Ionospheric Delay Estimation In a Single Frequency Mode for Civil Aviation

Transcription

1 Ionospheric Delay Esimaion In a Single Frequency Mode or Civil Aviaion Chrisophe Ouzeau, ENAC/TéSA/DTI Chrisophe Macabiau, ENAC Benoî Rourier, DSNA-DTI Mikaël Mabilleau, EGIS AVIA auren Azoulai, Airbus Jacqueline evan, ENAC Frédéric Besse, ENAC BIOGRAPHIES Chrisophe OUZEAU graduaed in wih a maser in asronomy a he Observaory o Paris. He sared he same year his Ph.D. hesis on degraded modes resuling rom he muli consellaion use o GNSS, suppored by DTI and supervised by ENAC. Chrisophe MACABIAU graduaed as an elecronics engineer in 99 rom he ENAC in Toulouse, France. Since 994, he has been working on he applicaion o saellie navigaion echniques o civil aviaion. He received his PhD in 997 and has been in charge o he signal processing lab o he ENAC since. Benoî ROTURIER graduaed as a CNS sysems engineer rom Ecole Naionale de l Aviaion Civile (ENAC), Toulouse in 98 and obained a PhD in Elecronics rom Insiu Naional Polyechnique de Toulouse in 99. He was successively in charge o Insrumen anding Sysems a DGAC/STNA (Direcion Générale de l Aviaion Civile/Service Technique de la Navigaion Aérienne), hen o research aciviies on CNS sysems a ENAC. He is since head o GNSS Navigaion subdivision a DGAC/DTI (Direcion de la Technique e de l Innovaion, ormerly known as STNA) and is involved in he developmen o civil aviaion applicaions based on GPS/ABAS, EGNOS and GAIEO. He is also currenly involved in sandardizaion aciviies on uure muliconsellaion GNSS receivers wihin Eurocae WG6 and is he chairman o he echnical group o ICAO Navigaion Sysems Panel. Mikaël MABIEAU graduaed in 6 as an elecronics engineer rom he Ecole Naionale de l Aviaion Civile (ENAC) in Toulouse, France. He is currenly working or EGIS AVIA as a consulan engineer in he GNSS Navigaion domain. auren AZOUAI is Radionavigaion R&T eader wihin Navigaion Deparmen a Airbus Design Oice. He is involved in Research aciviies on Navigaion Archiecures or uure Airbus A/C, ocusing on he oreseen eended use o GNSS including Galileo and GBAS. He has been in charge o developmen and ceriicaion o he irs MMR wih GS uncion on Airbus A/C. He graduaed in 996 o Insiu Supérieur d'eleconique de Paris as an engineer specialized in auomaic sysems and joined irs an inerial navigaion sysems supplier beore joining Airbus. He has more han en years eperience in Navigaion domain. Jacqueline EVAN and Frédéric BESSE will graduae in 9 as elecronics engineers rom he Ecole Naionale de l Aviaion Civile (ENAC) in Toulouse, France. ABSTRACT Ionosphere is a dispersive medium ha can srongly aec GPS and GAIEO signals. I is he larges source o ranging error in GNSS. In uure GNSS civil aviaion cone, o remove his eec rom pseudoranges, i is necessary o use wo dieren requencies o obain "ionospheric-ree" measuremens, in a dual requency mode o operaion. A receiver can lose one or more requencies, or insance in he case o disurbance due o RFI leading o he use o only one requency o esimae ionospheric delay in a degraded mode o operaion. Thereore, i is el by he auhors as an imporan ask o ideniy and deermine he perormance o echniques ha would ry o susain muli-requency ionospheric delay esimaion perormance when a muli-consellaion receiver insalled in an aircra is losing one requency componen, during criical phases o ligh. This problem is ideniied or insance in [NATS, 3]. Those single requency echniques can be based on he ac ha he ionospheric delay encounered in GNSS may be esimaed by using he remaining code and phase measuremens hanks o he dispersive eec o he ionosphere on GNSS elecromagneic waves crossing his medium.

2 Indeed, ionosphere generaes a delay in code measuremens as well as an advance in carrier phase wih he same ampliude. Making he dierence beween he wo measuremens a he same requency, i is consequenly possible o esimae ionospheric delay insead o using "ionospheric-ree" pseudorange measuremens as in a dual requency mode. Neverheless, carrier phase ambiguiies mus be esimaed beore esimaing single requency ionospheric delay. Indeed, he dierence beween code and carrier phase measuremens provides wice he ionospheric delay plus phase ambiguiy, residual noise and mulipah. However, carrier phase measuremens are subjec o cycle slips ha would resul in a variaion o he phase ambiguiy and so in an addiive error on he ionospheric delay esimaion. Consequenly, cycle slips in carrier phase measuremens mus be moniored o comply wih civil aviaion requiremens o ensure inegriy o he sysem. This is done in [Ouzeau, 6], he availabiliy o such a echnique is also discussed and evaluaed in [Ouzeau, 7]. To esimae code minus carrier ionospheric delay, a Kalman iler is implemened, whose saes are boh ionospheric delay and carrier phase ambiguiies. This allows esimaing ionospheric delay and monioring cycle slips hanks o ambiguiies or each saellie in view [Ouzeau, 7]. During simulaions on acual measuremens, he iler behavior is sudied and he accuracy o he esimaion is discussed. This algorihm is epeced o bridge a gap beween one nominal mode o operaion and a degraded mode and hus o ry o mainain he level o perormance during he degraded mode as long as possible aer he degradaion occured. In paricular, in his paper, he accuracy o he echnique is sudied. The paricular case o APV phase o ligh requiremens is discussed and acual aircra measuremens are used o validae he model and o observe he iler behavior under acual condiions. The main goals o his paper are hen o describe he mehodology used o esimae ionospheric delay and in paricular he seings o he Kalman iler used, and o presen he accuracy o he ionospheric delay esimaion obained. The paper sars wih a descripion o he proposed algorihm and he seings o he Kalman iler. The accuracy o single and dual requency esimaions will be hen compared. INTRODUCTION Fuure GNSS combined receivers will have o be complian wih requiremens ha are deined by means o perormances speciied in erms o inegriy, coninuiy, availabiliy and accuracy or Civil Aviaion communiy. The archiecure o hose receivers is currenly deined rom invesigaions abou he advanages and risks linked o he muliple consellaion use o GNSS signals. GNSS componens (consellaions, requencies) combinaions are epeced o provide dieren levels o perormance compared wih he argeed phase o ligh requiremens. From he level o perormance ha can be reached by he proposed GNSS componens, operaional combinaions are classiied ino modes o operaion. Each mode is ideniied by aking ino accoun he ac he level o perormance is complian or no wih he requiremens or each phase o ligh. Thus, nominal, alernae and degraded modes characerize he ideniied associaions. Combinaions ha allow reaching he speciied requiremens linked o a phase o ligh are included in nominal and alernae modes. Nominal means are preerred o alernae ones or various reasons as eplained in [EUROCAE, 7]. I all hose nominal and alernae combinaions are unavailable, he use o remaining componens is ideniied as a degraded mode. Consequenly, o ake ull beneis o all available GNSS componens, WG 6 proposed a swiching archiecure beween nominal, alernae and degraded combinaions [Mabilleau, 7]. Ionosphere delay miigaion requires he use o a minimum o wo requencies ransmied by one saellie in view. In a civil aviaion nominal case, dual requency measuremens allow o direcly esimae ionospheric code delay rom pseudorange measuremens. Ionospheric delay can be obained via a linear combinaion o he pseudoranges a wo dieren requencies (deined by he inde and ): P = φ = P P φ φ Those new epressions are called «ionospheric-ree» combinaions. However, in case o radiorequency inererence (RFI) or insance, he loss o one requency may be a problem i one wans o keep he same perormance as in he nominal dual requency case and so we need o use alernae echniques o esimae he ionospheric delay.. IONO FREE MEASUREMENTS In he dual requency civil aviaion case, smoohed ionospheric-ree range measuremens are used. The ionospheric delay is esimaed and

3 correced hanks o he use o dual requency. Indeed, in a nominal mode, he pseudo range measuremens ha are available o he aircra receiver are he GPS, GPS, Galileo, Galileo Ea, Galileo code and phase measuremens. In order o ge rid o ionospheric delay in he measuremens, a hybrid ionosphericree pseudo range measuremen is derived rom he muli-requency measuremens available. Indeed, he ranging error due o ionosphere is proporional o he raio o he Toal Elecron Conen (TEC) encounered by he signal when propagaing hrough he ionosphere, divided by he squared carrier requency and muliplied by a acor 4.3 which depends upon he medium crossed by elecromagneic waves. Thereore, dual-requency measuremens can be used o sample he TEC, and ha esimaed TEC value can be used in urn o predic he ionospheric delay on one speciic requency. For uure civil aviaion GNSS receivers complying wih EUROCAE requiremens, dual requency measuremens will be combined ino a single composie measuremen called he ionospheric-ree measuremen, correced or ionospheric delay. Once elaboraed, hese wo GPS and Galileo ionospheric-ree measuremens are hen smoohed o reduce he inluence o noise and mulipah. Wih he availabiliy o muliple requencies, i is likely ha ionospheric delay will no be a major hrea or code and phase measuremens under nominal Galileo and modernized GPS condiions. Thus, mulipah remains as he main source o error or code measuremens under low inererence environmen. The code and carrier phase measuremens are smoohed o reduce he inluence o noise and mulipah, because carrier phase measuremens are less aeced by noise and mulipah han code pseudorange measuremens. The smoohing iler used is a Hach iler wih seconds ime consan [RTCA, ]. This smoohing sep allows reducing he measuremens sandard deviaion o he iler by an amoun evaluaed by [Hegary, 993]: raw smoohed α = Where α is he iler weighing uncion (uni less), equal o he sample inerval in seconds divided by he ime consan, being he raw pseudo range sigma and smoohed raw he smoohed one. From GPS, and rom Galileo E, wo disinc ionospheric-ree code measuremens are buil, ogeher wih wo ionospheric-ree phase measuremens: ϕ P ϕ P (GPS) ( k ) = P ( k ) + P ( k ) (Galileo) E ( k) = P ( k ) + P ( k) E E E E ( k) = ϕ ( k) + ( k) (GPS) ϕ E ( k) = ϕ ( k) + ( k) (Galileo) E ϕ E E In his applicaion:,.6 E = E,.4 E E E = =.76 E b E b E, and.6, and E.4 =.87 The obained code and carrier phase sandard deviaions are hen: = + E E E E = E + E E E E E. SINGE FREQUENCY MODE The objecive o his paper is o evaluae ionospheric delay measuremens in a single requency mode ideniied as alernae (NPA) or degraded (APV) mode o operaion. Dieren kinds o invesigaions can be processed. One way o use single requency measuremens is o use code and carrier phase measuremens o deduce ionospheric delay rom he dispersive behavior o he medium and he derived properies on elecromagneic waves. Anoher way o esimae ionosphere hanks o only one requency, is o use he broadcased parameers used by ionosphere models o calculae TEC. Anoher soluion can consis in using oher available GNSS componens such as SBAS as proposed in [Shau-Shiun Jan, 3]. Through a ionospheric hrea model echnique, he receiver can use a ionospheric grid ha can provide a bound or ionospheric delay sandard deviaion value. This esimaion depends upon he aircra posiion around he reerence geoids. However, his sysem is only regional. Firs, he used SBAS depends upon he area crossed by he aircra. Indeed, i may be locaed in WAAS or EGNOS coverage area. Secondly, he SBAS coverage is no suicien o proec he user everywhere on he Earh. This

4 sysem robusness agains ionosphere irregulariies generaed by sorms mus be sudied in deails. Indeed, magneic sorms are characerized by abnormal variaions in he magneic ield o he Earh. I causes ree elecrons disribuions o be disurbed. The use o a sorm deecor is consequenly required. Fourhly, he case when an aircra lies in border line he SBAS coverage has o be sudied in deails o know he availabiliy o he componen. In his sudy, he problem o esimaing ionospheric code delay in single requency mode is addressed wihou use o SBAS. Several cases can be encounered due o a loss o requency aer an RFI area crossing or insance. For eample, or a dual requency GPS C/A / receiver, he loss o or implies he use o he remaining or requency. Single requency siuaion can be classiied as alernae mode i an augmenaion is used or NPA as menioned in Table, [Eurocae, 7]. En roue o NPA Nominal Galileo So Galileo E + SBAS GPS + SBAS Alernae GPS single requency + SBAS Galileo single requency + SBAS Galileo single requency + So Combinaion o all available pseudoranges + RAIM APV I Galileo So Galileo E + SBAS GPS + SBAS GPS single requency + SBAS Galileo single requency + SBAS Degraded No inegriy inormaion Galileo single requency + So Combinaion o all available pseudoranges + RAIM Table : nominal, alernae and degraded combinaions ideniied by Eurocae WG 6. I appears ha Code Minus Carrier divergence echnique is he mos promising echnique ha may be used as menioned in [NATS, 3]. This echnique is described urher in his paper. The characerisics o his echnique are ha i doesn need an ionospheric model bu carrier phase ambiguiies have o be removed rom he esimaion o ge ionospheric delay. I a cycle slip occurs, phase measuremens are biased in consequence and esimaions mus be correced so as o provide a good esimaion o ionospheric code delay. In he ollowing pars, Code Minus Carrier divergence esimaions are calculaed hrough a Kalman iler. 3. CODE MINUS CARRIER DIVERGENCE TECHNIQUE AND KAMAN FITERING Aer a loss o several requencies leading o a single requency degraded mode, resuling rom a perurbaion like inererence, a receiver can use code and carrier phase pseudoranges made on only one requency. To esimae ionospheric code delay, he dierence beween code and carrier phase measuremens can be used. Indeed, his is modelled as ( requency): P φ = I N λ + w + v Where: P is he code pseudorange measuremen in meers φ is he phase measuremen in meers I is he ionospheric delay in meers N is he ineger ambiguiy λ is he carrier wavelengh in meers w is he code mulipah and noise error v is he phase mulipah and noise error Indeed he dierence beween code delay and phase advance provides us wo imes he shi caused by he ionosphere propagaion o he elecromagneic waves. The ionospheric delay can hereore be eraced rom his dierence assuming N is consan. The assumpion made is ha v and w only depend upon noise and mulipah i.e. ha clock errors a he receiver and saellie levels, ropospheric errors ge cancelled in he dierence compuaion. The ionospheric delay can be eraced rom ha dierence, provided he ambiguiy is known and consan, i.e. no cycle slip occurs. I a cycle slip occurs, he code carrier divergence mehod is no adaped o his siuaion as phase measuremens are biased dierenly. I is hereore necessary o be able o deermine eacly when his ype o phenomenon occurs, whaever amospheric condiions. Cycle slips may have various causes, or insance mulipah and ionospheric scinillaion, or receiver dynamics as menioned previously. The Code Minus Carrier divergence echnique is described in he ollowing.

5 The iler is iniialized hanks o dual requency ionospheric delay esimaion. Indeed, in realiy, he iler will no have o run beore loss o requency, only dual requency ionospheric delay esimaion mus be kep in memory, or each saellie in view. In case o loss o requency, his value is hen used o iniialize he saes o he Kalman iler. Each sae is hus iniialized as described in he ollowing: I is iniialized hanks o he ollowing ormula: Figure : Ampliude o ionospheric delay or a receiver locaed a ENAC, Toulouse, France, on 4/3/6. A cycle slip occurs or a low elevaion angle o abou degrees, which may correspond o a mulipah. Figure shows he esimaion o ionospheric code delay using single requency CMC esimaion on, we can noe ha a cycle slip occurs or a low elevaion angle. Those eamples are known o generae cycle slips, bu he ampliudes o he generaed rupures srongly vary rom case o case. I would be possible o deec high ampliude cycle slips bu i is really hard o deec small ones ha don allow esimaing correcly ionosphere code delay wih regards o civil aviaion requiremens in erms o inegriy, or criical phases o ligh. Cycle slips are sudied in deails in [Ouzeau, 6] and i appears he simples way o monior cycle slips is a mehod using Doppler predicions o phase measuremens described in he menioned reerence. A Kalman iler is used in order o evaluae he ionospheric code delay and o ollow he evoluion o ambiguiies o all saellies in view. The observaion and sae propagaion models are described in he ollowing. Each ambiguiy value is no epeced o vary along each corresponding saellie course rom he receiver poin o view. The acquisiion and loss o each saellie are aken ino accoun in he esimaion algorihm by updaing he saes according o he dieren saellies in view. When a cycle slip occurs, he ambiguiy on he corresponding phase measuremen varies abnormally. I Nb _ sa I k k = Obk = Nb _ sa Where: Nb _ sa is he number o saellies in view. The ionospheric delay can hen be deduced by summing zenihal delay and spaial gradiens ha are evaluaed in [esarqui, 997]. Ob is he obliquiy acor corresponding o k k he k h saellie in view I is he slan ionospheric delay esimaion coming rom he k h saellie in view Ambiguiy or each saellie in view is derived rom he dierence beween dual requency and single requency code minus carrier esimaions. The mean o his dierence over he irs measuremens is used as iniial value or each saellie in view. The obliquiy acor, which is he raio beween slan and zenihal elecronic conen, depends upon he ransmiing saellie elevaion. I is a uncion o elevaion o each considered saellie in view [RTCA, ]: R e Ob = cos( E) Re + h Where: R e is he Earh equaorial radius, h he aliude and E he elevaion angle. As a consequence, he sae vecor is deined in he ollowing, as in [Nisner, 99] or [esarqui, 997]: X = I N ) ( N n T Figure : obliquiy acor as a uncion o elevaion

6 Here, or a zenih posiion o a space vehicle, he obliquiy acor equals, is values are 3 or GPS mask angle ( degrees) and.7 or Galileo mask angle ( degrees). The Kalman iler provides real ime esimaion o he ionospheric delay hanks o measuremens rom all saellies in view and o ambiguiies or hese saellies or he same requency. The relaionship beween observaion vecor Y and sae vecor X a he insan is: Y = H X + V l l Where: Y is he observaion vecor, composed o he dierence beween code and carrier phase measuremens or all saellies in view. Noe ha he obliquiy acor is muliplied by wo in he algorihm or he consrucion o he mari H so as o obain wo imes he ionospheric code delay: or each saellie. V is he observaion noise H is he observaion mari ' Ob H = M ' ObNb _ sa l M l O The sae ransiion ormula is: X = F X + W + F is aken equal o he ideniy. M An eensive sudy o he error covariance values impac has already been perormed as menioned in [esarqui, 997], in his sudy, he same values are used and recalled in he ollowing. W is a noise process, i is here o model random lucuaions in linear predicion model imperecions. The covariance mari o W is Q: Q is in m². 36 Q = M 4 M O M 4 The covariance mari o he measuremen noise V is: R = 3. Ob * M O M Ob n Where is he measuremen inerval, 3. is a muliplicaive empirical erm used in [esarqui, 997]. The measuremen rae is one second. When he receiver loses rack o one saellie signal, is corresponding sae in he sae vecor o he Kalman iler is suppressed, is ambiguiy is no kep in memory. When a new saellie signal appears, he sae vecor is redeined aking ino accoun he corresponding ambiguiy, ha is o say, he ambiguiy is added in he sae vecor and he Kalman iler is reiniialized, he iniial sae and covariance are redeined aking ino accoun he new number o saellies, he previously deined mari. As proposed, he code minus carrier calculaion is based on raw measuremens and hus, he remaining noise and mulipah componens sill aec he measuremens. I is consequenly o ineres o discuss he sensibiliy o he iler o mulipah. During calculaion o raw code minus carrier, mulipah eecs on boh code and carrier phase measuremens are accumulaed as hese eecs are no he same on code and on carrier phase. However, as his sudy ocuses on APV phases o ligh, he mulipah are no srong and heir impac on he iler are no epeced o be signiican. In presence o high dynamics, cycle slip probabiliy increases as calculaed in [Ouzeau, 6]. Dynamics parameers such as he receiver acceleraion and jerk could be esimaed by he iler. Bu, he more he number o esimaed parameers, he more diicul he iler seing. As a consequence, a rade-o beween he iler robusness agains perurbaions and he accuracy o he iler esimaions mus be made. In his sudy, dynamics parameers are no esimaed. 4. CIVI AVIATION REQUIREMENTS AND AGORITHM PERFORMANCES In his sudy, he proposed algorihm accuracy is sudied. Indeed, he main goal o Kalman ilering code minus carrier measuremens is o provide an accurae esimaion o ionospheric delay while using only one GNSS requency. One mus provide an esimaion ha minimizes he residual ionospheric delay in order no o add a large bias on pseudoranges. The ocus here is made on APV phases o ligh as i is he irs approach phase o ligh aer NPA ha requires verical guidance and ha has resricive requiremens in erms o accuracy.

7 The zenih delay I in he Kalman saes, is iniialized by using a weighed mean o all saellies measuremens o ake ino accoun he elevaion o each saellie in view. Anoher poin ha mus be addressed is he ime o convergence o he iler. This ime o convergence can be observed on ambiguiies esimaions as hose ones are no epeced o vary and consequenly, a convergence es can be made o evaluae he iler esimaions availabiliy aer a loss o requency. Indeed, he ambiguiies esimaions are no noisy as he ionospheric delay. The las poin o menion is he algorihm compleiy. Indeed, in a nominal dual requency case, he esimaion o ionospheric delay is provided by simple combinaion o wo requency pseudoranges o obain ionospheric-ree measuremens. This esimaion provides suicien perormances in erms o accuracy. In case o single requency mode, his esimaion is made by using code minus carrier divergence echnique. Cycle slips are moniored hough algorihms proposed in [Ouzeau, 6]. The Kalman iler is used on he one hand o esimae ambiguiies rom all saellies in view (ha can also allow o monior cycle slips), and on he oher hand, o provide an esimaion o mean ionospheric delay rom all saellies measuremens. The compleiy o he algorihm is consequenly higher han he compleiy o nominal dual requency esimaions. The compleiy o he algorihm is dependen upon he number o saellies in view, indeed, he number o saes increases wih he number o saellies in view. In addiion, he number o saes depends upon he ac boh GPS and Galileo saellies measuremens are aken ino accoun or i one iler is used or each sandalone consellaion. Even i his echnique is no used all along aircra lighs, because o he compleiy, his algorihm can be implemened wihin receivers o coninue APV phase o lighs while he receiver only uses one requency during degraded mode o operaion. A discussion can be made abou he uiliy o such an algorihm because o he low probabiliy o alling ino single requency mode and a rade-o mus be made beween he compleiy (number o measuremens esimaed) and he uiliy o he algorihm. This discussion is no in he scope o his sudy as he probabiliy o losing one requency is diicul o assess. The proposed algorihm is esed over acual aircra measuremens, using dual requency measuremens rom a ew laps o an aircra lying around he Blagnac Airpor.. MEASUREMENTS CAMPAIGN Code and carrier phase measuremens were colleced during a ligh around Toulouse-Blagnac airpor (France), which pah is drawn in he ollowing Figure 3 and Figure 4. Figure 3: aircra pah, daa colleced rom Airbus campaign, zoom on he Blagnac Airpor (Toulouse, France), Airbus, all righs reserved. Figure 4: aircra pah, daa colleced rom Airbus campaign around Blagnac Airpor (Toulouse, France), Airbus, all righs reserved. Dual requency measuremens were colleced during hose lighs around Blagnac airpor (France), on boh GPS C/A and. The objecives o processing such measuremens are muliple. Firs, i is convenien o es he algorihm on real measuremens during aircra ligh o eperience aircra approaches wih acual condiions. Indeed, aircra dynamics and mulipahs allow esing he iler robusness agains hose ypes o inererences during APV and even during oher phases o ligh. Secondly, even i he goal is o esimae single requency ionospheric delay, a dual requency basis is necessary o compare he perormances o he esimaion algorihm. As a consequence, dual requency measuremens are needed. Neverheless, hose measuremens are /. The dual requency measuremens in nominal modes will be / or GPS and E/Ea or E/ or Galileo. Since is

8 sill no available, his sudy will unorunaely be based on hose dual requency measuremens. Pegasus soware (Euroconrol) is used o process he colleced daa beore using he algorihm presened under Malab environmen. Figure 7: GPS C/A code measuremens during recording or all saellies in view Figure : Euroconrol Pegasus Soware Dual and single requency ionospheric delays are calculaed or all saellies in view during he measuremen campaign. The scenario presened here is he loss o GPS leading o single GPS C/A requency mode. The Airbus collec was made during h, he measuremens available are provided each. second. In he ollowing, he presened igures are all as a uncion o he number o samples, samples are available each second. The oal number o ime samples is 4. Noe ha he number o saellies in view varies along ime as i is presened in ne paragraph. The minimum number o saellies in view equals 7 or shor periods o ime ideniied in igure 6. This graph allows ideniying he onse or he loss o saellies rom he receiver poin o view. Figure 8: GPS code measuremens during recording or all saellies in view Figure 9: GPS C/A carrier phase measuremens during recording or all saellies in view The abrup changes ha appear in code and phase measuremens show clock shis (regular rupures) or losses o saellies (i is correlaed wih he number o available saellies and can be observed or boh requencies and on code and carrier phase measuremens). When a saellie is los, is corresponding sae is no kep in memory. When a new saellie appears, is corresponding sae is iniialized. 6. TEST RESUTS Figure 6: saellies in view as a uncion o ime samples To know precisely he perormance o he esimaion algorihm, i is necessary o ideniy he insans o loss or recovery o saellies, he ime o sar and end o ligh.

9 Figure : Ionospheric code delay a he zenih o he aircra hrough Kalman ilering (in red) versus mean dual requency esimaion (in green). In igure, he mean dual requency esimaion o zenih ionospheric code delay or all saellies in view is ploed in green. The red curve represens he Kalman esimaion as described in he previous secion. This esimaion concerns he zenih ionospheric code delay or all saellies in view and is iniiaed wih dual requency measuremens. Each jump in he esimaion corresponds o a cycle slip observed. Indeed, derivaives o he carrier phase measuremens show we are dealing wih cycle slips as i is shown in igure. Cycle slips may have been deeced hanks o Doppler-prediced phase measuremens as proposed in [Ouzeau, 6], bu Doppler values were no available in he daa se used. measuremens. Those momens are calculaed over he measuremens no aeced by cycle slips. Recall ha hose momens concern he accuracy o he verical ionospheric code delay esimaed or a saellie locaed a he zenih o he aircra. Slan ionospheric code delay can be esimaed by muliplying hose values by he obliquiy o he corresponding saellie in view, aking ino accoun is elevaion. Thus, o obain he same saisics or a saellie near he horizon, a he limi o he mask angles deined in [Eurocae, 7], i is necessary o muliply he obained mean and STD values by he corresponding obliquiy values. As he elevaion mask angles correspond o degrees or GPS saellies and degrees or Galileo saellies, he weighing obliquiy value is 3 or a GPS saellie and.7 or a Galileo saellie near he horizon. Those values are provided in he ollowing able as a uncion o he number o samples esed. Dual req Sing req N sample m m Zenih Mask Mean STD Mean STD. m.3 m GPS: 8.77m Galileo:.89m GPS: 9.6m Galileo: 6.4m GPS: 6.33m Galileo:.7m GPS:.93m Galileo:.84m Table : Mean and STD o dual and single requency esimaions o mean ionospheric code delay a he zenih o he aircra. As i can be seen on igure, here is a ime o convergence ha mus be aken ino accoun and compared o ime o aler or he corresponding phase o ligh. This ime o convergence can be evaluaed by looking a he convergence o he esimaed ambiguiies as hose ones do no vary when no cycle slip occurs. Figure : irs order derivaives o carrier phase measuremens on he ideniied cycle-slip biased measuremens The problem o cycle slip deecion is no addressed here, a discussion abou he impac o his phenomenon and cycle slip deecion algorihm are proposed in [Ouzeau, 6]. The accuracy o he iler is evaluaed by comparing he mean and he sandard deviaions (STD) o dual and single requency esimaions a he zenih o he receiver, over all he available Figure : Ambiguiies esimaion hrough Kalman ilering. Figure shows he esimaion o he ambiguiies or he saellies in view all along he

10 collec. I can be seen ha hose ambiguiies do no vary wih large ampliudes. Neverheless, in case o cycle slip, wih a zoom over he impaced ambiguiies, some irregulariies can be observed. Each ime a cycle slip occurs, he corresponding ambiguiies esimaions presen peaks. The iler esimaions hen converge aer his ype o irregulariy. The higher he cycle slip ampliude, he higher he irregulariy in he ambiguiy esimaion. The ime o convergence o he iler or he corresponding impaced sae depends upon his cycle slip ampliude. As he measuremens are colleced onboard a lying aircra, due o is high dynamics, he probabiliy o cycle slip occurrence increases as i is described in [Ouzeau, 6]. Thus, i cycle slips are deeced, inegriy is mainained as menioned in [Ouzeau, 6]. Bu in his sudy, only a ew cycle slips were eperienced. Furher invesigaions can esimae he mean ime o convergence o he iler over a large number o cycle slips, wih varying ampliudes and he obained ime o convergence will have o be evaluaed as a uncion o he cycle slip ampliudes during inensive sudies. Bu his implies a very large number o samples and a very large ime o simulaion. The obained ime o convergence saisics mus be hen compared o TTA. The archiecure o a complee algorihm including ionospheric code delay esimaion and cycle slip deecion mus be buil or single requency mode. ACKNOWEDGMENTS The auhors would like o acknowledge Airbus or providing onboard measuremens o es he proposed algorihm. REFERENCES Figure 3: Kalman iler esimaion o ambiguiy or saellie 7 [EUROCAE, 7] Inerim Minimum Operaional Perormance Speciicaion For Aiborne Galileo Saellie Receiving Equipmen, Whie Paper, EUROCAE, 7. [Hegary, 993] Hegary Chrisopher J., "An Assessmen o Alernaive Mehods o Miigaing Ionospheric Errors or WADGPS Users", MITRE Technical Repor MTR93W, The MITRE Corporaion, Mcean, Virginia, 993. Figure 4: Disribuion o Kalman iler esimaion o ambiguiy or saellie 7 7. CONCUSION The perormance o ionospheric code delay esimaion has been esimaed in single requency mode or civil aviaion applicaion. Three parameers mus be aken ino accoun: he mean and he sandard deviaion o he ionospheric code delay esimaion and he Kalman iler ime o convergence. I appears rom his processing o he h daa se ha he esimaion provided by he Kalman iler can allow keeping he accuracy o dual requency esimaions aer a loss o requency, when no cycle slip occurs, because he accuracy o he esimaed ionospheric delay is beer han he accuracy o he dual requency ionospheric delay esimaion. [Holmes, 99] Coheren Spread Specrum Sysems, Rober E.Krieger Publishing Company, Malabar, Florida, Holmes, 99. [Kalman, 993] Kalman Filering, Theory and Pracice, Mohinder S.Grewal, Angus P. Andrews, Prenice Hall Inormaion and Sysem Sciences Series, Thomas Kailah, Series Edior. [Kaplan, 996] Undersanding GPS, Principles And Applicaions, Ellio D.Kaplan, Arech House, Boson, ondon, 996. [esarqui, 99] Deerminaion o he Ionosphere Error Using Only Frequency GPS Receiver, auren esarqui, Norber Suard, Jean- uc Issler, CNES, 99. [Mabilleau, 7] Combined GAIEO-GPS receiver based on a swiching logic presened by Paul Flamen, prepared by Mikaël Mabilleau (DTI), Paul Nisner (NATS), auren Azoulai (Airbus), Jean Pierre Arenhens (Thales), Gerard Alcoue

11 (Thales), Chrisophe Ouzeau (ENAC), Navigaion Sysem Panel, New Delhi, India, March, 7. [NATS, 3] Susainable Mobiliy and Inermodaliy Promoing Compeiive and Susainable Growh, Mainaining Dual Frequency Navigaion Perormance in he Presence o Inererence, 3. [Nisner, 99] GPS Ionosphere Deerminaion Using Only, Paul Nisner, UK Naional Air Traic Services, Mike Trehewey, Signal Compuing d, ION 99. [Ouzeau, 6] Ionospheric Code Delay Esimaion In Case O Radio Frequency Inererence For Civil Aviaion, Chrisophe Ouzeau, Frederic Baside, Chrisophe Macabiau, Benoî Rourier, Proceedings o he Insiue O Navigaion, Global Navigaion Saellie Sysem, For Worh, Teas, Sepember, 6. [Ouzeau, 7] Compliance O Single Frequency Ionospheric Delay Esimaion And Cycle Slip Deecion Wih Civil Aviaion Requiremens, Chrisophe Ouzeau, Chrisophe Macabiau, Anne-Chrisine Escher, Benoî Rourier, Proceedings o he Insiue O Navigaion, Naional Technical Meeing, San Diego, Caliornia, January, 7. [RTCA, ] Minimum Operaional Perormance Sandards or Global Posiioning Sysem/Wide Area Augmenaion Sysem Airborne Equipmen, RTCA, DO 9c, prepared by SC 8, 8 November. [Shau-Shiun Jan, 3] Aircra anding Using a Modernized Global Posiioning Sysem And The Wide Area Augmenaion Sysem, Shau-Shiun Jan, May 3.