INFLUENCE OF IONOSPHERE PERTURBATIONS IN GPS TIME AND FREQUENCY TRANSFER

Transcription

1 40 th Annual Precse Tme and Tme Interval (PTTI) Meetng INFLUENCE OF IONOSPHERE PERTURBATIONS IN GPS TIME AND FREQUENCY TRANSFER Sohe Preaux, Pascale Defragne, Ncolas Bergeot, Quentn Bare, and Carne Bruynnx Royal Observatory of Belgum Avenue Crculare,, B-80 Brussels, Belgum E-mal: Abstract The stablty of GPS tme and frequency transfer s lmted by the fact that GPS sgnals travel through the onoshere. In hgh-recson geodetc tme transfer (.e. based on recse modellng of code and carrer-hase GPS data), the so-called onoshere-free combnaton of the code and carrer-hase measurements made on the two frequences s used to remove the frst-order onoshere effect. In ths aer, we nvestgate the mact of resdual second- and thrd-order onoshere erturbatons on geodetc tme transfer solutons, usng the ATOMIUM software develoed at the Royal Observatory of Belgum (ROB). The mact of thrd-order onoshere effects was shown to be neglgble, whle for second-order effects, the tests erformed on dfferent tme lnks and at dfferent eochs show a small effect of the order of some coseconds, on a quet day, and u to more than 0 coseconds n case of hgh onoshere actvty. INTRODUCTION Tme and frequency transfer (TFT) usng GNSS satelltes s wdely used wthn the tme communty, for examle for the realzaton of TAI (Tems Atomque Internatonal), the bass of the legal tme UTC (Unversal Tme Coordnated), comuted by the Bureau Internatonal des Pods et Mesures (BIPM). TFT s characterzed by ts very good resoluton ( observaton ont/0s or ossbly ont er second) and a hgh recson and frequency stablty thanks to the carrer hases (uncertanty ua of about 0. ns). The resent uncertanty n GPS equment calbraton s 5 ns (uncertanty ub systematcs, hence calbraton errors n the BIPM Crcular T). Snce onoshere erturbatons on electromagnetc waves are frequency deendent and snce GPS sgnals are broadcast n two dfferent frequences, onoshere effects are commonly removed through a gven combnaton (named onoshere-free) of the sgnals n the two frequences f and f. However, t s well known that ths combnaton removes only frst-order erturbatons, whch corresond to about 99.9% of the total erturbaton. The resent study ams at evaluatng the mact of the remanng art, concentratng on second- and thrd-order effects. These hgher-order terms are, therefore, mlemented n the software ATOMIUM [], develoed at the Royal Observatory of Belgum. ATOMIUM s based on a least-squares analyss of dual-frequency carrer-hase and code measurements and s able to rovde clock solutons n Precse Pont Postonng (PPP), as well as n sngle dfference (also called Common Vew, CV) mode. 87

2 40 th Annual Precse Tme and Tme Interval (PTTI) Meetng The resent aer s organzed as follows. The frst secton recalls the rncles of GPS TFT and the onoshere-free analyss n Precse Pont Postonng or Common Vew mode. In Secton, the onoshere-free analyss, as mlemented n the ATOMIUM software, s revewed. Then, the Slant Total Electron Content (TEC) s defned n Secton, whch also summarzes TEC relevance to onoshere erturbatons. In Secton 4, the selected method used to mlement hgher-order onoshere correctons n ATOMIUM onoshere-free analyss s descrbed. Our corresondng results are resented n Secton 5, n terms of onoshere delays of second and thrd orders comared to frst-order onoshere effect, and then n terms of the mact of hgher-order onoshere delays n the recever clock soluton comuted wth ATOMIUM. Ths secton also rovdes a dscusson about the use of rerocessed satellte orbts, accountng for hgh-order onoshere correctons. Some conclusons are fnally resented n Secton 6.. GEODETIC TFT AND IONOSPHERE IN GPS SIGNALS For a staton or smlarly q, the GPS measurements, relatve to observed satellte, on the sgnal code P k and hase L k, at frequency k ( for f =575.4 MHz or for f =7.6 MHz) wth corresondng wavelength λ k, can be wrtten n length unts as ( P ) = ρ + cδt + cδτ + zd ε k ( L ) k = ρ + cδt + cδτ ( + I + I + I ) + + P k k k + zd + N λk + ε L + ( Ik I k Ik where ρ s the geometrc dstance - ; Δt s the staton clock synchronzaton error; Δτ s the satellte clock synchronzaton error; zd s the trooshere ath delay for staton ; I k, I k and I k are onoshere frst-, second-, and thrd-order delays on frequency k; N are hase ambgutes; ε P and ε L are the error terms n code and hase, contanng nose and multath. When a dual-frequency GPS recever s avalable at staton, the so-called onoshere-free combnaton (k=) s used: f f P = P P (a) ( f f ) ( f f ) f f L = (b) L L ( f f ) ( f f ) wth f and f the two GPS carrer frequences. Ths combnaton removes, from the GPS sgnal, the frstorder onoshere effect, I, snce the latter s roortonal to the nverse of the square frequency. The corresondng onoshere-free observaton equatons therefore do not contan any frst-order onoshere term, but new factors for second- and thrd-order onoshere effects wth resect to the revous Equaton (): ( P ) = ρ + cδt + cδτ + zd + ε P + ( + I I ) (a) ( L ) = ρ + cδt + cδτ + zd + N λ + ε + I + I (b) Note that about 99.9% [9] of onoshere erturbatons are removed wth I n the so-called onosherefree combnaton. Note also that whle the frst order has the same magntude on GPS hase and code measurements (but wth ooste sgn), the mact of second- and thrd-orders effects s larger on code than on hase observatons (twce for I, three tmes for I). 88 L ) ( ) (a) (b)

3 40 th Annual Precse Tme and Tme Interval (PTTI) Meetng GPS observatons and ther modelng gven by Equatons (a) and (b) are drectly used n Precse Pont Postonng. For Common-Vew analyss,.e. usng the sngle dfferences between smultaneous observatons of a same satellte n two remote statons and q n order to determne drectly the synchronzaton error between the two remote clocks, the observaton equatons for recevers and q wth satellte are subtracted. Ths sngle dfference cancels the satellte clock bas n the GPS sgnal, assumng that the nomnal tmes of observaton of the satellte by the two statons are the same. When formng onoshere-free combnatons, the sngle-dfference code and carrer-hase equatons are: P ( + I I ) q + ε + ( I + I ) q ( ) q ρ q t q d q + ε P + ( L ) q where, for any quantty X, = = ρ q + cδ + cδt q + z + zd X q q + N X Now, all the terms n above Equatons (), (), or (4) can be estmated va an nverson rocedure usng some a ror recse satellte orbts and satellte clock roducts. Ths fnally rovdes the soluton for ether Δt n PPP,.e. the clock synchronzaton error between the atomc clock connected to the GPS recever and the IGS Tme scale at each eoch, or Δt q n common vew,.e. the synchronzaton error between the remote clocks connected to two GPS recevers. In arallel, the staton oston and trooshere zenth delays are estmated as a by-roduct. q λ X q L (4a) (4b) (5). THE ATOMIUM SOFTWARE The resent study on onoshere hgher-order erturbatons n TFT s based on the ATOMIUM software [], develoed at the Royal Observatory of Belgum. ATOMIUM uses a weghted least-squares aroach wth onoshere-free combnatons of dual-frequency GPS code (P ) and carrer-hase (L ) observatons. ATOMIUM was ntally develoed to erform GPS PPP and later adated to sngle dfferences, or Common Vew (CV), of GPS code and carrer-hase observatons. In the aragrahs below, we descrbe ATOMIUM, followng the dagram resented n Fgure. When runnng ATOMIUM, GPS onoshere-free code and hase combnatons are constructed accordng to Equatons (, 6) from L, P, L, P observatons read n RINEX fles. By default, the ATOMIUM software uses as a ror the Internatonal GNSS Servce (IGS) roducts []. IGS satellte clocks (tabulated wth a 5-mnute nterval) are used to obtan Δτ at the same samlng rate as rovded. IGS satellte orbts (tabulated wth a 5-mnute nterval) are used to estmate ρ (or ρ q ) va a -ont Nevlle nterolaton of the satellte oston every 5 mnutes. The staton oston s corrected for ts tme varatons due to degree and sold Earth tdes as recommended by the IERS conventons [] and for ocean loadng accordng to the FES004 model [4]. The relatve (f GPS observatons were made before GPS week 400) or absolute (f after) elevaton- (no azmuth) and nadr-deendant correctons for recever and satellte antenna hase center varatons are read from IGS atx fle avalable at [5]. Pror to the least-squares nverson, the comuted geometrc dstance s removed from both hase and code onoshere-free combnatons. Those are also corrected for a relatvstc (erodc only) delay and a trooshere delay. Trooshere delays are modeled as the sum of a hydrostatc and a wet delay, resultng 89

4 40 th Annual Precse Tme and Tme Interval (PTTI) Meetng from the roduct of a gven mang functon and of the corresondng hydrostatc or wet zenth ath delay (zd). For the hydrostatc art, we use the Saastamoen a ror model [6] and the dry Nell mang functon [7]. For the wet art, we use the wet Nell mang functon [7], whle the wet zd s estmated as one ont every hours, and modeled by lnear nterolaton between these onts. Carrer-hase measurements are further corrected for hase wndu [8], takng nto account satellte alttude and eclse events. The mlementaton of addtonal hgher-order onoshere correctons on hase and code s done at ths level, as correctons aled on the code and hase measurements. Fgure. ATOMIUM software dagram. The least-squares analyss used n ATOMIUM s detaled n Reference []. As outut, ATOMIUM rovdes the staton (or relatve -q) oston for the whole day, the recever clock (or relatve -q) synchronzaton error every 5 mnutes, and trooshere wet zenth ath delays (and q) at a gven rate ( hours n our case). Furthermore, the onoshere Slant Electron Content (STEC) s comuted from dual-frequency measurements (see Secton 4) for each satellte-staton ar wth a samlng rate of 5 mnutes.. RELEVANCE OF STEC FOR IONOSPHERE PERTURBATIONS A good ndcator of the state of the onoshere s the Total Electron Content (TEC), whch s the ntegrated electron densty nsde a cylnder column of unt base area along a certan drecton between Earth ground and satellte alttude. Slant TEC (STEC) s taken along the satellte - staton drecton. 90

5 40 th Annual Precse Tme and Tme Interval (PTTI) Meetng STEC s functon not only of the satellte elevaton or staton oston, but also of the tme of the day, of the tme of the year, of the solar cycle, and of the onoshere artcular condtons (as seen n Fgure b durng the onoshere storm of November 0, 00 for statons BRUS,.e. Brussels, at lattude 50 8 and longtude 4, OPMT,.e. Pars at lattude 48 0 and longtude, ONSA.e. Onsala at lattude 57 4 and longtude ). Hence, GNSS onoshere-nduced errors wll ncrease n the next few years due to the ncreasng solar actvty assocated wth the ascendng hase of the 4 th sunsot cycle (maxmum forecast around 0-0 deendng on the model). Ionoshere effects n GPS (I, and I) are drectly roortonal to STEC. Fgure. STEC above Brussels, Onsala and Pars statons a) on an onosherequet day (left) or b) on a stormy day (left). TECU=0 6 e - /m. 4. METHOD TO CORRECT IONOSPHERE PERTURBATIONS FOR FREQUENCY K As the I term contans 99.9% of the onoshere erturbatons on GNSS sgnal, t can be used to estmate STEC. The second- and thrd-order terms, also drectly roortonal to STEC, are then comuted usng ths estmated STEC. The STEC n I can be determned usng the geometry-free combnaton (noted as P 4 and L 4 ). The latter only contans a gven combnaton of onoshere erturbatons on f and f sgnals, some constant terms assocated wth the dfferental hardware delays n the satellte and n the recever, lus the hase ambgutes: P 4 = P + P (4a) L = f 4 L L f (4b) 9

6 40 th Annual Precse Tme and Tme Interval (PTTI) Meetng Note that the bendng effect s neglected n the resent study, meanng that the trajectory consdered to comute those onoshere correctons on GPS observatons s a straght lne from satellte to staton (and q). FIRST-ORDER IONOSPHERE PERTURBATIONS The frst-order onoshere effect, s gven by [0] I = α k k STEC (a) wth the factor for GPS frequences and beng α, 40. = + f, (b) Ths mles that the corresondng factors for the onoshere-free (k=) or geometry-free (k=4) combnatons are α = 0 α = f f (c) As stated here above, for each ar of code or hase measurements (on f and f ), the geometry-free combnaton can be used to comute the STEC [], whch s needed n hgher-order onoshere correctons. Neglectng the I and I contrbutons nducng errors n estmated STEC of the order of 0. TECU at the most, one gets: STEC α4 ( ) = ( L ) ( L ) ( P ) arc wthout cycle sls c DCB c DCB (a) In the above formula, P -P Dfferental Code Bases (DCB) are assumed constant durng a day, and we read them from the CODE (IGS Analyss Center) IONEX fles; < > means takng the average. Alternatvely, STEC can be comuted usng P P codes that have been smoothed wth the corresondng hase, STEC α4 ( ) = ( P ) ( P ) { } smoothed c DCB c DCB wth hase (b) Ths leads to smlar results as those obtaned from Equaton (a) wth resect to the same DCB roduct. 9

7 40 th Annual Precse Tme and Tme Interval (PTTI) Meetng SECOND-ORDER IONOSPHERE PERTURBATIONS Whereas the magntude of I for a gven frequency deends solely on STEC and s always ostve, the magntude and sgn of I deend on the - sgnal drecton, the actual STEC, and the geomagnetc feld B values (Fgure ). We used the followng ntegrated formula [] n the no-bendng aroxmaton I k = α k BIPP cosθ B LOS STEC (4a) wth frequency factors α = 757 c f f ( f + f ) (4b) α, 757 c = f, (4c) STEC s obtaned from L 4 P 4 (Equaton (a)) and B IPP s comuted usng the accurate Internatonal Geomagnetc Reference (IGR) model [], as the latter allows us to reduce errors n I u to 60% wth resect to a dolar model [9,0]. Fgure. The thrd-order onoshere effect s not only a functon of STEC, but t s also functon of the angle between the Lne Of Sght (LOS) and the geomagnetc feld B at the Ionoshere Percng Pont (IPP), and of the magntude of B at IPP. THIRD-ORDER IONOSPHERE PERTURBATIONS In the onoshere thrd-order contrbuton, the magnetc feld term can be safely neglected at submllmeter error level, leadng to the smle formula [] 9

8 40 th Annual Precse Tme and Tme Interval (PTTI) Meetng I = α k k STEC (5a) wth frequency factors also beng functons of the electronc dstrbuton n the onoshere: α, 47 N = f max 4, 47 N α = f max f η η (5b) (5c) where the shae factor η s taken around 0.66 and the eak electron densty along the sgnal roagaton ath, N max, can determned by a lnear nterolaton between a tycal onoshere stuaton and a solar maxmum one [,4]: N [( 0 6) 0 ] ( ) 0 [ ] ( 8 ) VTEC max = 0 The Vertcal TEC (VTEC), whch s TEC along a vertcal trajectory below the satellte, s taken as the rojecton, va the onoshere Modfed Sngle Layer Model mang functon, of (STEC) from Equaton (a) wth α MSLM =0.978, R =67 km, H=506.7 km, as n [5]: (6) STEC = f ( z) VTEC MSLM (7a) f MSLM ( z) R R + H cos ( α z) MSLM (7b) Fnally, usng the above equatons for the frst-, second- and thrd-order onoshere effects on GPS sgnal roagaton, one fnds the orders of magntude of ther mact on the code and carrer-hase measurements gven n Table. Table. Orders of magntude of onoshere effects I, I, and I. Orders of magntude of onoshere effects I, I, I on GPS hase measurements (for codes, see convertng factor n code measurement Equatons (, ), Secton ) Ionoshere effect Delay n LL Delay n L Relevance [9] (absolute value) er 00 TECU er 00 TECU 94

9 40 th Annual Precse Tme and Tme Interval (PTTI) Meetng I ~0 ns -00 ns % of I I ~0 0 s ~ 0 45 s 90% of I I ~0 s ~ 0 s 5. RESULTS The I and I correctons comuted accordng the rocedure descrbed above were aled to the onoshere-free combnatons P and L used n ATOMIUM. The resent secton shows some relmnary results: estmated second- and thrd-order delays on GPS sgnals (and on combnatons of ther measurements) and the mact of these on the tme and frequency transfer solutons. IONOSPHERE DELAYS The frst results concern the onoshere erturbatons n terms of delays as comuted wth ATOMIUM, accordng to the models detaled n revous secton. Frstly, recall that the Total Electron Content of the onoshere s usually hgher on average at hgh lattude wth resect to md-lattude statons (Fgure ). Snce I, I, and I are roortonal to Slant TEC, the amltude of onoshere erturbatons n GPS sgnal follow accordngly. Secondly, as TEC reaches normally ts maxmal value at local noon, on a normal day, the onoshere erturbatons n GPS sgnal reflect ths daly varaton of TEC. And fnally, for any observed satellte, as the onoshere thckness crossed by the sgnal s roortonal to the nverse of the sne of the satellte elevaton, the STEC durng one satellte track, as well as the onoshere delays, takes the shae of a concave curve. Fgures 4, 5, and 6 llustrate I, I and I resectvely on a quet (left) versus an onoshere-stormy day, the onoshere storm of 0 November 00 (rght). The selected staton n ths llustraton s Onsala (ONSA). The frst-order onoshere erturbatons n L can reach more than 00 nanoseconds durng the storm (Fgures 4a and 4b), whle t s less than 50 nanoseconds n normal tmes. I n L s slghtly smaller accordng to factor f / f. The amltude of the I effect on the codes s the same as that on the hases, but wth ooste sgn, as shown n Equaton (). The I effect s removed from the onoshere free combnaton. The second-order onoshere erturbaton n the onoshere-free combnaton (Fgure 5a) s about to 4 orders of magntude smaller than the frst order n L. I can reach about 0 coseconds durng the storm, about the double of ts maxmum value durng a quet day (Fgure 5b comared to 5a). We also recall that, n the onoshere-free combnaton, the second-order onoshere erturbaton, I, affects twce more the codes than the hases, as seen n Equaton (). 95

10 40 th Annual Precse Tme and Tme Interval (PTTI) Meetng Fgure 6 llustrates the thrd-order onoshere erturbaton, whch s agan an order of magntude smaller than the second order. Here, the effect of the storm s also clear, as the thrd-order effect n the onoshere-free combnaton can reach about coseconds durng the storm (Fgure 6b), whle ts maxmum value on a non-stormy day s about 0.4 coseconds (Fgure 6a). Agan, the contrbuton of I s three tmes more mortant for codes than for hases, as seen n Equaton (), but remans neglgble wth resect to the resent recson of GPS tme and frequency transfer. IONOSPHERE IMPACT ON RECEIVER CLOCK ESTIMATES FROM A L P ANALYSIS Table and the results resented n the above aragrah llustrate the need to take second-order onoshere correctons nto account n P and L measurements for TFT. However, to be coherent, n addton to the I (and I) correcton(s) on GPS code and hase data, we should also use satellte orbt and clock roducts comuted wth I (and I) correcton(s) n order to estmate the mact of the onoshere on staton clock synchronzaton errors va ATOMIUM. Indeed, n Reference [], t was estmated that second-order onoshere effects n satellte clocks were the largest and could be more than centmeter (.e. ~0 coseconds); the same authors mentoned that the second-order onoshere effects on the satellte oston are of the order of several mllmeters only, and consst n a global southward shft of the constellaton. Current IGS roducts do not take I or I nto account. But rerocessed orbts [6], takng, among others, hgher-order onoshere effects nto account, are avalable at analyss centers [7, 8]. Unfortunately, they do not rovde satellte clocks roducts. Ths s why we resent here the mact of our onoshere correctons on clock solutons va ATOMIUM n CV mode (Fgures 7, 8, and 9), as the satellte clock s elmnated n CV. We choose the lnk BRUS-ONSA,.e. Brussels-Onsala (Sweden), and the day of an onoshere storm, 0 November 00. Fgure 7 resents the effect of usng the rerocessed orbts from [7,8] together wth I and I correctons on code P and hase L. Snce satellte clocks are removed n Common-Vew mode, the varatons are larger than what s exected (from the I and I delays, and from the satellte oston varatons due to I and I n rerocessed orbts). These dfferences could, therefore, be attrbuted to other dfferences between the IGS orbts and the rocessed ones. Fgure 8 shows the effect of alyng the I and I correctons on GPS P L analyss, wthout usng rerocessed orbts. We see an effect u to 0 coseconds durng the onoshere storm on the lnk BRUS- ONSA. The I effect shown n Fgure 9 s at the resent nose level of GPS observatons; only a very small sgnal aears out of the nose durng the onoshere storm. Consequently, n resdual onoshere erturbatons n P L (when P L s not corrected for hgher-order effects), the man contrbuton s I. An I delay of 0 coseconds eak to eak durng the storm (Fgure 5b) for a gven staton A nduces a varaton wth the corresondng dfferental I A - I B amltude n CV frequency transfer wth staton B, as the shae of the curve s determned by the GPS hases for whch the I correcton s aled wth a factor. Furthermore, I nduces twce as much an offset on the absolute tme synchronzaton error (Fgure 8), as the calbraton of the curve s determned by the code data for whch the I correcton s aled wth a factor (Equaton ()). However, ths of course s stll well below the resent calbraton caabltes of GPS equment. Note that the results resented here corresond to the tme lnk BRUS-ONSA. It s, therefore, the dfferental onoshere effect between those two statons (here, Brussels and Onsala) that matters for the clock soluton n Common -Vew mode. The mact of I on a clock soluton n PPP could, therefore, be hgher and nduce larger effects on ntercontnental tme lnks. Ths wll be nvestgated n further studes. 96

11 40 th Annual Precse Tme and Tme Interval (PTTI) Meetng Fgure 4. Frst-order onoshere delay n GPS frequency, for staton Onsala a) on an onoshere-quet day, March 007 (left), versus b) on an onoshere-stormy day, 0 November 00 (rght). Fgure 5. Second-order onoshere delay n GPS so-called onoshere-free combnaton, for staton Onsala a) on an onoshere-quet day, March 007 (left), versus b) on a onoshere-stormy day, 0 November 00 (rght). Fgure 6. Thrd-order onoshere delay n GPS so-called onoshere-free combnaton, for staton Onsala a) on an onoshere-quet day, March 007 (left), versus b) on an onoshere-stormy day, 0 November 00 (rght). 97

12 40 th Annual Precse Tme and Tme Interval (PTTI) Meetng Fgure 7. Effect of takng hgher-order onoshere effects nto account both n the measurements and n a-ror roducts for the Brussels-Onsala lnk, on the onosherestormy day 0 November 007. The dfference s taken between ATOMIUM-estmated staton clock synchronzaton error when no hgher-order onoshere correcton s taken nto account n L P, usng IGS roducts, versus when takng them nto account together wth usng rerocessed roducts. Fgure 8. Effect of takng hgher-order onoshere effects, or not, nto account n the L P GPS measurements for the Brussels-Onsala lnk, on the onoshere-stormy day 0 November 007. The dfference s taken between two ATOMIUM-estmated staton clock solutons, both usng IGS roducts. 98

13 40 th Annual Precse Tme and Tme Interval (PTTI) Meetng Fgure 9. Effect of takng thrd-order onoshere effect, or not, nto account n the L P GPS measurements for the Brussels-Onsala lnk, on the onoshere-stormy day 0 November 007. The dfference s taken between two ATOMIUM-estmated staton clock solutons, both usng IGS roducts. 6. CONCLUSIONS Ths study resented a least-squares analyss usng the so-called onoshere-free combnaton of GPS codes and hases to estmate recever clock synchronzaton errors for recse frequency and tme transfer. We used the ATOMIUM software, n whch we mlemented hgher-order onoshere contrbutons (second and thrd orders) n the onoshere-free combnaton. We then comared these onoshere resduals wth the frst-order onoshere effect on the GPS dual frequency sgnal, whch s cancelled n onoshere-free combnatons of GPS codes and hases. It was shown that the onoshere frst-order delay of several tens of nanoseconds on an onoshere-quet day, s doubled n case of onoshere storms. Though second-order delays n the onoshere-free combnaton are about to 4 orders of magntude smaller than the frst-order, they can reach about 0 coseconds on a stormy day, whch s relevant when erformng geodetc tme and frequency transfer wth very stable clocks. Thrd-order delays n the onoshere-free combnaton are yet an order of magntude smaller, and are at the level of resent nose of GPS observatons. The mact of those hgher-order delays on onoshere-free tme and frequency transfer clock solutons was estmated for the tme lnk BRUS-ONSA. It reaches more than 0 coseconds durng the onoshere storm of 0 November 00. ACKNOWLEDGMENTS Ths work has been suorted by the Solar and Terrestral Center of Excellence [9]. The authors also acknowledge the IGS for ther data and roducts, as well as the GFZ Potsdam and TU Dresden analyss centers for ther rerocessed roducts used n ths study. 99

14 40 th Annual Precse Tme and Tme Interval (PTTI) Meetng REFERENCES [] P. Defragne, N. Guyennon, and C. Bruynnx, 008, GPS Tme and Frequency Transfer: PPP and Phase-Only Analyss, Internatonal Journal of Navgaton and Observaton, 008, Artcle ID [] IGS roducts, ft://gscb.jl.nasa.gov/ [] D. McCarthy and G. Pett, "IERS Conventons 00, Techncal Note on Dslacement of Reference Ponts (IERS). [4] T. Leteller, F. Lyard, and F. Lefebre, 004, The new global tdal soluton: FES004, Jason SWT Meetng, -4 November 004, St. Petersburg, Florda, USA. [5] IGS satellte antenna hase center varatons fles gs0.atx and gs05.atx, ft://gscb.jl.nasa.gov/ub/staton/general/ [6] J. Saastamonen, 97, Atmosherc correctons for the trooshere and stratoshere n rado rangng of satelltes, Geohyscal Monograh 5, Use of Artfcal Satelltes for Geodesy, (AGU). [7] A. E. Nell, 996, Global mang functons for the atmosherc delay at rado wavelengths, Journal of Geohyscal Research, 0(B), [8] J. T. Wu, S. C. WU, G.A. Hajj, W.I. Bertger,and S.M. Lchten, 99, "Effects of antenna orentaton on GPS carrer hase," Manuscrta Geodetca, 8, [9] M. Hernandez-Pajares et al., 008, Methods and other consderatons to correct for hgher-order onosherc delay terms n GNSS, resented at IGS Analyss Center Worksho, -6 June 008, Mam, Florda, USA. [0] S. Bassr and G. A. Hajj, 99, Hgher-order onosherc effects on the global ostonng system observables and means of modelng them, Manuscrta Geodetca. 8, [] M. Hernandez-Pajares, J. M. Juan, J. Sanz, and R. Oruz, 007, Second-order onosherc term n GPS: Imlementaton and mact on geodetc estmates, Journal of Geohyscal Research,, B0847, -6. [] N. A. Tsyganenko, 005, Geoack: a set of FORTRAN subroutnes for comutatons of the geomagnetc feld n the Earth's magnetoshere, verson of 4 May 005, avalable on htt://modelweb.gsfc.nasa.gov/magnetos/tsygan.html, as geoack-005.doc and full Fortran routnes. [] M. Frtsche, R. Detrch, C. Knöfel, A. Rülke, and S. Vey, 005, Imact of hgher-order onosherc terms on GPS estmates, Geohyscal Research Letters,, L, -5, Formula (4). [4] F. K. Brunner and M. Gu, 99, An mroved model for the dual frequency onosherc correcton of GPS observatons, Manuscrta Geodetca, 6,

15 40 th Annual Precse Tme and Tme Interval (PTTI) Meetng [5] R. Dach, U. Hugentobler, P. Frdez, and M. Mendl, 007, Bernese GPS Software, Verson 5.0,. 59. [6] P. Stegenberger, M. Rothacher, R. Detrch, M. Frtsche, A. Rülke, and S. Vey, 006, Rerocessng of a global GPS network, Journal of Geohyscal Research,, B0540, -. [7] Informaton Systems and Data Center of GFZ Potsdam, htt://sdc.gfz-otsdam.de/gs-dr [8] Techncal Unversty of Dresden, htt:// [9] Solar-Terrestral Center of Excellence (STCE), htt:// 40

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