z). The odd-umbered row-paels shows mea absolute residuals of each coordiates (x, y, z respectively), while the eve-umbered row-paels show correspodig stadard deviatios. It is clearly visible that i each case the less accurate are GLONASS oly measuremets. GPS-oly ad GNSS results are similar i Tehički vjesik 25, 3(208), most cases. I some cases, more accurate ad precise are sigle GPS results i other two-systems GNSS results. For better uderstadig of the results, Tab. 2 presets the accuracy aalysis mea, absolute residuals ad stadard deviatios of fial coordiates. Rows are divided by cut-off agles (0, 25, 40 ) ad system i use (GPS, GLO - GLONASS, GNSS - GPS+GLONASS). Colums are divided by statios (WROC, ZYWI) ad coordiates (x, y, z). The odd-umbered row-paels shows mea absolute residuals of each coordiate (x, y, z respectively), while the eve-umbered row-paels show correspodig stadard deviatios. It is clearly visible that i each case the less accurate are GLONASS oly 937

6 measuremets. GPS-oly ad GNSS results are similar i most cases. I some cases more accurate ad precise are sigle GPS results i other two-systems GNSS results. Cut-off agle Table 2 Mea coordiates residuals ad stadard deviatios (mm) WROC ZYWI x y z x y z σ σ σ σ σ σ System GPS GLO GNSS GPS GLO GNSS GPS GLO GNSS x y z 2,7 2,7 2,7 3,3 7,7 7,6,8 4,6 5,4 2, 5, 5,2 5,0 7,8 20,7 8,0,0 20, 4,4 6,,9 9,4,4 20,0 2,7 4,0 8, 3, 4,0 5,4,8 3,2 8,7 2,3 3,3 8,5 2,8 5,3 4,5 5,3 5,6 7,5 2,3 5,6 2,0 3,5 4,0, 5,9 9,4 8,9 9,2 5,5 40,4 5,0 6,6 7,5 9,6 7,7 42,8 3,2 4,6 4,6 4, 5,8 9,5 2, 3,7 0,9 2,8 5,4 2,,4 8,0 24,3 5,6 8,6 24,4 3, 6,5 8,4 6,2 8,9 23,6 2,7 5,4 6,0 5,7 9,8 8,,3 2,4 53,0 3,4 5,5 85,2 4,8 5,8 20, 8,3 0,5 3,6 3,7 5,0 5,8 6,5 0,4 25,6 Bold fots i Tab. 2 are the smallest values of residuals ad stadard deviatios for each statio ad cut-off agle. The most accurate results i majority are with the usage of GPS-oly observatios; it is see especially o ZYWI statio. Addig GLONASS sigals to GPS does ot sigificatly improve the accuracy ad i some cases makes it eves worse. Mea residuals show that for horizotal coordiates usig PPP techique esures dow to 4 mm accuracy (GNSS mode), i case of Up coordiate it is 7-20 mm (all modes) for 0 cut-off agle. I case of 25 cut-off elevatio horizotal coordiates ad height are determied with 3-6 mm (GPS-oly ad GNSS) ad 5-20 mm (GPS-oly ad GNSS) respectively. At 40 cut-off elevatio horizotal coordiates were determied at 5- mm (GNSS) accuracy ad height at 24 mm (GPS-oly). 5 CONCLUSIONS Growig umber of available GNSS satellites activate ew stadard i satellite techiques. New sigals added to the existig GPS sigal make a possible tool for the improvemet of accuracy ad quality of measuremets. The developmet of global avigatio satellite sigals etails also progress i solutios algorithms. Performed research ra o GPS-oly, GLONASS-oly ad hybrid GNSS daily static observatios with usage of PPP techique i differet sky visibility level. Research shows that curretly existig software does ot improve sigificatly results comparig GPS-oly solutios with multi-gnss. Addig GLONASS sigals to GPS does ot affect oticeable improvemet of coordiates accuracy ad i some cases eve caused accuracy s deterioratio. Sigle GLONASSoly solutios are loaded by the biggest errors ad due to that are ot recommeded for precise purposes. The author shows that daily measuremets with usage of PPP techique provides < cm accuracy. I future additioal x y z ehacemet i software s algorithms should certaily improve the GNSS quality, especially i the case more tha two GNSS systems are used. ACKNOWLEDGEMENTS The paper is the result of research carried out withi statutory research o ad grat i the Departmet of Itegrated Geodesy ad Cartography, Faculty of Miig Surveyig ad Evirometal Egieerig, AGH Uiversity of Sciece ad Techology. 6 REFERENCES [] ftp://ftp.trimble.com/pub/eph/almaac.alm ( ). [2] Pirti, A. (206). The seasoal effects of deciduous tree foliage i CORS-GNSS measuremets (VRS/FKP). Tehicki vjesik - Techical Gazette, 23(3), [3] Wo D. H., Lee E., Heo M., Sug S., Lee J., & Lee Y. J. (204). GNSS itegratio with visio-based avigatio for low GNSS visibility coditios. GPS Solutios, 8(2), [4] Al-Shaery A., Zhag S., & Rizos C. (205). A ehaced calibratio method of GLONASS iter-chael bias for GNSS RTK. GPS Solutios, 7(2), [5] Witchayagkoo, B. (2000). Elemets of GPS precise poit positioig. The Uiversity of Maie, p [6] Wag, G. (20). GPS Ladslide Moitorig: Sigle Base vs. Network Solutios - A case study based o the Puerto Rico ad Virgi Islads Permaet GPS Network. Joural of Geodetic Sciece, 3(), [7] Jie, Z., Fei, L., Weimig, T., & Lifeg, G. (203). Crossocea GPS log distace rapid static positioig methods. Geodesy ad Geodyamics, 4(), [8] Sisma, Y., Elevli, S., & Sisma, A. (204). A statistical aalysis of GPS positioig usig experimetal desig. Acta Geodaetica et Geophysica, 49(3), [9] Ge, M., Gedt, G., Rothacher, M., Shi, C., & Liu, J. (2008). Resolutio of GPS carrier-phase ambiguities i Precise Poit Positioig (PPP) with daily observatios. Joural of Geodesy, 82(7), [0] Rabbou, M. A. & El-Rabbay, A. (205). PPP Accuracy Ehacemet Usig GPS/GLONASS Observatios i Kiematic Mode. Positioig, 6(), [] Lou, Y., Zheg, F., Gu, S., Wag, C., Guo, H., & Feg, Y. (206). Multi-GNSS precise poit positioig with raw sigle-frequecy ad dual-frequecy measuremet models. GPS Solutios, 20(4), [2] Tabatabaei, A., Mosavi, M. R., Khavari, A., & Shahhoseii, H. S. (207). Reliable Urba Cayo Navigatio Solutio i GPS ad GLONASS Itegrated Receiver Usig Improved Fuzzy Weighted Least-Square Method. Wireless Persoal Commuicatios, 94(4), [3] Liu, Y., Ye, S., Sog, W., Lou, Y., & Gu, S. (207). Rapid PPP ambiguity resolutio usig GPS+GLONASS observatios. Joural of Geodesy, 9(4), Techical Gazette 25, 3(208),

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