Multi-Constellation GNSS Precise Point Positioning using GPS, GLONASS and BeiDou in Australia

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1 Internatonal Global Navgaton Satellte Systems Socety IGNSS Symposum 215 Outrgger Gold Coast, Australa July, 215 Mult-Constellaton GNSS Precse Pont Postonng usng GPS, GLONASS and BeDou n Australa Xaodong Ren School of Geodesy and Geomatcs,Wuhan Unversty, Chna Phone: Emal: xdren@whu.edu.cn Suelynn Choy School of Mathematcal and Geospatal Scences, RMIT Unversty, Australa Phone: Emal: suelynn.choy@rmt.edu.au Ken Harma School of Mathematcal and Geospatal Scences, RMIT Unversty, Australa Phone: Emal: ken.harma@rmt.edu.au Xaohong Zhang School of Geodesy and Geomatcs, Wuhan Unversty, Chna Phone: Emal: xhzhang@sgg.whu.edu.cn ABSTRACT GNSS Precse Pont Postonng (PPP) s a promsng approach to hgh accuracy (centmetre to decmetre-level) postonng wth a sngle recever,whch does not need a nearby reference staton lke tradtonal precse postonng technque such as dfferental postonng. The advent of mult-constellaton satellte systems, such as Chna s BeDou and European Unon s Galleo, offers addtonal satelltes and observables, whch can strengthen the postonng model thereby mprovng the accuracy and convergence tme of PPP. Ths paper descrbes the prospects and challenges n combnng multple GNSS systems such as GPS+GLONASS+BeDou n a PPP model. In partcular, t ams to assess the performance of the combned system n terms of postonal accuracy, relablty and tme of convergence n statc and knematc PPP modes. The result ndcates that the combned GPS+GLONASS+BeDou knematc PPP soluton sgnfcantly mprove the postonng accuracy by approxmately 2% and 3% n the horzontal and vertcal components, respectvely; and also shorten the convergence tme by more than 2% compared to GPS-only knematc PPP soluton. However, for the statc PPP soluton, the postonng accuracy and convergence tme of the combned system s margnally mproved compared to the GPS-only statc PPP soluton. KEYWORDS: Precse Pont Postonng (PPP), mult-constellaton, GNSS, BeDou, accuracy, convergence tme

2 1. INTRODUCTION Precse Pont Postonng (PPP) technque usng Global Postonng System (GPS) s a costeffectve hgh accuracy (centmetre to decmetre-level) postonng technque whch has been wdely used n many postonng and scentfc applcatons n recent years (Zumberge et al.,1997; Defragne et al., 27; Korsvk et al., 26; Larson et al., 23; Leandro, 29; Leandro et al., 211; L et al., 213; Wrght et al., 212). However, the prmary lmtaton of PPP s that t has long soluton convergence tme and also has low accuracy when the number of vsble satelltes s small n GNSS-challenged envronment, such as urban canyons, open pts and mountans. Fortunately, several new global and regonal navgaton satellte systems (GNSS), such as the Chnese BeDou satellte navgaton system, Europe s Galleo, and the Japan s Quas-Zenth Satellte System (QZSS) have emerged provdng accurate poston, navgaton, and tmng (PNT) servce. Fgure 1 shows the total number of satelltes that were expected n 21 from the varous navgaton satellte systems (Kogure, 21). Multconstellaton systems can provde many advantages to stand-alone GPS navgaton system(montenbruck, 214; Rzos, 213). For example, new sgnals wth hgher power and better trackng performance, as well as ncreasng number of vsble satelltes could mprove postonng n GNSS adverse envronments.on the other hand, three frequences postonng could provde new approaches to speed up ambguty resoluton process (e.g. Geng et al., 21; Ge et al., 28; Geng and Bock, 213; Laurchesse et al., 29) and elmnate hgherorder onosphere path delay.. Fgure 1. The number of SVs n mult GNSS systems (Kogure, 21). The Internatonal GNSS Servce (IGS) has set up the Mult-GNSS Experment (MGEX - to promote the use of new emergng navgaton satellte systems. The man obectves of the IGS MGEX are to establsh a global mult-gnss sgnals trackng network; to develop processng software capable of handlng multple GNSS observaton data; and to provde hgh-qualty data and products for all GNSS constellatons (Montenbruck, 214). Snce the establshment of the IGS MGEX, more than 9 GNSS statons across the world has contrbuted offlne and/or real-tme data to the MGEX network (see Fgure.2). In addton, there are fve MGEX Analyss Centres provdng dfferent product types, e.g., precse satellte orbts, clocks and nter-system bases (see Table.1) makng mult-gnss PPP possble. Many researchers around the world have been nvestgatng and evaluatng the

3 performance (accuracy and relablty) of mult-constellaton PPP (Ca and Gao, 213; L and Zhang, 214; Tegedor, 214; Chen and Zhang, 215; L and Zhang et al., 215). In ths paper, we present a study of mult-constellaton GNSS PPP performance (GPS, GLONASS, BeDou), both n statc and knematc mode, usng GNSS observaton data collected from three GNSS statons located n Melbourne, Australa. The accuracy, relablty and convergence tme are also compared and analysed n GPS-only, GLONASS-only, BeDou-only; and combned GPS+GLONASS, GPS+BeDou, GLONASS+BeDou, GPS+GLONASS+BeDou. The fnal precse satelltes clock and orbt products are obtaned from the MGEX products webste (IGS, 215a). 8 o N 4 o N o 4 o S 8 o S 18 o W 12 o W 6 o W o 6 o E 12 o E 18 o W BeDou GPS GLONASS Galleo Fgure 2. The IGS MGEX trackng statons network. Reference staton trackng BeDou are ndcated as red trangle, GPS as hollow black crcle, GLONASS as blue dot and Galleo as cross Table 1. The nformaton of mult-gnss precse orbt and clock products are provded from dfferent MGEX analyss centres (IGS, 215a). Avalablty Insttuton Products Constellaton (week/day) CNES/CLS grmyyyyd.sp3 Orbts and Clocks (15 mn) GAL Snce 1692/1 CODE GFZ comyyyyd.sp3 Orbts and Clocks (15 mn) GPS+GLO+ Snce 1689/5 GAL/GIO comyyyyd.clk Clocks (5 mn) gfmyyyyd.sp3 Orbts (15 mn) GPS+GAL 168/-1683/ gfmyyyyd.clk Clocks (5 mn) gfbyyyyd.sp3 Orbts (15 mn) Snce 1777/2- GPS+BDS gfbyyyyd.clk Clocks (5 mn) 1781/5 JAXA qzfyyyyd.sp3 Orbts and Clocks (5mn) GPS+QZS Snce 1751/6 TUM tumyyyyd.sp3 Orbts and Clocks (5mn) GAL+QZS Snce 1711/1 Wuhan Unv wumyyyyd.sp3 wumyyyyd.clk Orbts (15mn) Clocks(5mn) BDS snce 1721/2

4 2. Mult-GNSS PPP Model The basc observaton equatons of GNSS pesudorange and carrer phase observables ( P and L ( 1,2 )) between recever r and satellte, could be wrtten as: P c ( dt dt ) d I m ZTD B B (1) r, r r orb r, r r, r, P r, r ( r ) orb r, r r, + r, r, L L c dt dt d I m ZTD N b b (2) where r denotes the non-dspersve delay ncludng the geometrc dstance, the phase center offsets and varatons and staton dsplacements by tdal loadng, etc. (m); c s the speed of lght n vacuum (m/s); dt and dt are the recever r clock error and satellte clock error (s), respectvely; r d orb s the satellte orbt error (m); r, I s the onospherc delay of the sgnal path from recever r to satellte at at frequency (m); mr and ZTD are mappng functon and zenth tropospherc delay, respectvely; N s the nteger phase ambguty on L (m); Br, and B are the recever and satellte hardware code bases (m) on P, respectvely; b r, and b are the recever and satellte phase bases on L (m); phase observaton noses ncludng the multpath (m), respectvely. rp, and rl, are code and To elmnate the onosphere effects on satellte sgnals, we adopt the onosphere-free lnear combnatons of code pseudorange and carrer phase observatons. The observatons equatons could be wrtten as: f P f P P c P c P r,1 2 r,2 r, r,1 2 r,2 f1 f2 f1 f2 c ( dt dt ) d m ZTD ( c B c B ) ( c B c B ) r r orb r 1 r,1 2 r, r, P c ( dt dt ) d m ZTD B B r r orb r r, r, P Lr,1 1 Lr,2 r, r,1 2 r, L c L c L c ( dt dt ) d m ZTD ( c N c N ) ( c b c b ) ( c b c b ) r r orb r 1 r,1 2 r,2 1 r,1 2 r, r, L c ( dt dt ) d m ZTD N b b r r orb r r, r, r, L (3) (4) where L and P are the onosphere-free phase and code pseudorange observable n meters, respectvely; B and B are the recever and satellte hardware code bases (m) on the r, onosphere-free pseudorange combned P ; whereas b r, and b denote those on L (m); and N represents the onosphere-free lnear combnaton of ambgutes. The hydrostatc tropospherc zenth delay can be modelled usng a tropospherc model wth an accuracy level of 1.5-3mm (Nell, 1996). The non-hydrostatc (wet) delay component, on the other hand, s estmated as part of the parameter estmaton (Heroux and Kouba, 21). IGS precse ephemers products nclude the onosphere free satellte clock ( cdt cdt B ) and precse satellte orbts. When corrected for these products, equatons (3) and (4) becomes

5 P cdt cdt m ZTD (5) r, r r, r r, P r, r r, r Nr, r, L L cdt cdt m ZTD (6) Where cdtr, cdtr B s the ono-free recever clock, orbt errors are consdered r, nsgnfcant when usng IGS precse orbts, and N c N c N b b B B (7) r, 1 r,1 2 r,2 r, r, s the float ambguty whch s estmated as an addtonal parameter. It s worth notng that dfferent satellte navgaton systems refer to dfferent reference tme, and the recever clock error s the offset related to a sngle common reference tme. When usng the IGS clock products, the clocks are referenced to GPS tme hence the recever clock errors are estmated wth reference to GPS tme. The Inter-System Bas (ISB) between dfferent satellte systems (GPS/GLONASS/BeDou) must be taken nto consderaton when processng mult-gnss observatons. Apart from the ISB parameters, the Inter-Frequency Bas (B) needs to be consdered as the GLONASS system uses Frequency Dvson Multple Access (FDMA) sgnal scheme, whch result n recever- and satellte-bases that are frequency dependent. If GPS tme s used as the reference tme, Equatons (5) and (6) can be expanded to mult-constellaton PPP observatons model for GPS+GLONASS +BeDou, P cdt c dt m ZTD, G, G, G G, G, G r, r r r r, P L cdt c dt m ZTD N, G, G, G G, G, G, G r, r r r r, r, L P cdt ( c dt ISB ) m ZTD, R, R, R G, GR, R, R r, r r r r r, P L cdt ( c dt ISB ) m ZTD N, R, R, R G, GR, R, R, R r, r r r r r, r, L P cdt ( c dt ISB ) m ZTD, B, B, B G GB, G, B r, r r r r r, P L cdt ( c dt ISB ) m ZTD N, B, B, B G GB, B, B, B r, r r r r r, r, L (8) GB where ISBr denote the ISB parameters of GPS-BeDou, whch s only dependent on satellte system not frequency because that BeDou satellte systems adopted to the Code Dvson Multple Access (CDMA) scheme. Whereas, GLONASS sgnals are generated based on, FDMA scheme and thus the ISB for GPS-GLONASS ISB GR r are dfferent for each satellte for a trackng staton. 3. Test Results and Analyss 3.1 Data collectons and processng strategy To valdate the above-mentoned mathematcal model and evaluate the performance of multconstellaton PPP n Australa, three GNSS reference statons equpped wth dual frequency recever capable of mult-gnss trackng from the Vctoran Contnuously Operatng Reference Statons (CORS) network - GPSnet were selected. The statons were Benalla (BNLA), Marengo (MNGO) and Worr-Yallock (WORI). Seven days of GNSS observatons from 9-15 January 215 (DOY 9 to 15) were recorded at a samplng rate of 3-second. These GPSnet statons support trackng of GPS, GLONASS, and BeDou constellatons and ther nformaton are provded n Table 2.

6 Table 2. Informaton of the GNSS statons. ITRF8 Coordnates (dd.mmsssssss) Staton Recever Type Antenna Ellpsodal Lattude Longtude Heght BNLA TRIMBLE NETR9 TRM MNGO TRIMBLE NETR9 TRM WORI TRIMBLE NETR9 TRM In ths study, an extended Kalman Flter was used to estmate the state parameters. The parameters estmated at each epoch were the recever poston nformaton (dx, dy, dz), the recever clock error ( dt r ), the tropospherc zenth delay (ZTD), and tropospherc gradent n the NS and EW drectons, as well as the float carrer phase ambgutes (N). The recever dynamc coordnates and clock are modelled as Random Walk (Zumberge et al.,1997; Larson et al., 23; L et al., 213; Grover and Hwang, 1992). The ambguty s estmated as a constant f no cycle slps are detected over tme. Meanwhle, the statc coordnates, ISB and B are assumed to be constant (L and Zhang et al., 215). The tropospherc zenth wet delay s modelled as a random walk process. All satellte systems precse orbt and clock products were obtaned from Deutsches GeoForschungsZentrum (GFZ), whch s an IGS MGEX Analyss Centre (Table 1). The Phase Centre Offset (PCO) and Phase Centre Varaton (PCV) for satellte and recever of GPS and GLONASS were corrected usng the IGS antenna products (IGS, 215b). However, there s presently no avalable antenna products for BeDou, thus PCO only can be corrected usng conventonal antenna offsets for these satellte (BeDou about [,,.6] n meters (IGS, 215c)). PCV for satellte antennas and PCO as well as PCV correctons n the recever sde were not taken nto consderaton n the processng. The staton dsplacement (.e., sold Earth tdes, ocean tdes, sold Earth pole tdes and relatvstc effects) models suggested by the IERS conventons (Pett and Luzum, 21) and the phasewnd up effects model (Wu et al., 1993) were also appled. All solutons were algned to the IGS8 reference frame and GPS tme was used as the reference tme. The detals of the mult- GNSS PPP processng strategy are lsted n Table 3. Table 3. The strateges for Mult-Constellatons (GPS/GLONASS/BeDou) PPP. Item Models/Constrants - Ionosphere-free combnaton measurements Observatons - GPS: L1/L2; GLONASS: L1/L2; BeDou: B1/B2 - Elevaton-dependent weghtng strategy Elevaton Angle Cut-off - 7 Samplng Rate - 3s Precse Satellte Orbt - GFZ precse orbt products(gfmyyyyd.sp3:15mn) Precse Satellte Clock - GFZ precse clock products(gfmyyyyd.clk:5mn) - GPS+GLONASS:IGS antenna products(igs8.atx) Satellte PCO - BeDou: Conventonal Antenna Offsets ( - GPS + GLONASS: IGS antenna products (IGS8.atx) Satellte PCV - BeDou: not appled Recever PCO and PCV - GPS + GLONASS: IGS antenna products (IGS8.atx) - BeDou: Not appled. Phase wnd-up - Corrected (Wu et al.,1993) Ionosphere - Frst order effect removed by onosphere-free combnaton Troposphere model - Saastamonen model Dsplacement - Sold earth tdes, sold earth pole tdes,ocean tdes and

7 relatvstc effects modellng by IERS Conventon 21 Reference tme system - GPS Tme - Statc: Constant - Knematc: A Random Walk process for each epoch at a rate of Staton poston 1m/s - An ntal uncertanty of 1m - A Random Walk process for each epoch at a rate of 1m/s Recever clock error - An ntal uncertanty of 3km - A Random Walk process for each epoch at a rate of 36cm/h Troposphere delay - An ntal uncertanty of.15 m Ambguty - Constant for each satellte arc System tme dfference - A Random Walk process for each epoch at a rate of 1m/s 3.2 Statc PPP Results Fgure 3 shows the PPP postonal errors tme seres n the East, North and Up components for BLNA, MNGO and WORI statons on 11 January 215 as an example. The postonal errors were computed based on the dfferences between the estmated PPP soluton and the known staton coordnates. The symbols G, R and B n the fgure denote the abbrevatons of GPS, GLONASS and BeDou, respectvely. It can be seen that the combned trp leconstellaton PPP,.e., GPS+GLONASS+BeDou, shows the hghest precson and the fastest convergence n all of the three poston components. The performance of GPS-only PPP s better than the other sngle constellaton system. Conversely, BeDou-only PPP requred longer convergence tme and the up component converged sgnfcantly slower than the east component. However t should be noted that comparable postonng accuracy could be obtaned n the case of BeDou-only PPP after a long soluton convergence tme. Table 4 presents the RMS values (3 sgma) n metres and the measured convergence tme n mnutes for sx processng scenaros: GPS-only, GLONASS-only, BeDou-only, GPS+GLONASS, GPS+BeDou, GPS+GLONASS+BeDou. The statstcs were computed usng all seven days of data. In ths study, the statc poston flter s consdered to have converged when the postonng errors n all drectons reach ±.5 m and reman wthn ±.5 m. The convergence tme can be nterpreted as the perod from the frst soluton epoch to the converged epoch. It can be nferred from Table 4 that the combned GPS+GLONASS, GPS+BeDou and GPS+GLONASS+BeDou PPP show relatvely faster convergence tme and hgher poston accuracy n every component as compared to a sngle-constellaton soluton, especally GLONASS-only and BeDou-only PPP. For the sngle-constellaton soluton, GPS-only PPP soluton has already reached a hgh accuracy poston result under 7 cut-off elevaton angle because the number of vsble satelltes for GPS s suffcent for postonng. However, the BeDou-only PPP has poorer accuracy than the GPS-only and GLONASS-only soluton. In fact, t dd not provde any contrbuton to the combned GPS+BeDou or GPS+GLONASS+BeDou solutons because of the BeDou orbtal errors caused by the Inclned Geosynchronous Orbt (IGSO) satelltes and Geostatonary Orbt (GEO) satelltes. These errors are results of the satelltes havng small geometrc changes relatve to the trackng statons on the ground, as well as the number and dstrbuton of the global trackng statons used to compute the orbts s relatvely small and uneven. It s envsoned that the qualty of the BeDou satellte orbts and clock products wll mprove n the future as the dstrbuton and number of ground trackng statons ncrease. Ths wll be of great beneft to

8 mprovng the accuracy and convergence tme of PPP (Geng et al., 21; L and Qu, 214). E Bas[m] N Bas[m] U Bas[m] E Bas[m] N Bas[m] U Bas[m] E Bas[m] N Bas[m] U Bas[m].4 G R B GR GB GRB Epoch[Sample:3s] Epoch[Sample:3s] (a) BNLA G R B GR GB GRB Epoch[Sample:3s] Epoch[Sample:3s] (b) MNGO G R B GR GB GRB Epoch[Sample:3s] Epoch[Sample:3s] (c) WORI Fgure 3. Dfferences n poston between dfferent statc PPP postonng solutons,.e., GPS-only, GLONASS-only, BeDou-only, GPS+BeDou, GPS+GLONASS, GPS+GLONASS+BeDou, for

9 BNLA, MNGO and WORI GNSS statons on 11 January 215. Table 4. RMS ( 3 sgma ) n centmetres and convergence tme n mnutes for the daly statc PPP solutons. Staton Item GPS GLO BDS GPS+GLO GPS+BDS GPS+GLO +BDS Tme (<5cm) 58mn 1mn 52mn 53mn 6mn 51mn BNLA MNGO WORI East North Up D D Tme (<5cm) 65mn 15mn 4mn 51mn 66mn 5mn East North Up D D Tme (<5cm) 51mn 11mn 412mn 52mn 74mn 37mn East North Knematc PPP Results Up D D To assess knematc PPP n a mult-gnss scenaro, the same dataset used n statc processng was used to smulate knematc processng mode. Fgure 4 shows the a daly tme seres of the knematc PPP results n the East, North and Up components for sngle- and combnedconstellaton at BNLA, WORI and MNGO statons on January 11, 215. The green, pnk, red and black lnes represent the knematc PPP results for GPS-only, GPS+GLONASS, GPS+BeDou and GPS+GLONASS+BeDou, respectvely (GLONASS-only and BeDouonly PPP solutons are not presented as they showed less than deal results). Fgure 4 show that the combned GPS+GLONASS+BeDou PPP solutons have the shortest convergence tme as well as mproved postonng accuracy than the GPS-only PPP soluton. Table 5 presents the mean convergence tme and RMS values (3 sgma) n East, North and Up components after convergence of the postonng results usng seven consecutve days. The convergence crteron for the knematc PPP s that the postonng errors reach ± m and reman wthn ± m. It can be nferred from Table 5 that the GPS+GLONASS+BeDou PPP sgnfcantly mproves the PPP performance compared to the GPS-only soluton wth an average accuracy mprovements of 2% and 3% n the horzontal and vertcal components, respectvely. The postonng accuracy for the combned GPS+GLONAS+BeDou PPP solutons s better than 48 cm after a convergence tme. As for the convergence tme, all cases can acheve accuracy level of better than 2 cm wth less than 9 mnutes. The combned GPS+BeDou and GPS+GLONASS solutons sgnfcantly shorten the convergence tme

10 compared to the sngle-constellaton GPS-only soluton by about 23% and 2%. The combned GPS+GLONASS+BeDou PPP soluton shows the fastest convergence tme,.e., the solutons took about 32~48 mnutes to converge. In addton, the postonng accuracy of all cases n the horzontal component s better than the vertcal component whch s expected. Table 5. RMS (3 sgma) n centmetres and convergence tme n mnutes for the daly knematc PPP solutons. Staton Item GPS GPS+BDS GPS+GLO GPS+GLO+BDS BNLA MNGO WORI Tme (<2cm) 85mn 68mn 42mn 41mn East North Up D D Tme (<2cm) 89mn 62.5mn 45mn 48mn East North Up D D Tme (<2cm) 74mn 65mn 35mn 32mn East North Up D D E Bas[m] N Bas[m] U Bas[m].4 G GR GB GRB Epoch[Sample:3s] Epoch[Sample:3s] (a) BNLA

11 E Bas[m] N Bas[m] U Bas[m] E Bas[m] N Bas[m] U Bas[m].4 G GR GB GRB Epoch[Sample:3s] Epoch[Sample:3s] (b) MNGO G GR GB GRB Epoch[Sample:3s] Epoch[Sample:3s] (c) WORI Fgure 4. Dfferences n poston between dfferent knematc PPP postonng solutons,.e., GPSonly, GLONASS-only, BeDou-only, GPS+BDS, GPS/GLONASS, GPS/GLONASS/BDS) for BNLA, MNGO and WORI GNSS statons on 11 January Concluson The advent of mult-constellaton satellte systems, such as Russa s GLONASS and Chna s BeDou offers addtonal satelltes and observables, whch can strengthen the postonng model thereby mprovng the accuracy and convergence tme of PPP. Ths paper descrbes the performance of GPS+GLONASS+BeDou PPP n both statc and knematc modes. A multconstellaton GNSS PPP software for processng GPS, GLONASS and BeDou observatons was developed n ths study. The performance and the benefts of a combned GPS+GLONASS+BeDou PPP system were evaluated and compared usng data collected from the three Vctoran CORS network (GPSnet) n Australa. The combned multconstellaton (GPS+GLONASS+BeDou) knematc PPP mproves the postonng accuracy and shortens the convergence tme by about 2% when compared to a sngle-constellaton system PPP, e.g., GPS-only. Meanwhle, the tme seres of the mult-constellaton PPP were more stable than a sngle constellaton PPP soluton,.e., GPS-only soluton. Wth the modernsaton of GLONASS and the advancement of BeDou, Galleo and other satellte navgaton systems n the near future, t s antcpated that mult-gnss PPP wll provde

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