Multi Frequency Precise Point Positioning Using GPS and Galileo Data with Smoothed Ionospheric Corrections

Transcription

1 Multi Frequency recie oint oitioning Uing GS and Galileo Data with Smoothed Ionopheric Correction Franceco Baile, Terry Moore, Chri Hill Nottingham Geopatial Intitute Univerity o Nottingham Nottingham, UK ranceco.baile@nottingham.ac.uk Gary McGraw, Andrew Johnon Rockwell Collin Abtract The poor ignal viibility and continuity aociated with urban environment together with the low convergence/reconvergence time o recie oint oitioning (), uually make unuitable or land navigation in citie. However, reult baed on imulated open area demontrated that, once Galileo reache inal operational capability, convergence time will be cut in a hal uing dual-contellation GS/Galileo obervation. Thereore, it might be poible to extend the applicability o to land navigation in certain urban area. reliminary reult, baed on imulation, howed that GS/Galileo i poible where building are relatively hort and atellite minimum viibility requirement i met or mot o the time. In urban environment, ignal dicontinuity and reconvergence till repreent the major problem or traditional, which i baed on the ionophere-ree combination o tworequency peudo-range and carrier phae. An alternative method to mitigate the ionophere delay i propoed in order to enure the bet poitioning perormance rom multi-requency. Intead o uing the ionophere-ree combination, here low noie dual- or triple-requency peudo-range combination are corrected with ionophere delay inormation coming rom ederated carrier moothing (Hatch) iono-etimation ilter or each atellite. Thi method provide ater re-convergence time and enure the bet poible poitioning perormance rom the Galileo Alternative BOC modulation in multi-requency. Indeed, even though Galileo E5 ha mall tracking noie and excellent multipath rejection, it poitioning perormance i limited by the inluence o E ignal error in the ionophere-ree combination, degrading the quality o the meaurement. Keyword GS; Galileo; Multi-Contellation; Multi- Frequency; I. INTRODUCTION recie oint oitioning () [] i a carrier phae baed poitioning technique that enable centimeter-level (tatic proceing) to decimeter-level (kinematic proceing) accuracy, with no need or local reerence tation a required Thi project wa ponored through a tudenthip agreement between the Univerity o Nottingham and Rockwell Collin UK Limited. with Real Time Kinematic (RTK) technique. can be conidered a an improved verion o the claic peudo-range baed poitioning [], in which broadcat navigation data are replaced with precie orbit and clock etimate rom a global or regional network olution. Model or environmental and ite location eect are alo required. Uing carrier phae meaurement, in addition to code peudo-range, mean that the initial carrier phae ambiguitie have to be etimated, cauing long convergence time. Typically, 5 to 60 minute are required to have the inal accuracy. Thi long convergence time repreent a drawback o and explain why ha not been widely ued in contrained and tranient ignal environment aociated with urban area. Indeed, in cae the GNSS receiver loe track o carrier phae, the poitioning ilter need to be reinitialized, meaning that urther ten o minute are required beore re-convergence. With the advent o the new Global Navigation Satellite Sytem (GNSS), igniicant reearch eort have been dedicated to tudy the navigation perormance o multi-gnss, both in term o ignal availability and poitioning accuracy in multiple cenario, including urban environment. In particular, it wa demontrated that, on major road o citie, atellite availability i trongly improved when uing at leat two ytem (e.g. GS and Galileo) with repect to the GS-only cae [, 4]. However, or very dene urban canyon multicontellation GNSS ail to meet the minimum requirement or poitioning, mot o the time, even conidering three ytem together []. Analyi uing both imulated [5, 6] and real data [7, 8] howed that, once Galileo reache inal operational tatu, the convergence time will be cut by more than a hal when uing both GS and Galileo obervation. Thereore, multi-gnss will open to a wider range o application. Thi paper aee the perormance improvement oered by uture operational-tate dual-contellation (GS and Galileo) compared to the ingle-contellation cae, not only or

2 the environment or which ha traditionally been applied, namely open ky condition, but alo urban environment. II. MULTI-CONSTELLATION MULTI-FREQUENCY GNSS SIMULATOR Aeing inal operational tate multi-contellation GNSS perormance with real data i hampered by the current incomplete deployment o the Galileo contellation and the lack o reely available, real-time, precie orbit and clock product or modernized GNSS. Thereore a imulator or multi-gnss obervation and precie orbit and clock product wa developed in Simulink to upport thi reearch. The imulator input conit o the reerence trajectorie or the uer and the tranmitting atellite and the inormation about the receiver and atellite clock oet and drit. The imulator output GNSS meaurement in Receiver Independent Exchange (RINEX). obervation ormat. Code peudo-range u, k and carrier phae L u, k, tranmitted on requency k by atellite, are imulated conidering the main ource o error a decribed in []. rel u,k u r c dt dt δt u,k k u,k u,u,k c d d I T ε rel L u,k r c dtu dt δt u,k u k u,k L,u,k I T λ N ε Equation () and () are the generic peudo-range and carrier phae equation. They include: the geometric range r, the receiver and atellite clock oet dt and dt, the relativitic eect k rel δt, the group delay or receiver ( d u,k ) and atellite ( d ), the atmopheric delay due to ionophere I u, k and tropophere T u, the carrier phae initial ambiguity N u, k, and other error including peudo-range and carrier phae noie and multipath (,u,k and u L,u,k model to imulate thee error can be ound in [9]. ). Detail o the recie orbit and clock are alo required in. Thereore, the imulator alo output real-time quality precie product in Standard roduct (S) and RINEX clock.0 ormat. The imulated product error i baed on the comparion between the GS IGS real-time and ESA inal product between GS week 97 and 90. RT A decribed in [9], the error in the real-time product can be modelled a the um o two inuoid with period equal to the Earth rotation period T E ( hour and 56 minute) and to the orbital period o the contellation T O ( hour and 58 minute or GS, while or Galileo it i 4 hour and minute). π π Δ b a in t Φ a in t Φ RT E E O O TE TO The average biae b and amplitude component i ummarized in Table I. ao and a E III. OSITIONING IN OEN SKY CONDITIONS or each Over the year, ha largely been applied to many realtime application that require ub-decimeter level accuracy on a wide area or global cale. In preciion arming, or intance, can be ued to preciely navigate ield machine to ulil the high accuracy requirement over area o hundred o quare kilometer [0]. Alo, precie poitioning in ohore and deert area cannot expect to have any nearby tation due to logitical eaibility and cot, thereore can be ued or ocean drilling, ea loor and ea urace mapping or tunami monitoring. All thee cenario are characterized by open ky condition, where a receiver i more likely to have continuou track o the GNSS atellite. In thi ection, the poitioning perormance o GS and Galileo ignal, alone or ued together, in open ky condition will be aeed. To do thi, imulated obervation, 4 hour long, rom ten tatic receiver pread worldwide (ee Fig. ) were proceed with the OINT otware [] in tatic mode with loat ambiguity. For each tation, the imulator wa run 55 time; thereore a total o 550 point were conidered. TABLE I. RMS OF THE FITTING ARAMETERS. VALUES ARE IN UNITS OF CENTIMETERS. Radial Alongtrack Crotrack Clock b a O a E Fig.. Station conidered or the open ky tet.

3 For better GS-Galileo interoperability, reult baed on the ionophere ree (IF) combination between GS L and L5 and Galileo E and E5a were conidered. The metric ued to deine the poitioning perormance are the error in the north, eat and down component o the poition at the end o the proceing and the time thee error take to converge below 0 centimeter. The open ky condition alway guarantee excellent geometry and ignal continuity even conidering only one contellation. For example, Fig. how the epoch o the day in which a given GNSS atellite i viible rom tation SEY. Individual GS atellite were continuouly viible or up to 0 hour and 48 minute, while Galileo atellite or maximum 4 hour and 8 minute. Thi dierence i due to the higher altitude o the Galileo orbit, and conequently lower velocity o the atellite, with repect to GS. In term o ambiguity reolution, having ignal continuouly available or a longer time i beneicial, but ater change in atellite geometry lead to better obervability o the ambiguity itel. Fig. how the oition Dilution o reciion (DO) or the GS only, Galileo only, and GS plu Galileo cae a een by tation SEY. Over 4 hour, on average the DO or the GS only cae i 9% maller than the DO or the Galileo only cae, while uing two contellation the DO i urther improved by 6% with repect to the Galileo cae. A. reult Table II how the root mean quare (RMS) o the error and convergence time in the three component o poition or the dierent coniguration or the 550 point conidered. Both ingle and dual contellation ytem are able to provide a ubdecimeter level accuracy ater a ew ten o minute. On average, poitioning with Galileo E-E5a IF perorm better that GS L-L5 IF: it i more accurate and converge ater than the GS olution. Approximately 80% o improvement wa regitered in the horizontal accuracy, while the vertical error improved by %. However thi doe not really matter a both ytem can guarantee the target accuracy o better than 0 centimeter. DO Fig.. DO daily time erie a een by tation SEY or the ingle and two-contellation cae. TABLE II. COMARISON BETWEEN GS-ONLY, GALILEO-ONLY AND GS LUS GALILEO RESULTS. RMS OF THE OSITIONING ERRORS AND CONVERGENCE TIMES FOR THE STATIONS CONSIDERED. Error [cm] North Eat Down GS L-L Galileo E-E5a GS L-L5 Galileo E-E5a Galileo E-E Convergence time [minute] North Eat Down GS L-L Galileo E-E5a 7 4 GS L-L5 Galileo E-E5a 0 8 Galileo E-E5 7 6 Fig.. Satellite availability a recorded by tation SEY. What i really relevant i the improvement in the convergence time. In the Galileo cae, the vertical component converge 9% ater than the GS cae, while the horizontal component converge up to % ater. A it wa already highlighted in [9], the reaon or thi behavior i the lower noie on Galileo peudo-range []. Further improvement in the convergence time were oberved when uing the two ytem together. The time the vertical error take to go below 0 centimeter wa reduced by 50% with repect to the GS only cae and by 8% with repect to the Galileo only cae. The overall accuracy i hal way between the one obtained by GS and Galileo, but, a previouly tated, thi doe not repreent a major concern being well below the 0 centimeter threhold. Having demontrated that lower peudo-range noie lead to better poitioning perormance, one would expect ome improvement by employing the Galileo Alternative BOC

4 modulated ignal E5. It i known to have mall tracking noie and excellent multipath rejection. However, a hown in Table II, when comparing the olution obtained uing the Galileo E-E5 IF and E-E5a IF combination, they have nearly the ame perormance. The reaon can be ound in the inluence o E ignal error in the IF combination, which degrade the quality o the meaurement. IV. OSITIONING IN URBAN ENVIRONMENTS The poor ignal viibility and continuity aociated to urban environment together with the low (re-) convergence time o, uually make it unuitable or land navigation in citie. However, a demontrated in the previou ection, uing dualcontellation not only improve the viibility condition but alo reduce the convergence time. Thereore, it might be poible to extend the applicability o to land navigation in certain urban area. In order to ae the poitioning perormance o twocontellation GNSS in thee contrained environment, the ignal availability and geometry in ix dierent imulated ite in the neighborhood o the Univerity College o London (UCL) campu were analyzed. Building boundarie [], i.e. the minimum elevation angle above which GNSS ignal can be received due to building obtruction, were adopted. Fig. 4 and Fig. 5 illutrate the location and the building boundarie or each ite. Site B, C and D are three example o treet that might be travelled when navigating a ground vehicle in European citie. Site B (Gower Street) i a three lane treet plu ootpath with relatively mall building (our-ive torie) on each ide o the road. Site C (Univerity Street) i lightly narrower than Gower Street. It ha only one lane, plu parking lot and ootpath on each ide. Site D (Huntley Street) i a large a Univerity Street but it i urrounded by taller building (ix-even loor), which make thi ite to be the mot challenging in term o ignal obtruction. Indeed the minimum elevation angle or ignal viibility aociated to ite D can be a large a 79 degree. Site E correpond to the ront yard o the Wilkin Building in the UCL campu. Thi building oer very little obtruction to atellite viibility. For ite A and F, three and our treet, repectively, orm a junction. Traditionally, in uing IF code and carrier meaurement, the tate vector include the three component o the poition, the receiver clock oet, the reidual zenith wet tropopheric delay, and the carrier phae ambiguity. Thereore, the minimum number o atellite required or i ive. The geometry condition are alo an important actor to ae the GNSS poitioning perormance. For land navigation particularly relevant i the Horizontal Dilution o reciion (HDO), which provide inormation about the horizontal accuracy achievable. For many land application, uch a preciion agriculture and urban poitioning, horizontal accuracy i more critical than vertical accuracy. Auming that the ranging error in the carrier phae i 0 cm, in order to have decimeter level horizontal accuracy, HDO need to be no larger than 5. In mot cae HDO a little a are common. Table III i an overview o the viibility and geometry condition in thee ite. A two-contellation (GS and Galileo) receiver, placed at either ite E or at the two junction, will alway, or almot, ee at leat ive atellite with an HDO better than 5. In the two treet urrounded by horter building (ite B and C), the minimum requirement or ignal availability and geometry i met or more than 80% o the day. Thi percentage drop to about 4% (ite B) and 7% (ite C) i we want to have HDO value better than. The obtruction given by high building, a in ite D, allow to have decent geometry condition or only le than 6% o the epoch. Fig. 4. Location o the urban ite that were conidered in the analyi. TABLE III. ERCENTAGE OF EOCHS FOR WHICH TWO-CONSTELLATION GNSS MEETS THE MINIMUM VISIBILITY AND GEOMETRY REQUIREMENTS. Site N 5 N 5 & HDO 5 A 00% 00% 98.04% B 97.4% 8.% 4.8% C 98.78% 8.54% 6.6% D 6.0% 5.87% 0% E 00% 00% 00% N 5 & HDO F 00% 98.4% 70.5%

5 Fig. 5. Building obtruction mak to atellite viibility or each ite. From thi preliminary tudy, it eem clear that high accuracy poitioning in urban environment i poible, but only in ome area. Traditional European citie with narrow treet and ix or more tory building packed together aren t good candidate or. can in theory be perormed in thoe urban area where building are relatively hort that provide good ignal availability and geometry. However, it i well known that an additional obtacle o urban environment or i ignal dicontinuity. Indeed, in cae the GNSS receiver loe track o the carrier phae, the poitioning ilter need to be reinitialized, meaning that urther ten o minute are required beore re-convergence. To tet the re-convergence time o in tranient ignal environment, a pedetrian carrying a multi-gnss receiver i imulated to be walking along the path in Fig. 6. The receiver i uppoed to be located or the irt hal hour o the imulation in the ite E, beore tarting to move. Thi i to allow the initial convergence o the ilter. Fig. 7 how the viibility or a given GNSS atellite. Only the epoch when the receiver i moving are conidered. Thereore, the irt thirty minute, when the receiver i tatic, are not included in the plot. Data gap due to building obtruction are oten viible. A a conequence, the carrier phae ambiguitie need to be etimated all over again; thi proce uually require ten o minute beore re-convergence. Fig. 8 and 9 how the HDO and the horizontal component o the poition error or the kinematic tet when GS L and L5 and Galileo E and E5a, linearly combined into the IF combination, are proceed in kinematic mode with the OINT otware. It i poible to ee how the horizontal error i at centimeter level when, at the beginning o the kinematic tet, the HDO i well below 5. minute ater the beginning o the imulation, a ew atellite go behind the building, they are out o ight and the HDO rie to more than 0. At thi point the error are a large a.6 m. Ater the receiver ha lot track o thee atellite, the horizontal olution doe not converge to centimeter level. However the error go below 50 cm ater our minute. Toward the end o the imulation, the HDO jump to more than 90, with the eat error increaing to about 4 m. Fig. 6. ath or the kinematic tet in urban environment.

6 From thi imulation tet, it can be concluded that twocontellation ha in theory the potential to preciely navigate ground vehicle in ome urban environment, however it i too enitive to ignal dicontinuity. Solution reconvergence to decimeter-centimeter level till repreent the main limitation to the ue o or high accuracy application in citie. Nonethele, GS plu Galileo eaily enable ub-meter level horizontal accuracy or mot o the imulation. Ater ignal lo, it only took a ew minute to have a horizontal accuracy o better than a meter. Fig. 7. Satellite availability during the kinematic tet. HDO Fig. 8. HDO or the kinematic tet. V. SMOOTHED IONOSHERIC CORRECTION Approache or improving (re-) convergence o include ambiguity ixing method [4-6] baed on the IF and wide-lane combination and algorithm in which the ionopheric delay are etimated in the tate vector [7, 8]. Ambiguity ixing method are immature and require extenion to monitoring network proceing. The perormance o ionopheric etimation depend on patial and temporal contraint ued or etimating the ionophere in the ilter and on careul handling o the dierential code biae (DCB). Thee technique yield perormance improvement, particularly in the re-convergence time [9]. However, the computational penalty aociated with the ilter ormulated with dual-requency meaurement and ionopheric tate become more pronounced with increaing number o atellite aociated with the ue o multiple contellation, which i deirable or in degraded ignal environment. A an alternative, [9] propoed a method to mitigate the ionophere and intended to reduce the re-convergence time o the olution, ater initial convergence ha been achieved. Thi i baed on uing a moothed ionophere correction propoed in [0] or local area dierential proceing. In thi new approach, the ionopheric delay inormation, computed uing the geometry-ree combination o two-requency peudorange, i moothed by a Hatch ilter beore being applied to the peudo-range, while the two-requency carrier phae are linearly combined in the traditional IF combination. I,j, j I I I I I, j N j j L L I,j I%,j I,j I,j, j N N N % % L L,j,j,j,j,j Fig. 9. Horizontal component o the poitioning error when L-L5 IF and E-E5a IF are proceed in kinematic mode or the imulated urban tet in Fig. 6. The green dahed line repreent the 0 centimetre limit. I

7 L I L L range. The next generation GNSS atellite will broadcat open ignal over three requencie. A linear combination between the three peudo-range, and can be written in a impliied orm a in (). In thi coniguration, divergence doe not repreent a problem [], ince the oppoite ign o the ionopheric term in the peudo-range and phae i taken into account. Thereore, a moothing window (N) even a large a the whole obervation period can be elected, reulting in excellent moothing with no divergence, a hown in Fig. 0. Auming the noie on peudo-range k to be white with a tandard deviation σ k and that there i no correlation between the peudo-range, the error in the moothed ionophere correction can be etimated a in I I,j I,j σ% σ σ j j σ I σ σ % j σ I σ σ L σ L,j I,j I I α α α α α α α α g α I ε Where g include the geometric range, clock and the tropophere term, I i the ionopheric delay on and ε i the noie on the combination, which ha a tandard deviation σ. σ α σ α σ α σ σ α α n α n We can deine an ionophere ampliication actor q and a noie ampliication actor n o the combination a q q α α α α α q α σ L I L σ L σ Once the Hatch ilter ha converged, ideally we have IF peudo-range with lower noie than the traditional one. Thereore, in tranient ignal environment aociated with urban canyon and in cae the ilter need to retart, we can obtain a quicker re-convergence thank to the lower noie on the ionophere corrected peudo-range. Indeed, provided that the ignal gap i not very large, the ionophere moothing ilter doen t need to be retarted rom the raw value. Since the change o rate o the ionopheric delay doen t change that much rom epoch to epoch, the old inormation about how the ionophere change with the time can be ued to propagate even in cae o cycle lip. Ionophere delay [m] n α α n α n C- raw C-C5 raw C- mooth C-C5 mooth G0 - :00 :00 :00 4:00 5:00 6:00 7:00 A. Low noie multi-requency combination The reult preented in [9] proved that the convergence time in would be horter i the noie on peudo-range could be reduced. The method introduced in the previou ection allow uer to be ree rom the contraint o IF obervable and, thereore, to look or multi-requency combination aimed to minimize the noie on the peudo- Fig. 0. Ionophere delay computed rom C- combination (raw blue dot, moothed yellow line) and C-C5 combination (raw orange dot, moothed purple line). GS RN 0 oberved rom BOGT on the 6th September 06. On that day, a minor olar torm made the ionophere particularly active.

8 In order to preerve g in the combination, the ollowing condition mut be atiied α α α Together (), (4), and (5) decribe a urace in the pace q- α -n. The combination that guarantee the minimum noie ampliication actor can be ued or poitioning purpoe. Table IV ummarize the aumed value or n i. Fig. how a color map o the noie ampliication actor aociated with the geometry preerving combination between GS L, L and L5. The noie or thi combination can be a little a 0.57 time the noie on L, while the correponding ionophere ampliication actor i.49. Thi noie ampliication i 7% maller than the one or L5, which i the leat noiy GS peudo-range, and 77% le than the noie on the IF combination between L and L5. Thereore, we could potentially have even ater re-convergence i we apply the moothed ionopheric correction to thi combination rather than to the uncombined L5 peudo-range. Similar concluion can be drawn by conidering Galileo ignal. Uing E, E5a and E5b we can obtain 5% le noie than E alone and 7% le noie than E5a or E5b alone. Triple requencie combination involving E5 don t bring a large improvement repect to uing E5 alone. Indeed maximum 6% le noie can be regitered when combining E, E5a and E5 repect to the E5 uncombined cae. Table V illutrate the minimum noie ampliication actor or each triple-requency combination and it ionophere ampliication actor. ~ i, I The noie aociated to the ionophere corrected multirequency peudo-range combination, σ, depend both on the error in the peudo-range and in the moothed correction. The latter i a large a meter-level beore converging to centimeter-level. For thi reaon, a proper weighting method, that conider the varying noie on the ionophere correction, need to be deined. The noie on the ionophere corrected peudo-range combination can be expreed a in (7), where σ repreent the covariance between the peudorange i and the moothed ionophere inormation. α α α qi~ σ α σ ασ ασ q σ% I α qσ α qσ α qσ,i%,i%,i% Auming that the ionophere delay i computed rom the geometry ree combination between and, the covariance σ ~ at epoch k are a in i, I TABLE IV. ASSUMED NOISE ON GS AND GALILEO SEUDO- RANGES AND THEIR IONOSHERIC DELAY RESECT TO L/ E. n i L..65 L E5a E5b E E6.5 Fig.. Geometry preerving urace in the pace q- α -n or GS L-L-L5 combination. σ ~ σ, I σ ~ σ, k, I σ ~ 0, I σ σ ~, I k σ σ ~, k, I k σ ~ 0, I To tet the beneit o the new approach to the reconvergence time, three hour o imulated GS and Galileo q

9 data were proceed with the OINT otware in kinematic mode. Ater 90 minute, the ilter wa orced to retart to imulate re-convergence. The perormance o the traditional L- L5 IF combination were compared with thoe o inglerequency L and L5, a well a the triple-requency peudorange combination, all corrected with the moothed ionophere delay coming rom the Hatch ilter. Fig. how the preciion (σ) o the horizontal component ater ilter retart. The new approach ha much ater re-convergence than the traditional baed on the IF combination, particularly when the low noie triple-requency combination i employed. Indeed, while the traditional method take about 5 minute to have an Eat error below 0 centimeter, uing the low noie combination, thi accuracy i achieved intantly. Good improvement are alo viible when applying the approach to the uncombined peudo-range. Similar concluion might be drawn conidering Galileo ignal (Fig. ). The E-E5 IF combination require more than 5 minute or North convergence, while uing E5 with the Hatch ilter we have the horizontal olution converged traight away. Alo, the new method wa teted with the kinematic imulation a in Section IV. Here, the GS triple-requency combined peudo-range and Galileo E5 peudo-range (both corrected with the moothed ionophere) are proceed in kinematic mode with the OINT otware. Fig. 4 illutrate the North and Eat poitioning error. Two minute ater the receiver lot track o mot o the atellite, the olution re-converged to centimeter-decimeter level and it took le than one minute to go below 50 cm. TABLE V. MINIMUM NOISE ACHIEVABLE THROUGH GS AND GALILEO TRILE-FREQUENCY SEUDO-RANGE COMBINATIONS AND THEIR IONOSHERIC DELAY RESECT TO L/ E. North error [m] Eat error [m] Combination n min q(n min) L-L-L E-E5a-E5b E-E5a-E E-E5b-E E-E5a-E E-E5b-E E-E5-E VI. CONCLUSIONS In thi paper, a comparion between GS-only, Galileoonly, and GS plu Galileo wa perormed. Reult baed on imulated open ky condition demontrated that Galileo perorm better than GS thank to an aumed lower E-E5a IF noie with repect to L-L5. Two-contellation enable ater (re-)convergence a compared to the ingle contellation cae. An analyi on GNSS ignal availability and continuity, and atellite geometry wa alo perormed to tudy the eaibility o in urban environment. reliminary reult, baed on imulation, howed that dual-contellation (GS plu Galileo) i poible in urban area with relatively hort building in which the atellite availability minimum requirement i met or mot o the time. However, ignal dicontinuity till repreent the major problem or traditional in urban environment, due to long re-convergence time. Finally, a new coniguration baed on triple-requency combination, intended to minimize the noie on the peudorange, and corrected by a moothed ionopheric delay wa propoed. Thi coniguration eem to provide ater reconvergence than the traditional with the IF combination. Fig.. Horizontal re-convergence comparion between traditional baed on GS L-L5 IF combination, ingle-requency ionophere corrected peudo-range, and triple-requency ionophere corrected peudo-range. North error [m] Eat error [m] Fig.. Horizontal re-convergence comparion between traditional baed on Galileo E-E5 IF combination and ingle-requency ionophere corrected peudo-range.

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