GLONASS Inter-frequency Biases and Their Effects on RTK and PPP Carrier-phase Ambiguity Resolution

Transcription

1 GLONASS Inter-frequency Bses nd Ther Effects on RTK nd PPP Crrer-phse Ambguty Resoluton Nco Reussner, Lmbert Wnnnger Geodetc Insttute, Technsche Unverstät Dresden (TU Dresden), Germny BIOGRAPHIES Nco Reussner s member of the GNSS reserch group t the Geodetc Insttute of TU Dresden. He receved hs Dpl.- Ing. n geodesy from TU Dresden n Lmbert Wnnnger s professor of geodesy t TU Dresden. He hs been nvolved n reserch on precse GNSS postonng snce He holds Dr.-Ing. degree n geodesy from Unversty of Hnnover, Germny, nd hbltton degree n geodesy from TU Dresden. ABSTRACT GLONASS uses frequency dvson multplexng (FDMA) to mke the sgnls from ndvdul stelltes dstngushble. Thus, n both frequency bnds the recevng equpment hs to del wth up to 14 dfferent frequences. Due to code nd crrer-phse nter-frequency bses n the recevng equpment, dt processng gets more dffcult s compred to GPS. The crrer-phse nter-frequency bses mnly depend on the recever type nd cn be modeled nd corrected bsed on lner functon of the sgnl s frequency. The code nterfrequency bses re more dffcult to hndle snce they mostly seem to be recever ndvdul nd of non-lner chrcter. GLONASS Rel-Tme Knemtc (RTK) postonng s very smlr to GPS RTK s long s pror correctons for the crrer-phse nter-frequency bses re ppled. Precse Pont Postonng (PPP), however, usully uses dulfrequency code observtons to resolve wdelne mbgutes wth the Melbourne-Wübben lner combnton. Due to the code nter-frequency bses ths technque does not work for the present GLONASS recevng equpment nd t must be substtuted by pure crrer-phse wdelne mbguty resoluton technque. INTRODUCTION Unlke GPS, GLONASS uses frequency dvson multplexng (FDMA). Ths technque requres unque crrer frequences for ll stelltes. In the two frequency bnds L 1 nd L 2 they re defned by: f k 1, = f 0,1 + k f1 = k [ MHz] 2, = f0,2 + k f 2 = k [ MHz] f k where k s the frequency chnnel number selected from the rnge [-7,6]. The lmtton to 14 dfferent frequences n ech bnd mde t necessry tht stelltes n ntpodl postons shre the sme frequency (ICD 2008). FDMA of the present GLONASS sgnls cuses nterfrequency bses n the recevng equpment nd n both prmry observbles nmely code nd crrer-phse. These bses re ble to complcte or prevent crrer-phse mbguty fxng. Strtng ths yer new GLONASS sgnls re dded tht wll use code dvson multplexng (CDMA) lke GPS does (Revnvykh 2010). But for the next decde or so only GLONASS FDMA-sgnls wll be ble to provde contnuous dul-frequency coverge. RTK (Rel-tme Knemtc) postonng requres (n lmost) complete nd relble fxng of the crrer-phse mbgutes n the bselne between reference stton nd rover stton (Hofmnn-Wellenhof et l. 2008). Ionospherc effects re gretly reduced due to dfferentl postonng n bselnes nd more nd more by regonl modellng of the onosphere wth Network RTK technques. Thus the mbguty resoluton lgorthms need not to be so clled onosphere-free technques, but nteger mbgutes my be estmted usng e.g. the wdelne lner combnton of L1 nd L2 crrerphse observtons nd subsequently the L1 (or nrrowlne) crrer-phse mbguty. Proc. of ION GNSS 2011, Portlnd, OR,

2 Precse Pont Postonng (PPP) s n bsolute postonng technque hs to del wth lrger onospherc effects. Here, onosphere-free technques should be ppled n mbguty fxng nd coordnte estmton. Usully the wdelne mbgutes re fxed usng the Melbourne-Wübben-combnton of code nd crrer-phse observtons nd fterwrds the nrrowlne mbgutes re fxed usng the onospherefree lner combnton of the crrer-phse observtons. Ambguty resoluton wth PPP requres nformton of the frctonl-cycle bses (FCB) whch must be determned utlzng network of reference sttons. For more nformton on PPP mbguty resoluton nd FCB see e.g. Bnvlle et l. (2008), Collns (2008), Ge et l. (2008), Lurchesse et l. (2008), Geng et l. (2010). OBSERVATION EQUATIONS In order to expln the dfferences between GPS nd GLONASS sgnls we look t the observton equtons of code C nd crrer-phse. In generl nd especlly for GLONASS they my be wrtten s: C = R = R + c 0 + c 0 System, ( δt + h, C δt ) + ε, C System, ( δt + h δt ) + λ N ε, + where subscrpt stnds for the stton nvolved, the superscrpt specfes the ndvdul stellte nd the superscrpt System ndctes the GNSS stellte system. Furthermore, R [m] s the stellte-recever rnge, c 0 [m/s] s the vcuum speed of lght, δt [s] s the recever clock error, h [s] s the recever hrdwre dely of the sgnl, δt [s] s the stellte clock correcton, λ [m] s the sgnl wvelength, N [-] s the crrer-phse mbguty, nd ε [m] s the sum of ll uncorrected systemtc nd rndom errors ffectng the observble. Unknowns to be determned re the coordntes of the recevng ntenn X,Y,Z hdden n the stellte-recever rnge R, the recever clock error δt plus the recever hrdwre dely h, nd n cse of the phse observtons the mbguty N. δt, h, nd N re lnerly dependent nd thus led to sngulrtes,.e. they cn not be fully seprted from ech other. GPS t, C GPS t, In cse of GPS wth ll stelltes trnsmttng on the sme frequency, the recever nstrumentl delys h re dentcl for ll sgnls nd thus we merge them wth the recever clock error to the stellte system specfc recever clock errors δ nd δ : GPS, C = R + c0 GPS, = R + c0 GPS ( δt,c δt ) + ε,c GPS ( δt, δt ) + λ N ε, +, GLONASS INTER-FREQUENCY BIASES OF THE CARRIER-PHASE OBSERVATIONS The detled nlyss of the crrer-phse nter-frequency bses of vrous GLONASS recevers (Wnnnger nd Wllstb-Fretg 2007, Znovev et l. 2009, Wnnnger 2011) leds to the followng conclusons: Recevers of the sme type nd usully even of the sme mnufcturer show very smlr nter-frequency bses. The nter-frequency bses cn be modeled very well s lner functon of frequency (or the chnnel number k): GLONASS ( δ t + k IFB δt ) + λ N = R + c0, + ε, where IFB [s] s the GLONASS nter-frequency bs per f or per k. For most recevers L1 nd L2 crrer-phse nterfrequency bses (IFB) hve very smlr vlues, thus sngle vlue per recever s enough to pre-correct the effects of the nter-frequency bses. Such pre-correcton (see Tb. 1) s necessry to llow complete nd relble RTK mbguty fxng n recever-mxed bselnes. After mbguty fxng IFB vlues should be estmted from the present observtons seprtely for L1 nd L2 (or t lest for the selected lner combnton used for coordnte estmton). IFB vlues do not only depend on the recever but sometmes lso on the selected ntenn. The often expected senstvty of the crrer-phse IFBs to temperture chnges could not be confrmed (Wnnnger 2011). Tb. 1: Proposed pror correctons of L1 nd L2 GLON- ASS crrer-phse nter-frequency bses IFB for recevers of 9 dfferent mnufcturers (Wnnnger 2011) recever mnufcturer pror IFB correctons [cm] Trmble 0.7 Ashtech (old), Jvd, JPS, TPS 0.0 Ashtech (new) 0.4 Lec, Novtel 2.3 Septentro 4.9 Utlzng pror IFB vlues (Tb. 1) n RTK postonng enbles GLONASS mbguty resoluton nd fxng to be performed very smlr to the one wth GPS sgnls. After mbguty fxng coordnte solutons should be estmted together wth recever ndvdul IFB vlues. In PPP dt processng the pror correctons of Tb. 1 should be ppled when frctonl-cycle bses (FCB) re estmted. They must lso be ppled on the rover sde so tht GLONASS crrer-phse mbguty fxng cn be per- 713

3 formed. Afterwrds ndvdul IFB vlues should be estmted. Unfortuntely, stndrd PPP mbguty resoluton nd fxng dffers from tht of RTK, snce code observtons ply n mportnt role n the mbguty estmton of the Melbourne-Wübben lner combnton. Here, t s not enough to del wth GLONASS crrer-phse IFBs, but the code IFBs hve to be tken nto ccount s well. GLONASS INTER-FREQUENCY BIASES OF THE CODE OBSERVATIONS The code IFBs ply n mportnt role n PPP. Frst of ll they must be tken nto ccount n the coordnte estmton bsed on the onosphere-free lner combnton of the code observtons. Furthermore, code observtons re used for wdelne mbguty estmton bsed on the Melbourne- Wübben lner combnton. We estmted men code resduls of the onosphere-free lner combnton P 0 (bsed on P 1 nd P 2 ) n PPP dt processng of 2 weeks of observtons (GPS week 1627 nd 1628) for severl reference sttons. In cse of GPS ll these estmtes re close to zero,.e. no stellte specfc delys exst. In cse of GLONASS, however, men delys rech up to severl meters (Fg. 1). These estmted delys lso depend on the GLONASS clock products ntroduced nto the dt processng. The exmples shown n Fg. 1 were computed wth the orbt nd clock correctons of the Europen Spce Opertons Centre (ESOC), Drmstdt, Germny. Fgure 1 shows the GLONASS delys for 4 selected sttons of the EUREF Permnent Network (EPN, epncb.om.be) s functon of the GLONASS chnnel number k nd thus of the sgnl frequency. In generl frequency-dependence s obvous; however no smple lner modelng seems to ft. The delys pper to be very much recever-ndvdul. There re some exceptons of the pure frequency-dependence: e.g. t stton/recever GARI nd for chnnel number k = 0 the estmted delys for the two ntpodl stelltes R11 nd R15 dffer by bout 2 m. Our concluson s tht nter-frequency bses of the GLON- ASS code observtons exst tht re mnly frequency dependent but seem to be recever ndvdul nd cn not be modeled wth smple modelng functon. Thus, we must expect lower code postonng ccurcy s compred to GPS. Furthermore, we cn expect dffcultes n the PPP wdelne mbguty fxng wth the Melbourne-Wübben method. The second spect s dscussed below. There my be chnce to clbrte the GLONASS codedelys of ndvdul recevers to mprove the code postonng ccurcy, but we hve not checked for ther long-term nd temperture stblty. Fg. 1: Men GLONASS onosphere-free code delys s functon of GLONASS chnnel number k for 4 dfferent sttons wth 3 dfferent recever types. 714

4 GLONASS WIDELANE AMBIGUITY RESOLUTION There re two wys to resolve the wdelne mbgutes n PPP dt processng. Usully t s done n comprson wth dul-frequency code observtons (Melbourne-Wübben method). Ths pproch hs the dvntges tht t s not ffected by the tmosphere (onosphere nd troposphere) nd lso not by geometrc spects lke orbt errors nd estmtes of the rover poston. Mjor drwbcks, however, re code multpth nd nose. ASS results s functon of chnnel number k. The frctonl-cycle bses (FCB) were clculted from observtons of one reference stton nd the frctonl prts of wdelne mbgutes were estmted wth observtons of nother stton. The results shown re bsed on observton dt from dy-of-yer 166/2011. Ambgutes were estmted for The second method estmtes the wdelne mbgutes from the crrer-phse observtons drectly. Here, we do not hve to cope wth code multpth but wth tmospherc effects (onosphere nd troposphere) nd geometrc errors (orbt errors, errors n the rover poston estmtes). In fct, the second method requres onospherc correctons, e.g. the Globl Ionospherc Mps (GIM) produced by the Interntonl GNSS Servce (IGS). But stll, remnng onospherc effects my prevent successful wdelne mbguty fxng. In order to test GLONASS mbguty resoluton we determned frctonl-cycle bses (FCB) t selected reference sttons for three lner combntons: Melbourne-Wübben lner combnton, wdelne crrer-phse lner combnton, nd onosphere-free crrer-phse lner combnton. We then ppled these FCB t rover sttons nd tred to fx the crrer-phse mbgutes. Here, we wll concentrte on the GPS nd GLONASS wdelne fxng wth the two methods dscussed bove. Fg. 2 nd 3 show frctonl prts of the wdelne mbguty estmtes of rover sttons, Fg. 2 of the Melbourne-Wübben lner combnton, Fg. 3 of the wdelne crrer-phse lner combnton. Both fgures present GPS results s functon of PRN number nd GLON- Fg.2: Frctonl prts of the PPP wdelne mbguty estmtes usng the Melbourne-Wübben lner combnton. observton durtons of 2 hours,.e. 12 ndependent estmtons were produced from the 24 h dt set. In cse of the Melbourne-Wübben method (Fg. 2) the FCB were estmted wth observtons of the Slovkn stton MOP2 t Modr-Pesok nd they were ppled to the Polsh stton REDZ t Redzkowo. Both sttons were equpped wth Trmble NetR5 recevers. All GPS frctonl prts of estmted wdelne mbgutes re well below 0.2 cycles, so tht successful mbguty fxng cn be performed. But the GLONASS frctonl prts vry between -0.5 nd +0.5 cycles so tht the true nteger vlue cn not be found. The GLONASS mbguty estmtes re bsed by code nd crrer-phse nter-frequency delys whch re lrger thn the wdelne wvelength (cf. Fg. 1). In cse of the wdelne method (Fg. 3) the FCB were est- Fg. 3: Frctonl prts of PPP mbguty estmtes of the crrer-phse wdelne lner combnton. The thrd pnel shows GLONASS results wth pror correctons of Tb. 1 beng ppled to the observton dt. 715

5 mted from observtons of the Brtsh stton HERS t Hlshm equpped wth Septentro PolRx3eTR recever nd ppled to second stton t Hlshm, HERT, equpped wth Lec GRX1200 GG PRO recever. By purpose we decded to show results of such very short bselne. Here, remnng onospherc effects n the wdelne FCB do not show up n the frctonl prts of the estmted mbgutes snce they cncel out by dfferencng. Thus, the effects of the crrer-phse nter-frequency bses (IFB) domnte nd they re clerly vsble n the centrl pnel of Fg. 3. The thrd pnel of Fg. 3 shows the frctonl prts of PPP wdelne mbgutes when the pproprte pror IFB vlues of Tb. 1 re ppled n both processng steps: FCB estmton (Septentro recever t HERS) nd PPP mbguty estmton (Lec recever t HERT). In prctce, ths method of wdelne mbguty estmton nd fxng requres onospherc correctons. But stll, remnng onospherc errors wll ffect FCB estmton nd wll complcte mbguty resoluton. The sze of the remnng onospherc errors depends very much on the ctul onospherc condtons nd of course on the qulty of the onospherc model. After successful wdelne mbguty fxng, the onosphere hs no further sgnfcnt nfluence on the PPP results, snce the second mbguty fxng step nd the coordnte estmton s performed wth the onosphere-free lner combnton of the crrer-phse observtons. SUMMARY AND CONCLUSIONS GLONASS crrer-phse nd code observtons re ffected by recever hrdwre delys whch cuse nter-frequency bses. Crrer-phse nter-frequency bses re very smlr wthn groups of recevers of the sme type (or even from the sme mnufcturer). Furthermore, nter-frequency bs dfferences between two ndvdul recevers cn be modeled very well s lner functon of the sgnl s frequency. GLONASS code nter-frequency bses re much more dffcult to hndle. They show lrge dfferences even between recevers of the sme type. These dfferences mnly seem to be functon of frequency but smple lner modelng s nsuffcent. As long s no code observtons re drectly nvolved n mbguty resoluton nd fxng, GPS nd GLONASS fxng lgorthms re very smlr. In cse of GLONASS, however, crrer-phse nter-frequency bs correctons must be ppled to the observtons dt. On the other hnd, mbguty resoluton lgorthms whch use code observtons (Melbourne-Wübben method) do not work t ll or t lest not s good wth present GLONASS observtons s compred to GPS observtons. They must be substtuted by other lgorthms whch re ndependent of the code observtons but usully hve ts own shortcomngs. We conclude tht stndrd RTK mbguty resoluton works s good for GLONASS s for GPS. In PPP mbguty resoluton, however, FDMA-GLONASS sgnls observed wth present recevng equpment re t dsdvntge s compred to CDMA-GPS sgnls.. ACKNOWLEDGEMENTS Ths study ws supported by the Germn Reserch Foundton (Deutsche Forschungsgemenschft, DFG). The uthors thnk EUREF Permnent Network (EPN) nd ts mny contrbutng nsttutons for mkng vlble GPS/GLONASS observton dt nd they thnk Europen Spce Opertons Centre (ESOC) for provdng precse GPS/GLONASS orbts nd clock correctons. REFERENCES Bnvlle, S., Snterre, R., Cocrd, M., Lngley, R.B. (2008): Stellte nd Recever Phse Bs Clbrton for Undfferenced Ambguty Resoluton. Proc. ION NTM 2008, Collns, P. (2008): Isoltng nd Estmtng Undfferenced GPS Integer Ambgutes. Proc. ION NTM 2008, Ge, M., Gendt, G., Rothcher, M., Sh, C., Lu, J. (2008): Resoluton of GPS crrer-phse mbgutes n Precse Pont Postonng (PPP) wth dly observtons. Journl of Geodesy, 82: Geng, J., Meng, X., Dodson, A.H., Teferle, F.N. (2010): Integer mbguty resoluton n precse pont postonng: method comprson. Journl of Geodesy, 84: Hofmnn-Wellenhoff, B., Lchtenegger, H., Wsle, E. (2008): GNSS Globl Nvgton Stellte Systems. Sprnger-Verlg, Wen. ICD (2008): GLONASS Interfce Control Document, edn 5.1, Russn Insttute of Spce Devce Engneerng. Lurchesse, D., Mercer, F., Berths, J.P., Bjc, J. (2008): Rel Tme Zero-dfference Ambgutes Fxng nd Absolute RTK, Proc. ION NTM 2008, Revnvykh, S. (2010): GLONASS Sttus nd Progress. Proc. ION GNSS 2010, Wnnnger, L., Wllstb-Fretg, S. (2007): Combned processng of GPS, GLONASS, nd SBAS code phse nd crrer phse mesurements. Proc. ION GNSS 2007, Wnnnger, L. (2011): Crrer-phse nter-frequency bses of GLONASS recevers. Journl of Geodesy, DOI / s y, n prnt. Znovev, A.E., Vetsel, A.V., Dolgn, D.A. (2009): Renovted GLONASS: mproved performnce of GNSS recevers. Proc. ION GNSS 2009,