GPS Precise Point Positioning for Assessing GNSS and Satellite Altimetry Combined Global Ionosphere Maps

Transcription

1 GPS Precse Pont Postonng for Assessng GNSS and Satellte Altmetry Combned Global Ionosphere Maps M. M. Alzadeh Insttute of Geodesy and Geophyscs, Venna Unversty of Technology Venna, Austra H. Schuh Insttute of Geodesy and Geophyscs, Venna Unversty of Technology Venna, Austra R. Weber Insttute of Geodesy and Geophyscs, Venna Unversty of Technology Venna, Austra S. Todorova Unversty of Archtecture, Cvl Engneerng and Geodesy Sofa, Bulgara ABSTRACT For the space geodetc technques, operatng n mcrowave band, onosphere s a dspersve medum; therefore sgnals travelng through ths medum are affected proportonal ther frequences. Ths effect allows ganng nformaton about the parameters of the onosphere n terms of Total Electron Content (TEC). The classcal nput data for development of Global Ionosphere Maps (GIM) s obtaned from dualfrequency Global Navgaton Satellte System (GNSS) observatons. However, the GNSS statons are n-homogeneously dstrbuted, wth large gaps partcularly over the sea surface, whch lowers the precson of the GIM over these areas. On the other hand, dual-frequency satellte altmetry mssons such as Jason-1 provde nformaton about the onosphere precsely above the sea surface. In our recent studes, we developed GIMs from combnaton of GNSS observatons, satellte altmetry. The combned GIMs provde a more homogeneous global coverage and hgher relablty than results of each sngle method. In ths study the obtaned combned onosphere models, referred to as the IGG (Insttute of Geodesy and Geophyscs) GIMs, are evaluated through GPS sngle-frequency Precse Pont Postonng (PPP), usng dfferent postonng technques. These technques are the dual-frequency PPP whch by the frst approxmaton s an onospherc-free combnaton and serves as a bass for our calculatons, the sngle-frequency postonng usng onosphere correctons from Center of Orbt Determnaton n Europe (CODE) GIMs and the sngle-frequency PPP applyng onospherc correctons from the IGG combned GIMs. Key Words: Sngle-frequency Precse Pont Postonng; Global Ionosphere Maps; Global Navgaton Satellte System; Satellte altmetry 1- Introducton 1-1- The onosphere Ionosphere s the uppermost part of the atmosphere, whch s extended from about 60 m to 1000 m and hgher alttudes. In the onosphere, solar radaton stres the atmosphere wth a power densty of 1370 Watts per meter, referred to as the solar constant. Ths ntense level of radaton s spread over a broad spectrum rangng from rado frequences through nfrared

2 radaton (IR) and vsble lght to X-rays. Solar radaton at ultravolet (UV) and shorter wavelengths s consdered to be onzng, snce photons of energy at these frequences are capable of dslodgng an electron from a neutral gas atom or molecule durng a collson. In the process, the atom absorbs part of ths radaton, and a free electron and a postvely charged on are produced. These free electrons and ons affect the propagaton of electromagnetc waves. Ths effect s called onosphere refracton and has to be consdered n determnaton of the propagaton velocty of the sgnals of all the space geodetc technques operatng n mcrowave band. In order to quantfy the propagaton effects on electromagnetc waves travelng through the onosphere, the refractve ndex of the medum must be specfed. The phase refractve ndex of onosphere can be expressed by the seres (Seeber, 1989): c c 3 c n 1 4 ph , (1) f f f where f s the carrer frequency and c, c 3, and c4 are coeffcents not dependng on frequency but on the number of electrons ( N e ) per m 3 along the propagaton path. Usng approxmaton by cuttng off the seres expanson after the quadratc term, c nph 1 () f and ntroducng an estmate for c by c 40.8N e Hz (3) leads to 40.8Ne nph 1. (4) f The delay experenced by sgnals travelng through onosphere s the dfference between measured and geometrc range, whch s called the onosphere delay or refracton: ono nds ds 0, (5) where nds s the measured range and ds0 s the geometrc range. By substtutng equaton (4) n equaton (5) and further smplfcaton we get: ono 40.8 ph N eds0 f. (6) Now the Total Electron Content (TEC) can be defned by: TEC N ds. (7) e 0 Thus, the phase delay s gven by: ono 40.8 ph TEC. (8) f Equaton (8) gves the delay n meters, for sgnals travelng through the onosphere at zenth. For an arbtrary lne of sght, the zenth dstance of the sgnal must be taen nto account. In other words, the Slant Total Electron Content (STEC) should be consdered: ono 40.8 ph STEC. (9) f For group measurements, the onosphere refracton follows the same equaton (9), but wth the opposte sgn. As t can be seen the onosphere refracton for both group and phase measurement s restrcted to the determnaton of the Slant Total Electron Content, whch s the ntegral of the electron densty along the sgnal path S. Ths quantty can be nterpreted as the total amount of free electrons n a cylnder wth a cross secton of 1 m, of whch the axs

3 s the sgnal path. TEC s measured n Total Electron Content Unts (TECU); 1 TECU s equvalent to electrons/m. 1-- Ionosphere parameters from GNSS In the last decade the Global Navgaton Satellte System (GNSS) ncludng GPS and GLONASS have become a promsng tool for montorng the onosphere. Dual-frequency observatons of these technques can be used to determne the slant total electron content. Tang the fundamental equaton for code pseudo-range at each frequency nto account: ( ) fl1 ( ) fl P L1 c t t, trop, on fl 1 c b b, (10.a) P L c t t, trop, on fl c b b, (10.b) where P L1 and P L are the code pseudo-range, s the geometrc dstance between the recever and the satellte, c s the speed of lght. t and t are the recever and satellte cloc offsets wth respect to GPS tme., trop s the delay due to the troposphere and, on the delay due to the onosphere. b and b are the satellte and recever hardware delays, expressed n unts of tme, and fnally ndcates the random error or resdual. We now form the so-called geometry-free lnear combnaton by subtractng observatons of equaton (10) at smultaneous epochs. In ths way all frequency-ndependent effects such as cloc errors, tropospherc delay, etc. are removed and the new observable whch contans only the onosphere refracton and the nter-frequency hardware bases b and b assocated wth the satellte and recever remans: P,4 P,1 P, 4 E ( F( z) Ev (, s)) cb b, (11) Where: E (, s),1, s the VTEC at onospherc perce pont, b b b s the satellte dfferental v code bases (DCB) and b b,1 b, s the recever DCB. Fzs () the mappng functon, f1 E 0.16 m/tecu s constant and fnally s a constant relatng L4 to L1. f Equaton (11) s the L4 geometry-free lnear combnaton for code pseudo-range. A smlar equaton can be wrtten for the phase pseudo-range. As t can be seen the geometryfree lnear combnaton contans only the onosphere refracton and the DCBs. Snce GNSS technques provde measurements of slant TEC, an elevaton-dependent mappng functon whch descrbes the relaton between the slant TEC (E(z)) and the vertcal TEC (E v ) s requred. The geometry-free lnear combnaton s very approprate for extractng nformaton about the onosphere. It has to be noted that the derved onosphere parameters are affected by the nter-frequency hardware bases (Mannuc et al., 1998), so when modelng the onosphere t s necessary to estmate them as addtonal unnowns Ionosphere parameters from satellte altmetry Satellte altmetry s a partcular way of rangng; what s measured s the vertcal dstance between a satellte and the ocean surface. The specfc characterstc of the method s that no ground statons are requred. The measurements are carred out from the altmeter on-board the satellte drectly to the sea surface. The range between the satellte and the sea surface s derved from the travelng tme of the radar mpulse transmtted by the radar altmeter and reflected from the ground. The method s best applcable over the oceans, due to the good

4 reflectve propertes of water. The sgnals are transmtted permanently n the hgh frequency doman (about 14 GHz) and the echo from the sea surface receved by the satellte s used for dervng the round-trp tme between the satellte and the sea (Todorova, 008). The TOPEX/Posedon (T/P) satellte was launched n August 199 for observng the ocean crculaton and was operatonal tll October 005. Jason-1, launched n December 001, s the follow-on to T/P and has nherted ts man features orbt, nstruments, measurement accuracy, etc. The orbt alttude of the two mssons s 1336 m. The prmary sensor of both T/P and Jason-1 s the NASA Radar Altmeter operatng at 13.6 GHz (Ku-band) and 5.3 GHz (C-band), smultaneously. The two wdely separated frequences allow TEC to be detected drectly from nadr altmetry samplng data along the satellte trac (Imel, 1994). - Global Ionosphere Maps -1- Modelng theory The GNSS-derved STEC values are extracted from the geometry-free lnear combnaton appled on dual-frequency carrer-phase smoothed code observatons. The phase-smoothed pseudorange observatons are adapted from statstc comparson of contnuous tme seres of dual-frequency code and phase measurements. Ths method allows the approxmate determnaton of the ambgutes of the L1 and L carrers and leads to sgnfcant reducton of the nose of the orgnal code measurements (Schaer, 1999). Wthn the geometry-free lnear combnaton the unnown parameters n the observaton equaton are the absolute TEC nformaton (, ) Ev s, satellte and recever code bases (DCBs) b, b and n the case of phase pseudo-range the ambguty parameter. Therefore t s not possble to drectly derve absolute TEC nformaton from sngle epoch GNSS data, but the process should cover a longer tme span. There are dfferent approaches n order to parameterze the dstrbuton of TEC; here we consder a global representaton usng Sphercal Harmonc expanson (SH) up to degree and order 15. In our study data from around 180 IGS statons were used wth samplng rate of 30 sec. In the case of satellte altmetry, the orgnal onosphere correcton from T/P and Jason-1 was adopted and converted nto Vertcal Total Electron Content (VTEC) by a factor dependng on the operatonal frequency of the altmeter. The VTEC can be expressed by E : v nmax n Ev (, s) Pnm(sn ) C nm cos( ms) S nm sn( ms) n0 m0, (1) where s the geomagnetc lattude of the onospherc perce pont, s UT (wth G geographcal longtude) s the sun-fxed longtude of the onospherc perce pont, the normalzed Legendre functon of degree n and order m, and C nm and S nm are the unnown coeffcents of the sphercal expanson. Usng the SH expanson, VTEC can be represented n form of Global Ionosphere Maps (GIM) wth specfed spatal and temporal resoluton. -- Combnaton technque TEC estmates from GNSS have usually been compared wth results from satellte altmetry measurements n order to assess the precson of both methods (Brunn et al., 005). Snce the GNSS statons are n-homogeneously dstrbuted, wth large gaps partcularly over the ocean area, GIMs derved from GNSS-only measurements have lower precson over these areas. On the other hand, dual-frequency satellte altmetry mssons provde nformaton about the onosphere precsely above the sea surface; so combnng GNSS data wth satellte altmetry measurements wll help compensatng the nsuffcent GNSS coverage over the ocean area. The combned GIMs provde a more homogeneous global coverage and hgher G Pnm s

5 relablty than results of each sngle method. For the combnaton of GNSS and altmetry data, least-squares adjustment s appled on each set of observatons and then the normal equatons are combned. Ths s done by addng the relevant normal matrces obtaned from the two types of observatons: T T NCOMB NGNSS NALT AGNSS. pgns. AGNSS AALT. palt. A. (13) ALT For the relatve weghtng of the altmetry data, dfferent strateges are possble. Due to the much hgher number of GNSS measurements compared to satellte altmetry, the T/P and Jason-1 data should be up-weghted, n order to ncrease ts mpact on the combned GIM. alt When adoptng the a pror varance of TECU ( palt 4 ) for the altmetry measurements, the dfferences between the combned and the GNSS-only GIM can reach up to ±10 TECU and the Root Mean Square (RMS) of the combned maps decreases by up to 1 TECU over the areas wth altmetry observatons. In the case of overweghtng, however, t becomes crucal to assess the bas between GNSS and altmetry TEC. On the other hand, f we tae nto account the hgher nose of the altmetry measurements compared to the carrerphase smoothed code observatons from GNSS, a lower weght should be appled on all T/P and Jason-1 derved observatons. Wthn ths study the adopted weght s 1/ 4 p, alt whch corresponds to an a pror varance 0 4TECU. It has to be ponted out, that the relatve weghtng acts le a scalng factor for the contrbuton of the altmetry data n the combned GIM. It s a very complex ssue, dependng on the dfferent spatal and temporal dstrbuton of the observatons and on ther specfc systematc errors. Therefore, the relatve weghtng of the two types of measurements needs to be optmzed and s a matter of further nvestgaton. -3- Combned soluton A Matlab-based software was developed for computaton of 1 GIM per day wth temporal resoluton of hours and spatal resoluton of.5 lattude and 5 longtude. The correspondng RMS maps and daly values of the DCB for all the GNSS satelltes and recevers were also developed as a b-product. The fnal outputs are n the IONEX format. Both the GNSS-only and the combned solutons developed wthn ths wor are referred to as IGG (Insttute of Geodesy and Geophyscs) GNSS-only and combned models. The current results of our study are presented below, consderng as example the outcomes for day 188 n 006, 9:00 UT, (Todorova, 008): ALT Fg. 1 (a) VTEC and (b) RMS map, IGG GNSS-only map, doy , 9:00 UT

6 Fgure 1 shows a snapshot of the IGG GNSS-only VTEC and RMS maps for 9:00 UT. As expected, the precson of the maps are lower n areas where no GNSS stes are located. Ths s manly above the sea surface and n the southern polar regon. The mean bas between the estmated VTEC maps and the GIM provded by the Center of Orbt Determnaton n Europe (CODE), whch s an IGS Analyss Center s 0.4 TECU wth a standard devaton of ±0.5 TECU. The ntegrated GIM for 9:00 UT on the same day 188, 006, s shown on Fgure. A closer loo at the dfference between the combned maps and the GNSS-only soluton (Fg. 3) shows a general lowerng of the RMS of the combned model especally over the areas concdng wth the footprnts of Jason-1. Fg. (a) VTEC and (b) RMS map, IGG combned model, doy , 9:00 UT Fg. 3 (a) VTEC and (b) RMS map, IGG combned mnus GNSS-only map, doy , 9:00 UT Wthn the fgure 3(a) there s a slght ncrease of the VTEC values (up to 0.8 TECU) partcularly over the oceans and n the low southern lattudes, where nearly no GNSS observatons are avalable. The decrease of VTEC n the equatoral area, concdng wth the regon of hghest onosphere actvty for ths map, can be nterpreted as the sgnature of the plasmaspherc component. (Todorova et al., 007). 3- GPS Precse Pont Postonng 3-1- Bascs

7 In the late 90s, the Jet Propulson Laboratory (NASA) poneered a new technque that dd not requre dfferencng to obtan precse postons; they labeled t Precse Pont Postonng (PPP) (Zumberge et al., 1997a). The largest dfference between relatve processng and PPP s the way that the satellte and recever cloc errors are handled. Instead of between-recever dfferencng to remove the satellte cloc errors, PPP uses hghly precse satellte cloc estmates. These satellte cloc estmates are derved from a soluton usng data from globally dstrbuted statons of GPS recevers. These ndvdual statons form a global networ whch s organzed by the Internatonal GNSS Servce (IGS). The IGS was formally recognzed n 1993 by the Internatonal Assocaton of Geodesy (IAG), and began routne operatons on January 1, 1994; provdng GPS orbts, tracng data, and other data products on-lne n near real-tme to meet the objectves of a wde range of scentfc and engneerng applcatons and studes n support of geodetc and geophyscal research (IGS Strategc Plan 007). In performng PPP, recever cloc errors are estmated as part of the least-squares soluton for the coordnates, nstead of beng removed by dfferencng between satelltes. The dfference between PPP and the Sngle Pont Postonng (SPP) methods n terms of coordnate accuracy s large: SPP produces coordnates accurate at the 1 to10 m level whle PPP can produce coordnates accurate at the centmeter level wth 4 hours of observatons, whch s comparable to relatve processng; thus precse absolute coordnates for a sngle recever at an unnown locaton may be obtaned wthout the need of a second recever at a nown locaton. (Kng et al., 00). 3-- Methodology For space geodetc technques operatng n mcrowave band onosphere s a dspersve medum. Ths means that sgnals travelng through the onosphere are affected proportonal to ther frequences (cf. equaton 1). Therefore by usng approprate combnaton of observatons on two dfferent frequences, the effect of onosphere s elmnated by an acceptable approxmaton. Ths s the man reason why all hgh precson space geodetc technques transmt ther sgnals n two dstnct frequences. It may be verfed that a lnear combnaton of the basc dual-frequency phase (or code) observables elmnates the onosphere refracton term. Ths combnaton for phase pseudo-range follows: L L L. (14) Wth the coeffcents: 3 1,3 1,3 f / ( f f ).546, (15.a) 1,3 1 1 f / ( f f ) (15.b),3 1 Equaton (14) s called the onosphere-free lnear combnaton. Formng ths combnaton from the un-dfferenced observaton equatons and neglectng the hardware delays b, leads to onosphere-free combnaton for phase and code pseudo-range, respectvely: L B, (16.a) P,3 3,3,3, (16.b) where 3 c / ( f1 f) 107mm s the so-called narrow-lane wavelength and B,3 s a realvalued ambguty parameter, expressed n narrow-lane cycles. Now performng PPP, we use the phase-smoothed code measurements for the sngle-frequency observatons: P,1 ( t) P,1 L,1( t) f L,1( t) L,( t), (17.a) f f 1 P ( t) P L ( t) f L ( t) L ( t) 1,,,,1, f1 f, (17.b)

8 wth L ( t) L ( t) L,1, L ( t) L ( t) L,. P,1, P, are the mean code measurements,1,1,, averaged over a common cycle slp-free nterval, L,1, L, are the mean phase measurements averaged over a common cycle slp-free nterval; and L,1 ( t), L, ( t ) are the correspondng phase measurements of each frequency at epoch t. 4. Results and Dscusson In order to correct the model for the onosphere refracton, PPP s performed by usng: Sngle-frequency measurements, applyng onosphere correcton from IGG GIMs. Sngle-frequency measurements, applyng onosphere correctons from Center of Orbt Determnaton n Europe (CODE) GIMs. Dual-frequency onosphere-free lnear combnaton. Observaton of 0 IGS statons world-wde s used n the duraton of doy , 006. The above mentoned approaches are processed wthn the Bernese GPS Software (ver. 5.0), applyng fnal orbts and weely Earth Rotaton Parameter soluton of CODE, the IAU000 model for nutaton and the absolute antenna phase-center model. The crtera for selectng the IGS statons are focused on the locaton of the staton wth respect to the sea-area. Fg. 4. Selected IGS statons Frst, usng the dual-frequency onosphere-free lnear combnaton the precse coordnates of the selected statons are calculated n a 4 hour soluton. In the second approach snglefrequency measurements are processed n the same 4 hour daly soluton, and for the onosphere correcton term, TEC s extracted from the IGG-GIMs. Smlarly n the thrd approach the coordnates are calculated by applyng onosphere correcton derved from CODE s GIMs to sngle-frequency measurements. Snce the onosphere-free combnaton s by tolerable approxmaton free of onosphere, t serves as a bass for comparng the two dfferent models of the onosphere. In order to have better vew for ths comparson, the results of poston coordnates of each of the onosphere models are subtracted from results of the L3 onosphere-free soluton. Fgure 5 depcts samples of sngle-frequency postonng wth onosphere correcton derved from CODE GIM, (thc lnes), vs. sngle-frequency postonng wth onosphere correctons derved from IGG GIMs (dashed lnes). Both methods have been subtracted by dual-frequency onosphere-free combnaton results n order to elmnate other effects except the onosphere. The process s done on a 4 hour soluton for days 18 to 191 of the year 006.

9 Fg. 5(a) PPP daly soluton for n-land staton: ALGO Fg. 5(b) PPP daly soluton for n-land staton: CONZ Fg. 5(c) PPP daly soluton for sea-sde staton: GUAM Fg. 5(d) PPP daly soluton for sea-sde staton: KERG Fgures 5 (a) and (b) show the results for statons ALGO and CONZ, whch are wthn the land area. It can be seen that the CODE derved onosphere correctons wth the mean horzontal bas of cm at staton ALGO, provde slghtly better results than IGG derved correctons wth cm mean horzontal bas at the same staton; though poston dfferences of both methods hardly reach 5 mllmeters wthn 10 days. Fgures 5 (c) and (d) show the results for statons GUAM and KERG whch are located over the ocean. Except for the heght component at staton GUAM, the poston dfferences of both methods at both statons are around 5 mllmeters. What s apparent for these two statons s that the IGG method provdes better results than the CODE method. For example the mean horzontal bas at staton GUAM wth the IGG model s cm, whle ths amount for CODE s 0.06 cm. Table 1 shows the mean bas n longtude, lattude, and heght over 10 days of both IGG and CODE solutons wth respect to the L3 onosphere-free combnaton: IGG BIAS (cm) CODE BIAS (cm) LONG LAT H LONG LAT H ALGO ALRT BAHR BRMU CONZ DARW Table 1- Daly solutons bas w.r.t. L3 soluton. Red boxes ndcate two n-land statons

10 DGAR GLPS GUAM HARB HERT HNLC KERG KOKB REUN SEY THTI WTZR Table 1 (contnued) - Daly solutons bas w.r.t. L3 soluton. Green boxes ndcate two sea-sde statons. The same solutons are carred out for the same statons on an hourly bass. Fgure 6 llustrates the PPP dfferences between both methods and the onosphere-free combnaton at day 18, of 006: Fg. 6(a) PPP hourly soluton for n-land staton: HERT Fg. 6(b) PPP hourly soluton for n-land staton: WTZR Fg. 6(c) PPP hourly soluton for sea-sde staton: BRMU Fg. 6(d) PPP hourly soluton for sea-sde staton: REUN Fgures 6 (a) and (b) show poston dfferences of the hourly soluton at statons HERT and WTZR, respectvely. Both of these statons are n the land regons. Fgures 6 (c) and (d) show the results for statons BRMU and REUN whch are located n the ocean area. The mean bas n longtude, lattude, and heght over 4 hours and also the RMS of heght wth respect to the L3 onosphere-free combnaton of both methods s represented n the table below:

11 Table - Bas and RMS of hourly soluton w.r.t. L3 soluton day 18, Summary and conclusons In our study we evaluated onosphere models usng GPS precse pont postonng (PPP) at 0 IGS statons worldwde wthn the land and at seasde. The PPP results usng the IGG GIMs and the CODE GIMs over 10 days (day , 006) were compared wth the L3-onosphere free combnaton, whch served as a bass (neglectng nd order onosphere term). It can be nferred that at the seasde statons the IGG model shows slghtly better results than the CODE model dependng on the weght of altmetry data whch s due to the lac of GNSS observatons over the sea surface. The CODE model behaves slghtly better than the IGG model n land, though the dfference s nsgnfcant. The combned GIMs from GNSS and satellte altmetry data have the potental of ncreasng the accuracy of the GIM, n partcular over the seas. Acnowledgements. Ths study s accomplshed wthn project COMBION whch s funded by the Austran Scence Fund (FWF). Thans to the Internatonal GNSS Servce (IGS) and to ADSCentral, GeoForschungsZentrum Potsdam (GFZ), for the free supply wth GNSS and altmetry data. References 1. Brunn, C. Global onospherc models from GPS measurements. PhD thess, Unversdad Naconal de La Plata, La Plata, Argentna, Hernández-Pajares, M., Juan, J.M., Sanz, J. New approaches n global onospherc determnaton usng ground GPS data. J. Atmos. Solar Terr. Phys. 61, , Kng, M., Edwards S., and Clare. P. Precse Pont Postonng: Breang the Monopoly of Relatve GPS Processng. Engneerng Surveyng Showcase October Hernández-Pajares, M. IGS Ionosphere WG Status Report: Performance of IGS Ionosphere TEC Maps (Poston paper), IGSWorshop, Bern, Imel, D.A. Evaluaton of the TOPEX/POSEIDON dual-frequency onosphere correcton. J. Geophys. Res. 99 (C1), , Mannucc, A.J., Wlson, B., Yuan, D., Lnqwster, U., Runge, T. A global mappng technque for GPS-derved onospherc total electron content measurements. Rado Sc. 33, , Schaer, S. Mappng and predctng the Earth s onosphere usng the Global Postonng System. PhD thess, Bern Unversty, Swtzerland, Todorova, S., Schuh, H., Hobger, T. Usng the Global Navgaton Satellte System and satellte altmetry for combned Global Ionosphere Maps. Advances n Space Research 4 (008) , 007.