Chapter 29 GPS/GLONASS System Bias Estimation and Application in GPS/GLONASS Combined Positioning

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1 Chapter 29 GPS/GLONASS System Bas Estmaton and Applcaton n GPS/GLONASS Combned Postonng Junpng Chen, Pe Xao, Yze Zhang and Bn Wu Abstract Mult-GNSS data analyss has become a new challenge wth the development of satellte navgaton systems. System bas s the key ssue n Mult-GNSS data analyss, whch has no recommended models wthn IGS communty. We ntroduce the ntegrated data analyss model developed at the GNSS data analyss center of Shangha Astronomcal Observatory (SHAO). Based on the routne GNSS data analyss at SHAO over 14 months, we analyze the precse GPS/GLONASS system bas product n detal. Results show: (1) system bas shows smlarty for same type of recevers, whle obvous dfference are observed for dfferent type of recevers; (2) varaton of system bas shows same pattern for all statons, whch ndcates that the long-term varaton of system bas s caused by the system tme offset; (3) system bas s nfluenced also by type of antenna type. A model s derved to separate hardware delay dfference (HDD) between GPS/GLONASS observatons at the same recever and the so-called nterfrequency bas (IFB). Analyss of the HDD and IFB tme seres shows that both terms are affected by the change of recever type, antenna type, frmware seres, cable type and length. Applyng the system bas nto PPP postonng, precson of GLONASS-only soluton s mproved by 55 % and precson of GPS/GLONASS combned soluton s mproved by 30 %. Keywords GNSS SHA Analyss center Inter system bas (ISB) IFB J. Chen (&) P. Xao Y. Zhang B. Wu Shangha Astronomcal Observatory, Chnese Academy of Scence, Shangha, People s Republc of Chna e-mal: junpng@shao.ac.cn P. Xao Y. Zhang College of Surveyng and Geo-Informatcs, Tongj Unversty, Shangha, People s Republc of Chna J. Sun et al. (eds.), Chna Satellte Navgaton Conference (CSNC) 2013 Proceedngs, Lecture Notes n Electrcal Engneerng 244, DOI: / _29, Ó Sprnger-Verlag Berln Hedelberg

2 324 J. Chen et al Introducton Coordnate and tme reference frame are both the key parameters of satellte navgaton system. As to tme reference frame, GPS s based on GPST, GLONASS s based on GLONASST. As to coordnate reference, GPS adopts WGS-84, GLONASS adopts PZ-90. There are dfferences n framework accuracy and scale for dfferent navgaton systems [1 4]. As navgaton system develops and updates, mult-system fuson has become the tendency of the development. In certan envronment, such as urban canyon and ravnes, sngle system can t provde servce because of lmted satellte condtons. Besdes, satellte constellaton has perodc regresson relatve to the Earth, the relatve relatonshp of navgaton satelltes Earth Sun also has regresson of dfferent perod. The perodc regresson of these relatve relatonshps wll add relevant perodc errors nto parameters such as coordnates and recever clock offset [5]. So mult-mode observaton ncreases the number of avalable satelltes. Meanwhle, the data fuson can reduce the nfluence of the perodc regresson of satellte constellaton, to mprove the precson of staton-relatve parameters (e.g. coordnate, troposphere) and other publc parameters (e.g. ERP) [6]. Hgh-precson ntegrated processng of mult-mode data s the guarantee of mult-system fuson. Mult-system ntegrated data processng need takng nto consderaton of varous system bas parameters. As to GPS/GLONASS ntegrated processng, the nter-system bas (ISB) of GPS and GLONASS system ncludes system s tme dfference TO and dfferent system s hardware delay bas dfference n recever (ΔDCB). Among them, system s tme dfference s the dfference between system tmes; ΔDCB s the hardware delay dfference n recever, t ncludes nter-frequency bas (IFB) of GLONASS satellte, whch s because GLONASS system s based on frequency dvson multple access (FDMA). Nowadays, IGS has not publshed ntegrated product and ts processng standard. Ths artcle ntroduces GPS/GLONASS ntegrated data processng model; analyses and dscusses the characterstcs of ISB and IFB parameter, whch s based on the 14 months routne results of global GNSS network provded by the GNSS data analyss center at SHAO (SHA). By ntroducng bas parameters to mult-mode postonng, the parameter resoluton precson can be greatly mproved GPS/GLONASS Integrated Data Processng Unfed Model Observaton functon of recever to GPS satellte j can be wrtten as: P j ¼ qj þ c dt dt j þ DCB j I j þ T j þ 1 j L j ¼ qj þ c dt dt j þ DPB j þ k N j I j þ T j þ e j ð29:1þ

3 29 GPS/GLONASS System Bas Estmaton 325 P j ; L j are respectvely the pseudorange and carrer phase observaton; q j s geometrcal dstance; c s lght speed, k s wavelength; dt s recever clock offset, dt j s satellte clock offset; DCB j and DPB j are pseudorange and carrer phase bas (ncludng both recever and satellte); N j s ambguty, I j s the onospherc delay error, T j s the tropospherc delay error, 1 j s other error correctons (ncludng relatvstc effect, tde, PCO, PCV, phase unwrappng and so on), e j s resdual. In practcal applcaton, I j could be gnored by formng the onosphere-free combnaton usng dual-frequency pseudo-range and carrer phase observatons. The pseudorange observaton n (29.1) provdes reference to clock offset parameters. The pseudorange bas DCB j (such as P1-P2, P1-C1) wll be absorbed by clock offset c ðdt dt j Þ: Nowadays, the carrer phase bas DCB j s not ncluded n GPS data processng, t wll be combned wth other parameters (manly ambguty). Then (29.1) can be rewrtten as: P j ¼ qj þ c dt dt j I j þ T j þ 1 j L j ¼ qj þ c dt dt j j þ k N I ð29:2þ j þ T j þ e j where: c dt dt j ¼ c dt dt j þ DCB j ð29:3þ k N j ¼ k N j þ DPB j j DCB Nowadays, IGS clock offset product reference s based on P1/P2 onospherefree combnaton. Under that bass, the DCB j of P1/P2 onosphere-free combnaton n (29.3) wll be absorbed by clock offset parameter. Other observatons need parameters provded by IGS to correct DCB j : Expend (29.2) to GPS/GLONASS dual-mode observaton, observaton functon of recever to GPS satellte k and GLONASS satellte j can be wrtten as : where: L kg L jr ¼ q kg ¼ q jr þ c dt dt k G I kg GþISB jk þ c dt dt j ISB jk ¼ c dt dt j ¼ TO þ DDCB j;k þ T kg þ k R N jr þ k G N kg I jr þ 1 k þ T jr R c dt dt k G þ e j ð29:4þ ð29:5þ In (29.4), the superscrpt R represents GLONASS, G represents GPS; ISB jk s nter-system bas on staton between GPS satellte k and GLONASS satellte j (ncludng system tme dfference TO and pseudorange delay bas n satelltes and recever DDCB j;k ; whch ncludes nter-frequency bas IFB j ). Defntons of other parameters are the same wth (29.1) and (29.2). TO n (29.5) s defned as a one-

4 326 J. Chen et al. day constant for all statons. DDCB j;k s manly because of GPS and GLONASS systems dfferent frequences, whch can be wrtten as DDCB sys : DDCB j;k s also slghtly effected by GLONASS satelltes dfferent frequences IFB j ; IFB j s varous to dfferent recevers and dfferent frequences. Formula (29.4) s the unversal observaton functon of mult-system ntegrated data processng, t also apples to the combned observaton of GPS and other satellte system. By defnng nter-system bas ISB jk ; estmatng c dt dt j G and unfng GLONASS clock offset to GPS tme system, we can realze the ntegrate of mult-system s tme reference. q j Contans satellte orbt and recever coordnates, restran staton coordnates to ITRF reference, then we can realze the unfcaton of mult-system s space reference. As to users, adoptng these orbt and clock offset and all knds of bas parameters under the same tme and space reference can unfes dfferent systems observaton to the same satellte system, thus smplfy the users applcaton and promote postonng precson. In (29.4), calculatng dt and dt j at the same tme s rank defcent, the general method s fxng one reference clock (usually the staton wth an external hghprecson atomc clock, fxng the clock offset by GPS pseudorange process). ISB jk contans TO, DDCB sys ; and IFB j ; IFB j can be absorbed n kr N jr whle TO and DDCB sys have correlatons wth clock offset. Consderng these correlatons above, there are two solutons: weght ISB jk to reduce the nfluence on correlaton; add zero mean condton to all the ISB jk n one staton (IGS AC Mal 643). Dfferent solutons cause the nconformty of GLONASS clock offset reference between IGS analyss centers [7] GPS/GLONASS Inter-System Bas Based on the mult-system ntegrated data processng modal above, Shangha Astronomcal Observatory developed ntegrated Geodetc Platform Of SHAO (GPOS) and establshed GNSS data analyss center (SHA) [8]. Fgure 29.1 shows the IGS network processed n the GNSS routne of SHA, among them about 70 statons can provde GPS/GLONASS combned observatons. Fgure 29.2 compares several analyss centers orbt precson (from to ). The precson of GPS orbts of SHA s 1.5 cm and the precson of GLONASS orbts s 3.2 cm, whch s about the precson of other IGS analyss centers. SHA adopts the strategy that EMR and GFZ uses to deal wth ISB: set the ISB of each recever to each GLONASS frequency as a one-day constant. Fgure 29.3 shows the GPS/GLONASS ISBs of staton BRMU (BERMUDA, UK) from to In ths fgure, dfferent color represents dfferent GLONASS satellte frequency. In ths perod ISBs are between 50 and 70 m, the dfference of

5 29 GPS/GLONASS System Bas Estmaton 327 Fg IGS network processed n the GNSS routne of SHA Fg Comparson of IGS analyss centers orbt precson. Results n mm adjacent day s less than 3 ns. Dfference of dfferent GLONASS frequency s less than 5 m (the mnus channel number s 7, the max s 6). IFB s order of magntude s obvously lower than ISB. Besdes, on BRMU s antenna type changed from TRM to JAVRINGANT_DM, ths change reflected to ISB obvously (about 10 m). It can be concluded that the type of antenna has nfluence on ISB. Fgure 29.4 shows the ISB seres of 26 LEICA recevers. Dfferent color represents dfferent antenna type. It can be seen that the ISB of statons wth LEICA antenna (LEIAT504GG and LEIAR25.R3), Topcon antenna (TPSCR3_GGD), Allen Osborne antenna (AOAD/M_T and AOAD/M_B) and Javad antenna (JAVRINGANT_DM) only have lttle dfference less than 5 m. Meanwhle Ashtech and AOAD/M_TA_NGS antenna (ths knd of antenna adopts Ashtech low nose amplfer technology [9]) and Trmble antenna (TRM ) have obvously bgger dfference. However, the dfference between dfferent antenna types s relatvely less than the dfference between recever types.

6 328 J. Chen et al. Fg ISBs of dfferent GLONASS satelltes on staton BRMU ( ) As mentoned, ISB ncludes 3 parts: system tme dfference TO, GPS and GLONASS systems hardware delay bas dfference DDCB sys ; and GLONASS satelltes nter-frequency bas IFB j : As t shows n Fg. 29.4, ISB s long-term changng tendency s consstent for the same type recevers, t manly reflects the long-term changes of TO and DDCB sys : Takng one frequency as reference frequency (such as channel 0) can reduce hardware delay bas dfference n staton and system tme dfference: Fg ISB seres of 26 LEICA recevers ( )

7 29 GPS/GLONASS System Bas Estmaton 329 Fg b0, b1 of all the 74 statons ISB m ISB n ¼ TO þ DDCB m;g TO þ DDCB m;g ¼ TO þ DDCB sys þ IFB m TO þ DDCBsys þ IFB n ¼ IFB m;n ð29:6þ IFB has lnear relatonshp wth the channel number [10, 11], so (29.6) can be rewrtten as: ISB m ISB n ¼ IFB m;n ¼ b0 þ b1 ðf m f n Þ ð29:7þ In (29.7), f m ; f n are GLONASS satelltes channel numble, b0, b1 are the fttng coeffcents. Take channel 0 as reference frequency, subtract ts ISB from other satellte s. By means of the least square ft accordng to formula (29.7), we obtan b0, b1 for each staton on each day. By usng 14 months ISB data, whch s provded by Shangha Observatory GNSS Analyss Center (SHA), we get all the b0, b1 of 74 statons (shown n Fg. 29.5). There are 7 recever types n total, t s shown that b0, b1 values of the same type recevers are consstent, and b0, b1 of dfferent recevers vary wdely. Antenna type s nfluence on b0, b1 s also obvous, the 11 statons wth Ashtech antenna has been marked by red crcles n Fg. 29.5, b0, b1 of these statons have obvous dfference.

8 330 J. Chen et al Applcaton of ISB n GPS/GLONASS Combned Postonng Introducng ISB to postonng can mprove the accuracy and valdty of postonng, especally when the vald satellte number s less [12]. ISB can be corrected drectly, then GPS and GLONASS can be seen as a sngle system. GPS/GLONASS combned postonng functon s: P kg P jr L jg L jr ¼ q kg ¼ q jr ¼ q kg ¼ q jr þ c dt I kg þ T kg þ c dt þ ISB I jr þ c dt þ k G N kg þ 1 k þ T jr I kg þ c dt þ ISB þ k R N jr þ e j þ T kg I jr þ 1 k þ T jr þ e j ð29:8þ The parameters n formula (29.8) are the same wth formula (29.4), GPS/ GLONASS satellte clock offset adopts SHA s precson product, ISB can be obtaned by usng the model above mentoned. To the staton wth known ISB, there are only 6 parameters (coordnates, recever clock offset and troposphere parameter) to be estmated. To the staton wth unknown ISB, we can gve ISB an ntal value accordng to the recever type and antenna type, use the IFB model above to correct ISB, we only need another parameter (ISB of channel 0), then we can reduce the number of parameters and promote postonng precson Pseudorange Postonng We choose 4 statons data (pots, casl, chur, aspa) on doy 120 to doy 126, 2012, the nterval s 30 s. These statons are nstalled wth dfferent manufacturers recevers, the recever and antenna nformaton of these statons s n Table Tests are conducted by usng pseudorange observatons n 2 strateges: GON- ASS only and GPS/GLONASS combned postonng. Every strategy s appled n 3 scenaros: 1. Wthout consderaton of GLONASS IFB; 2. Introduce GLONASS IFB from SHA; 3. Introduce GLONASS IFB modle of the correspondng recever; estmate a oneday parameter: ISB of frequency-0. The coordnates precson and ncrease rate are shown n Tables 29.2 and It can be seen from the statstcs n Tables 29.2 and 29.3 that wthout consderng GLONASS IFB obtans the lowest precson, whle drectly usng ISB provded by SHA obtans the hghest precson. The two ways to ntroduce IFB both greatly mprove the postonng precson, coordnate precson ncreases up to

9 29 GPS/GLONASS System Bas Estmaton 331 Table 29.1 Staton nformaton Staton Recever type Antenna type pots JAVAD TRE_G3TH DELTA JAV_RINGANT_G3T cas1 LEICA GRX1200GGPRO AOAD/M_T chur TPS NET-G3A ASH701945E_M aspa TRIMBLE NETR5 TRM Table 29.2 GLONASS pseudorange postonng coordnates precson and ncrease rate Staton Wthout IFB RMS (m) IFB model ISB from SHA RMS (m) Increase rate (%) RMS (m) Increase rate (%) chur aspa cas pots Table 29.3 GPS/GLONASS combned pseudorange postonng coordnates precson and ncrease rate Staton Wthout IFB RMS (m) IFB model ISB from SHA RMS (m) Increase rate (%) RMS (m) 提高率 (%) chur aspa cas pots %. Precson of combned postonng s up to 4 tmes better than of GLONASS sngle system (chur, from 7.60 to 1.89 m) Carrer Phase Postonng We make a test of Knematc PPP wth the carrer phase observaton data at the staton CHUR on 2012 doy 318. Ths test s appled n 4 scenaros: 1. GPS PPP 2. GLONASS PPP 3. Combned GPS/CLONASS PPP 4. Based on the thrd strategy, ntroduce the nter-system hardware delay bas IFB, whch s provded by Shangha Observatory GNSS Analyss Center. All of these four strateges obtan satsfactory fnal postonng results. Fgure 29.6 shows the postonng error and ts components n X, Y, Z drectons on the frst 50 epochs. It can be seen that the convergence speeds of these four strateges are all

10 332 J. Chen et al. Fg Knematc carrer phase PPP results on staton CHUR fast, among them the convergence of combned GPS/GLONASS PPP s faster than sngle system PPP. Introducng ISB only has lttle effect on the frst several epochs. The results of strategy (29.3) and (29.4) are almost the same, ths s because n strategy (29.3), the ISB values have been absorbed by ambgutes, although t gets good precson and fast convergence speed, ts ambgutes are not accurate Concluson As navgaton system develops and updates, mult-system fuson has become the tendency of the development. Mult-mode can solve the ssues of coverage and system bas that may exst n sngle system. In certan envronment, such as urban canyon and ravnes, sngle system could not provde servce because of lmted satellte condtons. We ntroduce the ntegrated data analyss model by GNSS data analyss center of Shangha Astronomcal Observatory (SHAO). Based on the routne GNSS data analyss at SHAO over 14 months, we analyze the precse GPS/ GLONASS system bas product n detal and put forward a model of nter-frequency bas (IFB). Results show: (1) ISBs have smlarty n recevers of the same type, whle obvous dfference are observed n recevers of dfferent type; (2) varaton of ISBs shows same pattern for all statons, whch ndcates that the long-term varaton of ISB s caused by the system tme offset; (3) ISB s nfluenced also by antenna type. Applyng ISB nto pseudorange postonng, precson of GLONASS-only soluton s mproved by 55 % and precson of GPS/GLONASS combned soluton s mproved by 30 %. Applyng ISB nto PPP, there s no obvous effect on coordnates, ths s because n PPP, ISB can be absorbed by ambguty.

11 29 GPS/GLONASS System Bas Estmaton 333 Acknowledgments Ths paper s supported by the 100 Talents Programme of The Chnese Academy of Scences, the Natonal Hgh Technology Research and Development Program of Chna (Grant No. 2013AA122402), and the Natonal Natural Scence Foundaton of Chna (NSFC) (Grant No and ). References 1. Brown K (1991) The theory of the GPS composed clock. In: Proceedngs of ION GPS-91, NM, Insttute of Navgaton, Albuquerque, pp GLONASS Interface Control Document (2008): Edn 5.1, Russan Insttute of Space Devce Engneerng 3. Delporte J (2009) The defnton and mplementaton of Galleo system tme (GST), ICG-4 WG-D on GNSS tme scales 4. We Z (2010) The tme and space reference n satellte navgaton system. Chna satellte navgaton conference (CSNC), Bejng 5. Flohrer C (2008) Mutual valdaton of satellte-geodetc technques and ts mpact on GNSS orbt modelng. Geodaetsch-geophyskalscheArbeten n der Schwez, vol Dach R, Schaer S, Lutz S, Mendl M, Beutler G (2010) Combnng the observatons from dfferent GNSS, EUREF 2010 Symposum, June 02 05, 2010, Gävle, Sweden 7. Dach R, Schaer S, Mendl M (2012) Comparson of GPS/GLONASS clock solutons, IGS workshop on GNSS Bases, Bern, Swtzerland, Jan 18 19, Chen J, Wu B, Hu X, L H (2012) SHA: the GNSS analyss center at SHAO. In: Lecture notes n electrcal engneerng (LNEE), vol 160, pp Wannnger L (2012) Carrer-phase nter-frequency bases of GLONASS recevers. J Geod 86 (2): do: /s y 11. Al-Shaery A, Zhang S, Rzos C (2012), An enhanced calbraton method of GLONASS nterchannel bas for GNSS RTK. GPS Solut (onlne-frst), DOI /s Pe X, Chen J, Wang J, Zhang Y, L H (2012) Applcaton of Inter-system Hardware Delay Bas n GPS/GLONASS PPP. Lect Notes Electr Eng 160(2): do: / _34