INVESTIGATION OF THE GPS SIGNALS IONOSPHERIC CORRECTION An Pul Mrins Chirdi Hélio Koiti Kug Antônio Fernndo Bertchini de Almeid Prdo INPE Av. dos Astronuts, 1758 - Jrdim d Grnj São José dos Cmpos - SP - Brzil CEP: 1 7-010 FAX: 55 1 345 6 6 emil: chir@dem.inpe.br ABSTRACT The purpose o this work is to investigte proper model to correct the ionospheric eect using single requency GPS mesurements, which it will be used in the rtiicil stellite orbit determintion tking in ccount tht stellite will be bove 1000 km o erth's surce. When the GPS signls re trnsmitted rom GPS stellite to receiver, they propgte through the ionosphere cusing errors on the mesurements which re the highest one on signl propgtion. To chieve the highest possible positioning ccurcies orm GPS, the ionospheric errors shll be neutrlized using some kind o model nd/or mesurement, nd they hve to be considered within the djustment process. Using dul requency GPS receivers, the ionospheric errors cn be lmost totlly ccounted or tking dvntge o the ionosphere's dispersive nture. However, this work dels with rel-time determintion o n rtiicil stellite orbit with single requency GPS receiver. So, some model o single requency ionospheric correction must be used. Such investigtion will deine to which extent the ionospheric error cn ect the inl ccurcy o the rel-time determintion when using the GPS constelltion. 1
Keywords: GPS signls, ionosphere, single requency INTRODUCTION The GPS System llows users to mesure rnge nd rnge rte inormtion simultneously rom our stellites to determine user's position nd velocity. Ech stellite trnsmits dt strem clled Nvigtion Messge on L1 nd L t rte o 50 bps. This dt strem contins: the stellite clock correction term; the clock reerence time; the dierentil group dely nd IODC (Issue o Dte, Clock) term; the Ephemeris prmeters or the trnsmitting stellite; the single requency ionospheric correction terms; the coeicients to convert GPS time to UTC; the Almnc o ll stellites (Leick, 1994). Moreover, the GPS stellite signls trnsmit other dt types which re code nd crrier phse pseudornges. They re cquired rom the trnsmitted signl t two L- bnd requencies, 1 = 1575.4 MHz nd = 17.60 MHz. Except or corruption by clock errors, tmosphere delys, nd instrumentl delys, pseudornge is n bsolute mesurement o rdio-metric rnge between GPS stellite nd receiver. Among the error sources, the lrgest one comes rom the dely when signl trvels through the tmosphere. Crrier requencies below 30 MHz re relected by the ionosphere nd only higher requencies penetrte the ionosphere.
There re two dierences between the crrier phse nd code pseudornges which re: the crrier phse pseudornge is bised by n unknown integer number o cycles nd it hs dt noise much lower thn code pseudornge, which mkes it more precise. To llow users to utomticlly correct the eects o both the rnge nd rnge rte errors induced by the ionosphere, the secondry requency ws incorported into the system. The dul requency GPS receivers tke dvntge o the dispersive nture o the ionosphere nd cn eliminte the ionospheric errors, t lest mthemticlly. For single requency users, it ws incorported into the system numeric model o ionospheric rnge error clled Klobuchr s model. IONOSPHERIC EFFECTS IN THE GPS MEASUREMENTS The tmosphere is usully subdivided into regions. These regions re bsed on common physicl properties nd ppernces such s tempertures, composition, stte o mixing, nd ioniztion. With respect to signl propgtion, it cn be divided in troposphere nd ionosphere. This division is mde ccording to the dierent conditions o propgtion. The ionosphere covers the region between pproximtely 50 km nd 1000 km bove the erth nd is chrcterized by the presence o ree electrons. In ct the upper boundry o the ionosphere is not well deined since it cn be interpreted s the electron densities thinning into the plsmsphere nd subsequently the inter plnetry plsm (Komjthy, 1997). 3
The ionosphere is dispersive medium or rdio wves implying tht the rerctive index is unction o the rdio wve's requency, the electron density, nd to minor degree, the intensity o the erth's mgnetic ield. The rerctive index is given by: c n = 1 ± (1) where the positive signl is or crrier phse pseudornge nd negtive one is or code pseudornge, is the requency, c = -40.3 N e, N e is the electron density which is lwys positive. Ater integrting the phse nd group rerctive indices long the pth o the GPS signl, the rnge obtined between the stellite nd the receiver which is dierent rom the true geometric rnge by the mount clled ionospheric error. The error is negtive or the crrier phse pseudornges (phses is dvnce; tht is, the mesured rnge is shorter thn the geometric rnge) nd positive or the code pseudornges ( group dely; tht is, the mesured rnge is longer thn the geometric) (Komjthy, 1997). The ionospheric dely is proportionl to the number o electron content (integrted density long the signl pth) nd inversely proportionl to requency squred used: 40.3 ION = TEC () where TEC is Totl Electron Content nd is given by: 4
TEC = N e ds (3) nd s is the pth rom stellite to the receiver. The density o ree electrons vries strongly with the time o the dy nd the ltitude. Thereore, the chnge o pseudornge mesurement cused by the ionospheric rerction my be restricted to the determintion o the TEC. However, the TEC itsel is irly complicted quntity becuse it depends on sunspot ctivities, sesonl, nd diurnl vritions the line o sight which includes elevtion nd zimuth o the stellite, nd the position o the observtion site. Tking ll eects into ccount, GPS pseudornge my be wrong rom bout 15 m to 50 m (Homnn-Wellenho, 1994). THE DUAL FREQUENCY IONOSPHERIC MODEL The expressions or the code nd crrier phse ionospheric corrections on L1 nd L derived rom the dul requency observtions re given by (Strng, 1997): P IF = (4) 1 P1 P 1 1 Φ IF = (5) 1 1 Φ 1 1 Φ 1 5
where P IF nd ΦIF re the ree ionospheric eect, P is the code, ϕ is the crrier phse, 1 nd re the requency on L1 nd L, respectively. The igures 1 nd show the ionospheric errors o crrier phse nd code pseudornges, respectively. These errors hve been obtined without the mbiguity solution nd dt pre-processing. According to Strng (1997), these errors should be round 0.5 to 1 m to crrier phse nd round 4 m to code. 3.00.00 Ionospheric Error (m) 1.00 0.00-1.00 -.00 0.0 0E+0.0 0E+4 4.00 E+4 6.00 E+4 8. 00E +4 1.0 0E+5 Time (sec) Figure 1: The crrier phse ionospheric error 6
0.00 on L1 -.00 on L Ionospheric Error (m) -4.00-6.00-8.00-10.00 0.00E+0.00E+4 4.00E+4 6.00E+4 8.00E+4 1.00E+5 Time (sec) Figure : The code Ionospheric error KLOBUCHAR S MODEL The Klobuchr s model is used to correct the ionospheric eect or single requency mesurements. It uses the cosine model or the dily vrition o the ionosphere, with the mximum being t 14:00 locl time nd is described by 8 coeicients α nd β which re trnsmitted s prt o the GPS stellite nvigtion messge. This model removes bout 50% o the totl ionospheric dely t mid-ltitudes nd is represented through one set o vribles tht re vlid or ew dys (Klobuchr, 1987). The ionospheric dely correction eqution is given by (Seeber, 1993): T ion ( t φ ) π = DC + Acos (dy) (6) P 7
T ion = DC (night) (7) where T ion is the verticl dely (ns), DC is the constnt midnight term (5 ns or 5 10-9 sec), A is the mplitude, φ is the constnt phse term (14 h locl time), t is the locl time, P is the period. The mplitude nd period re unctions o geomgnetic ltitude nd re represented by third-degree polynomils: A = 4 n= 0 α φ n n m (seconds) (8) P β φ = 4 n= 0 n n m (seconds) (9) EMPIRICAL MODEL OF THE EARTH S PLASMASPHERE This empiricl model consists o n nlyticl expression tht cn be used to reproduce hydrogen density t rbitrry loctions in the plmsphere or given conditions. The principl sptil dependence o plsmspheric electron density is governed by L-shell. The L-shell is the surce trced out by prticle moving round the erth's geomgnetic iled lines. For the electron densities, the Gllgher model uses the ollowing empiricl ormul (Gllher et l., 1988): ( N ) F ( L) G( L) H ( L) Log 10 e = 1 (10) 8
where N e is de electron densities; F h ( L, λ ) / ( ) ( 5 3 1 4e L e ) = (11) is modiied Chpmn lyer; ( L) 6L 7 G = + (1) is liner L-shell model which hs been ound to be the best representtion o the inner plsmspheric electron density proiles; ( ) 9 1 9 9 1 ( ) L H L = 1+ (13) 8 represents the shpe nd the loction o the plmspuse; nd 1 3 4 5 6 7 8 9 = 1.4 = 1.53 = 0.036 = 30.76 = 159.9 = 0.87 + 0.1e = 6.7 / 3 MLT 1 = 0.7cos π + 4.4 4 MLT = 15.3cos π + 19.7. 4 x (14) 9
The constnts i re ree prmeters used to it eqution to the logrithm o ion density. The prmeter 6 controls the density grdient in the inner plsmsphere, while 8 nd 9 determine the loction nd slope o the plsmpuse, respectively. L is the McIlwin L-shell prmeter, λ is geomgnetic ltitude, MLT is the geomgnetic locl time deined by the geomgnetic longitude o the men sun, nd, h(l,λ) is the height bove the erth s surce given by: ( L, λ) = R Lcos λ 6371 h e (15) with strting ltitude o 1000 km bove the surce o the erth; R e is the erth rdius. This model provides vritions in the plsmspheric electron density s unction o geomgnetic ltitude, L-shell vlues, nd geomgnetic locl time. The lgorithm does not model diurnl, sesonl or solr cycle vritions o the plmspehric electron content. The ionospheric eect is clculted t ech point. Ater this, it is necessry to clculte the eect long the pth between the user nd GPS stellites, tht gives the TEC. Knowing the TEC, it is necessry to clculte the ionospheric eect tht is given by: 40.3 I = TEC (16) 10
CONCLUSIONS The min gol o this study is to nlyze nd to choose proper model to correct the ionospheric error on single requency rnge mesurements or n rtiicil stellite bove 1000 Km. Despite being model tht providing good results, the dul requency model cn not be used in this work, but it will be used s reerence model. The Klobuchr s model must be used or n user on erth s surce nd it only corrects until 50% o the ionospheric error being necessry to use n estimtion model to correct the unmodeled errors. The empiricl model is good model or n user bove 1000 Km. However, through severl nlyzes, the ionospheric errors is very smll bove 1000 Km o erth's surce (round 1m) nd it should be better to estimte them s prmeters using Klmn iltering. REFERENCES Gllgher, D. L.; Crven, P. D.; Comort, R. H. An empiricl model o the erth s plsmsphere. Adv. Spce Reserch. Vol. 8, n. 8, pp. (8)15-(8)4, 1998. Homnn-Wellenho, B.; Lichtenegger, H.; Collins, J. Globl Positioning System Theory nd Prctice. Springer-Verlg Wien, New York, 1994. 355p. Klobuchr, J.A. Ionospheric time-dely lgorithm or single-requency GPS users. IEEE Trnsctions on Aerospce nd Electronic Systems, Vol. AES-3, n. 3, p35-331, 1987. Komjthy, A. Globl Ionospheric Totl Electron Content Mpping Using the Globl Positioning System. Ph.D. disserttion, Deprtment o Geodesy nd Geomtics 11
Engineering Technicl Report No. 188, University o New Brunswick, Fredericton, New Brunswick, Cnd, 1997. 48p 560p. Leick, A. GPS Stellite Surveying. nd edition. John Wiley & Sons, INC., 1995. Seeber, G. Stellite Geodesy: Foundtions, Methods, nd Applictions. Wlter de Gruyter, Berlim - New York, 1993. 531p. Strng, G.; Borre, K. Liner Algebr, Geodesy, nd GPS. Wellesle -Cmbridge Press, Wellesley, EUA, 1997. 64p. 1