Receiver Autonomous Integrity Monitoring of GNSS Signals for Electronic Toll Collection

Transcription

1 Recever Autonomous Integrty Montorng of GNSS Sgnals for Electronc Toll Collecton Danel Salós, Anaïs Martneau, Chrstophe Macabau, Bernard Bonhoure, Damen Kubrak To cte ths verson: Danel Salós, Anaïs Martneau, Chrstophe Macabau, Bernard Bonhoure, Damen Kubrak Recever Autonomous Integrty Montorng of GNSS Sgnals for Electronc Toll Collecton IEEE Transactons on Intellgent Transportaton Systems, IEEE, 014, 15 (1), pp <101109/TITS > <hal > HAL Id: hal Submtted on 19 Dec 015 HAL s a mult-dscplnary open access archve for the depost and dssemnaton of scentfc research documents, whether they are publshed or not The documents may come from teachng and research nsttutons n France or abroad, or from publc or prvate research centers L archve ouverte plurdscplnare HAL, est destnée au dépôt et à la dffuson de documents scentfques de nveau recherche, publés ou non, émanant des établssements d ensegnement et de recherche franças ou étrangers, des laboratores publcs ou prvés

2 1 Recever Autonomous Integrty Montorng of GNSS sgnals for Electronc Toll Collecton Danel Salós, Anaïs Martneau, Chrstophe Macabau, Bernard Bonhoure, and Damen Kubrak Abstract Varous Road User Chargng (RUC) mechansms are used to control the traffc and ts resultng polluton, as well as revenue sources for renvestment n the road nfrastructure Among them, Electronc Toll Collecton (ETC) systems based on user postons estmated wth Global Navgaton Satellte Systems (GNSS) are partcularly attractve due to ther flexblty and reduced roadsde nfrastructure n comparson to other systems lke tollbooths Because GNSS postonng may be perturbed by dfferent errors and falures, ETC systems, as lablty crtcal applcatons, should montor the ntegrty of GNSS sgnals n order to lmt the use of faulty postons and the consequent chargng errors The ntegrty montorng systems have been orgnally desgned for cvl avaton, so they need to be adapted to the ETC requrements Ths paper studes the use of Recever Autonomous Integrty Montorng (RAIM), whch are algorthms run wthn the GNSS recever, and therefore easer to tune to ETC needs than other systems based on external nformaton The Weghted Least Squares Resduals (WLSR) RAIM used n cvl avaton s analyzed, and an algorthm modfcaton for ETC s proposed Smulatons demonstrate that the proposed RAIM algorthm has a superor level of avalablty over cvl avaton based RAIM procedures, partcularly n urban envronments Index Terms Electronc Toll Collecton (ETC), Global Navgaton Satellte Systems (GNSS), Recever Autonomous Integrty Montorng (RAIM), urban envronment I I INTRODUCTION NTEGRITY of Global Navgaton Satellte Systems (GNSS) s defned as a measure of the trust that can be placed n the correctness of the nformaton suppled by the navgaton system [1] The concept of GNSS ntegrty was orgnally developed n the cvl avaton framework as part of the Internatonal Cvl Avaton Organzaton (ICAO) requrements for usng GNSS n the Communcatons, Navgaton and Survellance / Ar Traffc Management (CNS/ATM) system In partcular, cvl avaton standards specfy a set of mnmum accuracy, avalablty, ntegrty and contnuty performance on the GNSS Sgnal-n-Space (SIS) for each operaton and phase of flght [] Nevertheless, Manuscrpt receved December 19, 01 Ths work was supported n part by the Centre Natonal d'etudes Spatales (CNES) and Thales Alena Space D Salós, A Martneau, and C Macabau are wth the Ecole Natonale de l'avaton Cvle (ENAC), Toulouse, France (e-mal: salos, martneau, rechercheenacfr) B Bonhoure s wth the CNES, Toulouse, France D Kubrak s wth Thales Alena Space, Toulouse, France standalone GPS cannot meet the strngent cvl avaton requrements, and, specfcally, the GPS SIS ntegrty standard [3] does not assure ntegrty as specfed by the ICAO For ths reason, varous augmentaton systems have been developed to allow the use of GPS wthn the ICAO requrements These systems are classfed accordng to ther nfrastructure nto Ground, Satellte, and Arcraft Based Augmentaton Systems (GBAS, SBAS and ABAS) The need for relable satellte navgaton wth ntegrty montorng s not lmted to the cvl avaton feld Two types of applcatons need GNSS ntegrty: Safety-of-Lfe (SoL) applcatons, n whch undetected navgaton errors may endanger lfe, and lablty crtcal applcatons, n whch postonng errors may have negatve legal or economc consequences [4] A number of ntegrty-drven postonng applcatons have vehcular or pedestran users and take place n urban and rural envronments [5] A few examples of these applcatons are Electronc Toll Collecton (ETC), tran control, dangerous or valuable goods transport survey and emergency calls Each applcaton has ts own ntegrty constrants and needs an ntegrty montorng technque adapted to ts specfcatons Ths paper focuses on Electronc Toll Collecton (ETC) systems n urban and rural envronments based on GNSS postonng GNSS-based ETC schemes are partcularly nterestng because they are free-flow (pay-as-you-drve), hghly flexble systems wth a reduced quantty of roadsde nfrastructure Moreover, satellte navgaton s, together wth 58 GHz mcrowave and GSM-GPRS communcaton systems, one of the technologes the European Unon recommends for the European Electronc Toll Servce (EETS) [6] As of 01, toll systems for freght transport usng GPS as prmary postonng technology are already operatonal n German and Slovak hghways and natonal roads [7] [8] GNSS-based ETC systems are lablty crtcal applcatons because excessve and uncontrolled postonng errors may lead to ncorrect toll nvoces The act of levyng a toll lower than t should be s denoted underchargng and mples a loss of revenue, whereas the act of levyng a toll hgher than t should s known as overchargng and may orgnate user clams Thus, ETC specfcatons should bound the maxmum acceptable rate of underchargng and overchargng errors n order to assure the qualty of the servce to both users and the toll operator For ths reason, GNSS ntegrty montorng s a key element of ETC systems whch assures that postonng

3 errors are below the specfed lmts, detectng unacceptably large errors Dfferent solutons have been studed to montor the navgaton ntegrty n urban envronments, often hybrdzng GNSS wth dead-reckonng and map-matchng technques [9][10][11] The am of ths paper s to present an ntegrty montorng algorthm that only uses GNSS measurements, consstng of a snapshot RAIM talored to the needs of ETC n urban envronments Ths approach reduces the complexty of the on-board equpment and avods memory problems due to error propagaton n recursve loops, as well as the thorough characterzaton of errors due to non-gnss components requred by ntegrty mechansms The Least Squares Resduals (LSR) RAIM has been chosen because t s well known n cvl avaton and s commonly taken as baselne algorthm [1] A dgtal map s used to charge the user, but not n the ntegrty montorng process The paper s organzed as follows Frst, the GNSS-based ETC scheme wth ntegrty montorng s explaned n secton II Afterwards, the WLSR RAIM used n cvl avaton and a modfed verson adapted to the ETC needs n urban envronments are analyzed n Sectons III and IV The characterstcs of both RAIM algorthms are compared n secton V, and, fnally, secton VI presents ther performance calculated va smulatons II GNSS-BASED ELECTRONIC TOLL COLLECTION SYSTEMS The dscrete road lnks chargng toll scheme defned n the ISO standard [13] s studed The geo-fencng approach s followed, n whch the tolled road network s splt nto segments defned by vrtual permeters The areas wthn the permeters are denoted geo-objects and consttute the basc chargng unts, that s, users are charged the prce assocated to a geo-object whenever they are detected nsde t Each geoobject's fee s set ndvdually and can be desgned accordng to dfferent factors lke the user category, the tme of the day or the traffc state Moreover, dstance-based charge s possble when geo-objects are defned as road portons between ntersectons, wth only one entrance and one ext Geo-fencng s an approprate approach for GNSS-based ETC applcatons that allows hghly flexble systems wth a low number of roadsde nfrastructures The man task of the ETC system s to decde whether a user has drven through a road segment or not, and charge hm f he has Ths decson, known as geo-object recognton, can be taken as a functon of the number of user postons lyng nsde the geo-object boundares In order to bound the maxmum rate of erroneous geo-object recogntons (e erroneously charged segments), only postons declared vald by the ntegrty montorng system are used Moreover, only ndependent postons are taken to elmnate the effects of the postonng error temporal correlaton In ths context, two poston estmates are ndependent when they produce ndependent ntegrty montorng outputs The correlaton tme depends on the GNSS recever type as well as other constrants wthn the local envronment Summarzng, the proposed road segment chargng algorthm s: charge segment N N (1) vald INSIDE where N vald INSIDE s the number of vald and ndependent postons nsde the geo-object, and N Th s the geo-object recognton threshold The ntegrty montorng systems have been orgnally desgned to meet the cvl avaton requrements, so they need to be adapted to the ETC specfcatons From the varous possble ntegrty montorng systems, ths work studes the Recever Autonomous Integrty Montorng (RAIM), whch are algorthms run wthn the GNSS recever that montor ntegrty thanks to redundant pseudorange measurements Snce RAIM algorthms, as opposed to GBAS or SBAS, do not rely on external nformaton, they can be easly adapted to the ETC requrements and to the mult-frequency, multconstellaton case Ths paper consders the use of SBAS correctons, but not of ts ntegrty servce because t has been desgned manly to assure the cvl avaton requrements Only the ntegrty of the horzontal postonng s requred to be montored for ETC applcaton For each estmated poston, RAIM provdes a Horzontal Protecton Level (HPL), defned as a crcular area centered at the user real poston that s assured to contan the estmated poston wth a probablty equal to or hgher than (1- ), where the maxmum allowed probablty of mssed detecton s a desgn parameter The Horzontal Alert Lmt (HAL) s the maxmum allowed HPL and depends on the road network topography, and can be set as the half of the dstance between roads [14] A Introducton III WLSR RAIM FOR CIVIL AVIATION The Least Squares Resduals (LSR) RAIM [15], together wth the soluton separaton method [16], s one of the RAIM algorthms most frequently used n cvl avaton Moreover, the party matrx RAIM [17] and the range comparson technque [18] are equvalent to the LSR RAIM [19] The desgn of the LSR RAIM assumes that pseudorange nomnal errors are modeled as ndependent zero-mean Gaussan dstrbutons wth the same varance Ths was an acceptable condton when pseudorange errors were domnated by the Selectve Avalablty (SA), but at present pseudorange errors are better descrbed as ndependent zero-mean Gaussan dstrbutons wth varance dependent upon several factors lke the sgnal modulaton or the satellte elevaton angle In ths case, the Weghted Least Squares Resduals (WLSR) RAIM s used [0] B Algorthm Desgn The WLSR RAIM consders the followng lnear pseurorange measurement model: Th

4 3 Y H X E () where ΔY [N s x 1] s the lnearzed measured pseudorange vector, H [N s x N u ] s the observaton matrx, ΔX [N u x 1] s the lnearzed navgaton state vector, and E [N s x 1] s the pseudorange error vector N s s the number of pseudoranges, and N u s the number of unknowns n ΔX Two possble pseudorange error scenaros are assumed, namely fault-free and faulty In the fault-free case, pseudorange measurements are dsturbed only by nomnal errors, modeled as zero-mean ndependent Gaussan dstrbutons wth covarance matrx Σ In the faulty case, apart from nomnal errors, there s one based pseudorange measurement: E B (3) where ε [N s x 1] s the nomnal error vector and B [N s x 1] s the bas vector: b T B 0,,,0,, 0 (4) wth b =0 n the fault-free case The probablty of smultaneous faulty pseudoranges s assumed to be neglgble The WLSR RAIM montors the ntegrty of the navgaton state vector calculated wth the Weghted Least Squares Estmator (WLSE): X ˆ A Y (5) T T H H H A (6) The am of RAIM algorthms s to detect postonng errors exceedng the alert lmt wthn the requred probabltes of mssed and false alarm Snce postonng errors are not drectly measurable, the WLSR RAIM calculates, thanks to the resdual vector (R), a measurable scalar test statstc (t) that provdes nformaton about pseudorange measurement errors The test statstc s computed as the Weghted Sum of Squared Errors (WSSE): T 1 T 1 t WSSE R R Y I BY (7) R Y HX I BY I BE T T H H H (8) B H (9) The test statstc calculated n (7) follows a ch-squared dstrbuton n the fault free case, and a non-central chsquared one n the faulty case: t k f E ~ N 0, k, f E ~ N B, ~ (10) In both fault-free and faulty scenaros the test statstc's number of degrees of freedom (k) s the number of redundant pseudorange measurements: k N s N u (11) The ch-squared non-centralty parameter (λ) ntroduced by a faulty measurement, whch depends on the bas magntude and on the nomnal errors, s: I B (1) b where σ s the nomnal error varance of the based pseudorange, and ( ) s the th element of the th row Because we are nterested n the protecton aganst postonng falures, but the WLSR RAIM detects faults va the test statstc, the relatonshp between the horzontal postonng error e H and t needs to be nvestgated In the faulty case, there s a lnear relatonshp between the pseudorange bas projecton n the horzontal error doman ( b H ) and the square root of the test statstc λ, characterzed by the slope parameter: slope b slope (13) H A N, A E, I B (14) where A N, and A E, are the th element of the rows of matrx A n (6) correspondng to the state vector horzontal poston components The slope, whch vares from one satellte to another, s an ndcator of the relatonshp between the effect of a pseudorange bas n the test statstc and n the postonng error A pseudorange bas leadng to a gven noncentralty parameter λ wll have the hghest mpact on the postonng error when t appears n the satellte wth the hghest slope The statstc components of the test statstc and the navgaton state estmaton errors, caused by nomnal errors, are uncorrelated [1], e cov(t,e)=0 Therefore, the relatonshp between t and e H at a gven epoch can be descrbed as a D random varable wth the followng PDF: PDF t e PDF t PDF, (15) H e H Once the test statstc and ts relatonshp wth the poston error have been defned, the remanng RAIM parameters can be derved These are the fault detecton threshold (Th), the mnmum detectable non-centralty parameter (λ det ) and the Horzontal Protecton Level (HPL) Fg 1 depcts the dfferent RAIM desgn process steps n the t 1/ aganst e H plane, n a smlar way as n [] The bdmensonal PDF has been represented by an equprobable lne for clarty reasons Desgn parameters (, P FA ) The WLSR RAIM s desgned to meet a maxmum allowed probablty of mssed detecton ( ) and of false detecton (P FD ) If the RAIM only has fault detecton and not excluson functons, any mssed or false detecton results n a mssed or false alarm, and the maxmum allowed probablty of mssed alarm (P MA ) and false alarm (P FA ) are equal to and P FD respectvely A RAIM algorthm wth only a fault detecton functon s consdered, so the desgn parameters used throughout ths work are and P FA

5 4 e H c) HPL Fg 1 WLSR RAIM desgn process: a) Fault detecton threshold (Th) b) Mnmum detectable non-centralty parameter (λ det) c) Horzontal Protecton Level (HPL = slope MAX λ det 1/ ) Falure Detecton Threshold (Th) The WLSR RAIM detects a falure whenever the test statstc exceeds a threshold (Th) The threshold s chosen n order to assure the fault detecton probablty n fault-free condtons, e one mnus the cumulated densty functon of a ch-squared functon evaluated at the threshold value: P p D PDF (fault-free case) P FA t Th t 1 CDF Th ~ FA k k slope MAX D PDF (faulty case) a) Th 1/ b) λ det 1/ t 1/ (16) Therefore, Th s a functon of P FA and k, whch n turn depends on the number of pseudoranges N s algorthm does not detect ths pseudorange bas and that the postonng error s larger than the HPL s approxmately / The probablty of mssed detecton decreases f the based pseudorange s n other satellte wth a lower slope Larger bases lead to hgher λ det, so they are always detected wth a probablty below Smaller bas magntudes have smaller λ det, whch sets the probablty of not detecton over Fortunately, they also lead to lower postonng errors that offset the hgher non-detecton probablty, resultng n a probablty of mssed detecton of errors exceedng the HPL of less than Nevertheless, n some cases, especally wth low slopes, ths may not hold [] C Algorthm Implementaton at the GNSS Recever The algorthm run wthn the recever conssts of two modules, e the RAIM avalablty check and the Fault Detecton (FD) (Fg ) The FD could be replaced by a Fault Detecton and Excluson (FDE) module slope RAIM Avalablty Module MAX Maxmum Slope AN, A max 1 NS I B E, Horzontal Protecton Level slope HPL MAX det k Mnmum Detectable Non-Centralty Parameter (λ det ) In the faulty case, the test statstc λ ncreases wth the bas sze as n (1) The mnmum detectable non-centralty parameter (λ det ) s the λ that results n a mssed detecton rate equal to for the threshold calculated n (16): HPL HAL? Fault Detecton Module Unavalable RAIM x P p t Th t ~ CDF Th MD k, det k, det (17) Test Statstc 1 t Y I BY Therefore, λ det s a functon of, k (whch depends on N s ) and Th (whch also depends on P FA ) Horzontal Protecton Level (HPL) The HPL s calculated as the projecton n the poston doman of the pseudorange bas that would generate a noncentralty parameter equal to λ det n the satellte wth the maxmum slope (slope MAX ): HPL slope (18) MAX det The ratonale of the HPL calculaton of (18) s the followng The postonng error e H s dstrbuted approxmately centered around b H, f the bas s suffcently large Let us consder a pseudorange bas n the maxmumslope satellte wth a magntude such that the test statstc's non-centralty s equal to λ det The probablty that the RAIM t Thk? Fault Detected No Fault Detected (Vald Poston) Fg WLSR RAIM algorthm wth Fault Detecton capabltes run wthn the GNSS recever Frst, at each epoch, the slope of each pseudorange measurement s calculated thanks to the observaton matrx and the nomnal error covarance matrx The HPL s computed afterwards wth the maxmum slope and the correspondng ch-squared non-centralty parameter If the HPL exceeds the HAL, RAIM s not avalable because t cannot montor ntegrty wth the requred HAL, and P FA x

6 5 In ths case, the ntegrty cannot be montored, so the estmated poston s not vald for ts use n ETC If the HPL s equal to or lower than the HAL, the RAIM s avalable and proceeds to check whether the estmated poston s faulty or not The test statstc s computed wth the lnearzed pseudorange measurements, the observaton matrx and the nomnal error covarance matrx If the test s hgher than the correspondng detecton threshold, a fault s detected and the poston cannot be used n ETC When the test s lower than the threshold, the poston s vald for ETC The values of λ det and Th depend on, P FA and the number of redundant range measurements k They do not depend on current measurements, so they can be computed offlne and stored n the recever as look-up tables The WLSR RAIM can optonally perform FDE n order to reduce servce nterruptons Ths module tres to elmnate the based pseudorange measurement whenever a fault s detected If after the fault excluson HPL HAL and t Th, the poston estmated wthout the based pseudorange s vald for ETC A possble fault excluson technque creates N subgroups of N-1 range measurements each; assumng that there s only one faulty pseudorange, the FD module wll detect a fault n each subgroup except n the one excludng the faulty measurement The FDE module needs at least two redundant range measurements RAIM descrbed n ths secton s to maxmze the number of vald postons n the fault-free scenaro The modfed RAIM s desgned to assure a constant n order to set a known maxmum probablty that a faulty poston nsde the geo-object s declared vald when the user s actually outsde t As opposed to cvl avaton, ETC systems do not requre contnuty, so ther RAIM algorthms do not necessarly need to assure a maxmum allowed P FA Gven constant values of, slope MAX and k, the HPL can be decreased by ncreasng the P FA (Fg 3): e H HPL b HPL a PFA, b PFA, a HPL b HPL a (19) slope MAX D PDF (faulty case) D PDF (faulty case) P FA,a IV MODIFIED WLSR RAIM FOR ELECTRONIC TOLL COLLECTION A Motvaton and Ratonale of the Modfed WLSR RAIM User/satellte geometry n reduced satellte vsblty scenaros lke urban envronments s lkely to be much worse than n the open-ar scenaros commonly found n cvl avaton Ths fact generally ncreases the Dluton Of Precson (DOP), whch degrades the postonng accuracy Another consequence of bad user/satellte geometres s the augmentaton of the maxmum slope, whch n turn ncreases the HPL calculated as n (18), and consequently degrades the WLSR RAIM avalablty (whch also depends on the HAL) Therefore, a GNSS-based ETC system that montors ntegrty wth the WLSR RAIM n challengng envronments wth reduced vsblty s lkely to have a low number of vald postons per road segment, and consequently a hgh mssed geo-object recognton rate The am of ths secton s to present a modfed WLSR RAIM sutable for ETC applcatons that mproves the avalablty rate n envronments wth reduced satellte vsblty wthout ncreasng the effectve mssed detecton rate and therefore the toll lablty rsk Accordng to (1), a road segment s charged to the user when the number of ndependent postons declared vald by the RAIM nsde the geo-object s at least equal to the recognton threshold The WLSR RAIM may not declare vald a poston because t s not avalable, or because t has detected a falure, regardless of whether t s a correct or a false detecton (see Fg ) The am of the modfed WLSR D PDF (fault-free) Fg 3 Effect of the P FA n the WLSR RAIM wth a fxed PMD and a number of ch-squared degrees of freedom k The man dea behnd the modfed WLSR RAIM algorthm s to adapt the P FA to the maxmum slope varatons to provde a tradeoff between RAIM avalablty and false alarms, wthout any restrcton on the maxmum allowed P FA B Algorthm Desgn The objectve s to desgn a RAIM algorthm wth the WLSR test statstc descrbed n (7), that maxmzes the probablty that a fault-free poston (affected only by nomnal errors) s declared vald, e the RAIM s avalable and does not detect a fault Snce the WLSR test statstc s used, the formulas (-18) also apply for the modfed WLSR RAIM Moreover, the algorthm must assure that the probablty of not detectng, n the faulty scenaro, a postonng error larger than the HAL s always equal to or lower than a fxed value The frst desgn objectve s equvalent to fndng the detecton threshold (Th) that maxmzes the probablty of not detectng a falure n the fault-free scenaro, subject to the condton that the RAIM s avalable: Th arg max p Th Th a 1/ t λ det,a 1/ Th P FA,b Th b 1/ t ~ & HPL HAL (0) k λ det,b 1/ t 1/

7 6 Gven fxed values of and k, the HPL expresson of (17) s a monotoncally ncreasng functon of Th Hence, the detecton threshold that maxmzes (0) s the one that results n an HPL equal to the HAL Therefore, the proposed RAIM procedure s desgned to provde a constant HPL equal to the HAL The mnmum detectable ch-squared non-centralty parameter that corresponds to an HPL equal to HAL s derved from (18): det HAL slope (1) MAX The detecton threshold that maxmzes (0) s derved from equaton (17) wth the λ det calculated n (1): 1 Th CDF P MD () k, det The fault detecton algorthm can already be run once the detecton threshold has been calculated For performance analyss purposes, the P FA provded at each nstant can be derved from equaton (16) wth the Th calculated n (): P 1 CDF Th (3) k FA The resultng algorthm s a Constant-Probablty-of- Detecton (CPOD) RAIM [3] wth the partcularty of not havng a maxmum allowed P FA Ths modfed WLSR RAIM s always avalable (HPL=HAL), but very hgh slopes lead to hgh false alarm probabltes A fault-free estmated poston s declared vald by the RAIM wth a probablty of: P 1 PFA CDF Th (4) k vald C Algorthm Implementaton at the GNSS Recever The algorthm run at the recever can be ether the Fault Detecton (FD) module (Fg 4), or the Fault Detecton and Excluson (FDE) module There s no RAIM avalablty check module because the HPL s set to be always equal to the HAL Frst, at each epoch, the slope of each pseudorange measurement s computed as n the standard WLSR RAIM Afterwards, the mnmum detectable ch-squared noncentralty parameter s calculated wth the HAL and the maxmum slope The detecton threshold s then calculated wth () as the value for whch the Cumulatve Densty Functon (CDF) of a non-central ch-squared dstrbuton wth k degrees of freedom and non-centralty λ det s equal to Snce Th depends on current measurements, ts exact value cannot be computed offlne and stored lke n the WLSR RAIM used n cvl avaton Nevertheless, t s possble to create a look-up table of Th as a functon of k and dscrete values of λ det (for a gven ) Fnally, the test statstc s computed as n (7) wth the lnearzed pseudorange measurements, the observaton matrx and the nomnal error covarance matrx The estmated poston s declared vald for ts use n ETC f the test statstc does not exceed the threshold, and t s rejected f a fault s detected Test Statstc 1 t Y I BY No Fault Detected (Vald Poston) Fault Detecton Module slope MAX Maxmum Slope max 1 NS A I B Fg 4 Modfed WLSR RAIM algorthm run wthn the GNSS recever V COMPARISON BETWEEN THE WLSR RAIM USED IN CIVIL AVIATION AND THE MODIFIED ALGORITHM FOR ETC Both WLSR RAIM algorthms montor the ntegrty of the poston estmated applyng the WLSE to the lnearzed GNSS pseudorange measurements, assumng a known nomnal pseudorange error model and a sngle based pseudorange n the faulty scenaro (equatons (-6)) The two algorthms use the same test statstc descrbed n (7-1), related wth the postonng error as gven n (13, 14) Consequently, the relatonshps (15-18) depcted n Fg 1 between, P FA, Th, λ det and HPL apply to both algorthms The computatonal cost of the proposed algorthm s smlar to the cvl avaton one f t s mplemented wth a look-up table of dscrete values of Th Both WLSR RAIM algorthms assure a detecton rate equal to P FA n the fault-free scenaro Note that, assumng that nomnal errors do not cause postonng falures, any detecton n fault-free scenaro s a false detecton Both algorthms also assure that, n the faulty scenaro wth one based pseudorange, the mssed detecton rate of postonng errors exceedng the HPL s equal to or lower than The man dfference between both algorthms resdes n the fact that the WLSR RAIM used n cvl avaton provdes a tme-varant HPL and constant and P FA, whle the modfed algorthm provdes a tme-varant P FA and constant and HPL (equal to the HAL) A N, Mnmum Detectable Non-Centralty Parameter det HAL slope MAX Detecton Threshold 1 Th CDF k, t Th? det Fault Detected E, x

8 7 Fg 5 llustrates the false detecton probablty n the faultfree scenaro, and the probablty that a postonng error larger than HAL, e a postonng falure, s not detected n the faulty scenaro wth a based pseudorange such that the noncentralty parameter s λ det (the shaded area) It s mportant to note that the actual probablty of undetected postonng falures n the faulty scenaro depends on the slope of the based pseudorange, and on the bas magntude that moves the bdmensonal PDF along the slope e H HAL HPL Av P Undetected Falure, Av D PDF (fault-free) Th Av 1/ P FA,Av λ det, Av 1/ slope MAX D PDF (faulty case) a) WLSR RAIM used n cvl avaton (subscrpt Av stands for avaton) e H HAL P Undetected Falure, ETC D PDF (fault-free) Th ETC 1/ P FA,ETC λ det, ETC 1/ slope MAX b) WLSR RAIM modfed for Electronc Toll Collecton D PDF (faulty case) Fg 5 Graphcal example of the undetected falure probablty n the faulty case wth a based pseudorange such that λ=λ det, and of the false alarm probablty n the fault-free scenaro The WLSR RAIM for cvl avaton s desgned to provde at each epoch the lowest HPL that meets the requred and P FA The ntegrty s montored only f HPL HAL The RAIM detects postonng errors exceedng the HPL wth a probablty hgher than 1-, so the lower the HPL, the lower the actual mssed detecton probablty of postonng falures larger than the HAL (the shaded area n Fg 5) Postonng errors between HPL and HAL are treated as postonng falures and are detected wth a mssed detecton probablty below In the fault-free case, the algorthm constantly provdes the maxmum allowed false detecton rate P FA Therefore, the standard WLSR RAIM mnmzes the probablty of undetected postonng falures at the expense of the false detecton rate t 1/ t 1/ The WLSR RAIM for ETC s desgned to provde at each epoch, n the fault-free case, the lowest probablty of false alarm P FA that meets the requred and HAL The algorthm constantly provdes an HPL equal to the HAL For ths reason, the actual probablty of detecton probablty of postonng falures larger than the HAL (the shaded area n Fg 5) s less conservatve than n the orgnal algorthm Therefore, the modfed WLSR RAIM mnmzes the probablty of false detecton, at the expense of a less conservatve probablty of undetected postonng falures Hgh maxmum slopes due to bad user/satellte geometres result n hgh HPL n the cvl avaton RAIM procedure and n hgh P FA n the modfed algorthm Ths means that postons rejected by the cvl avaton algorthm due to RAIM unavalablty can be montored wth the new algorthm at the cost of ncreasng the P FA Fg 6 shows the probablty of rejectng a fault free poston for both RAIM procedures wth one redundant pseudorange measurement (k=1), as a functon of the rato HAL/slope MAX Let us remember that a poston s declared vald when the RAIM s avalable and does not detect a falure The avalablty condton for the RAIM used n cvl avaton can be rewrtten usng (18) as: det HAL slope MAX (5) Followng the example of Fg 6, equatons (16) and (17) gve a value of λ det 1/ =75 wth =10-3, P FA = and k=1 In that case, the RAIM s avalable f HAL/slope MAX s larger than 75, and unavalable f t s not When the RAIM s avalable, the false detecton s constantly P FA =, whle when t s unavalable ntegrty cannot be montored and the poston s always rejected On the other hand, the modfed WLSR RAIM presents a decreasng false alarm probablty as HAL/slope MAX ncreases For nstance, contnung wth the case depcted n Fg 6, a rato HAL/slope MAX equal to 7 would cause the orgnal RAIM to be unavalable and to reject the poston, but the modfed algorthm s able to montor ntegrty and valdate the poston wth a probablty of P vald P FA WLSR RAIM for cvl avaton WLSR RAIM modfed for ETC HAL / slope MAX HAL / slope MAX Fg 6 Probablty of not declarng vald a fault-free poston Confguraton: k=1, =10-3, RAIM for cvl avaton P FA =

9 σ PSR (m) PSR (m) 8 The modfed WLSR RAIM s sutable for applcatons lke ETC that need the maxmum number of postons assured to be wthn a gven HAL wth a gven, rather than a contnuty requrement Other studes have addressed the use of RAIM algorthms wth flexble P FA n applcatons wth contnuty constrants lke cvl avaton [4] VI SIMULATION RESULTS Ths secton presents the navgaton system performance; the fnal toll chargng performance should nclude other possble falures lke geo-object database errors The WLSR RAIM performance depends on the desgn parameters (HAL,, and, n the classc algorthm, P FA ) and on the maxmum slope, whch n turn depends on the envronment, e the user/satellte geometry The RAIM performance n rural and urban envronments has been obtaned va smulatons The smulated scenaro conssts of a user movng at a constant velocty of 50 km/h along the axs of a 0-metre wde straght street Buldngs are generated statstcally at both sdes of the street as n Table I, separated by a gap wth a probablty of 10-1 The nomnal 4-satellte GPS and 7- satellte Galleo constellatons are smulated, and only lne-ofsght satelltes wth an elevaton angle over 5 are assumed to be receved by the user The smulaton length s set to 7-hour to cover approxmately all possble GPS & Galleo satellte ground track combnatons Data s sampled every second TABLE I SIMULATED ENVIRONMENTS Envronment Urban Rural Buldng heght (H B) Buldng wdth (W B) Gap wdth (W G) H B ~Ñ(15 m, 3 m) 4 m H B 5 m W B ~N(0 m, 5 m) W B 10 m W G ~N(15 m, 5 m) W G 10 m H B ~Ñ(6 m, 15 m) 4 m H B 0 m W B ~N(0 m, 5 m) W B 10 m W G ~N(15 m, 5 m) W G 10 m Three GNSS recevers are studed A sngle frequency GPS L1 C/A wth a wdeband front-end of 16 MHz augmented wth SBAS correctons, a sngle frequency dual constellaton GPS & Galleo L1/E1 BOC(1,1) wth a 4-MHz frontend flter augmented wth SBAS correctons, and a dual frequency GPS & Galleo L1/E1MBOC & L5/E5a BPSK(10) wth a 14-MHz and a 0-MHz frontend flter respectvely The frst confguraton wll gve the performance of current hgh performance recevers, and the GPS & Galleo confguratons wth modernzed sgnals represent the performance attanable n a near future In the dual constellaton case, a modernzed SBAS capable to correct Galleo sgnals s assumed Varous chargng metrcs can be used to defne the ETC requred performance [13], but numercal values of these metrcs are not standardzed Ths secton consders, as n [14], a fault-detecton WLSR RAIM confguraton wth = 5 and two possble values of P FA, and 5 The HAL depends on the road topology; n ths paper numercal examples are gven for HAL of 5 and 50 meters [14] A pseudorange nomnal measurement model sutable for ntegrty applcatons n urban envronments s used Followng a smlar approach as n [1][], the pseudorange error s calculated as the result of varous ndependent error sources: onosphere and troposphere delays, trackng loops errors, multpath and ephemers and satellte clock errors The model s summarzed as follows The onospherc resdual error model s that of the cvl avaton standards for sngle frequency GPS and SBAS [], and zero for dual frequency users The troposphere resdual error model standardzed for cvl avaton s used [] The trackng loop errors are modeled as n [5], consderng a 1-Hz DLL, a 0-ms ntegraton tme, a dot-product dscrmnator and a carrer to nose rato C/N 0 of 30 db The multpath error model s detaled n [6] Fnally, the GNSS are assumed to be suffcently modernzed to assure ephemers and satellte clock nomnal errors wth a standard devaton of 85 cm The total pseudorange error model s a zero-mean Gaussan dstrbuton wth the standard devaton (σ PSR ) of Fg 7 It s mportant to note that σ PSR s expected to decrease wth hgher C/N 0, especally n dual frequency recevers that elmnate the onospherc delay at the cost of amplfyng the thermal nose error elevaton angle (degrees) Fg 7 Pseudorange nomnal error model wdeband L1 C/A + SBAS L1/E1 BOC(1,1) + SBAS E1 CBOC + E5a BPSK(10) L1 TMBOC + L5 BPSK(10) elevaton angle (degrees) The number of vsble satelltes and the HPL dstrbuton obtaned wth the classc WLSR RAIM remarks the relevance of the envronment and of the number of constellatons (Fg8 and Fg 9) Both dual constellaton recevers show smlar performances For nstance, n the dual constellaton case and a HAL of 50 m, the percentage of epochs n whch a RAIM confgured wth =5 and P FA = s avalable decreases from almost 100% n the rural envronment to approxmately 55% n the urban one In the GPS case, t decreases from 50% to around 7% Lower or P FA would decrease the avalablty rate Fg 10 shows the CDF of the number of vald postons for a dual constellaton user durng a 30-s trajectory trough a road segment The modfed WLSR RAIM provdes the hghest number of vald postons

10 p( N vald X ) p( Nvald N) p( N 0 ) p( Nvald vald = 0) p( HPL X ) p( HPL X ) p( p( N 0 ) Nvald = 0) p( p ( Nsat N sat N ) N 0 ) p( Nvald vald = 0) N N (number of vsble satelltes) Fg 8 Dstrbuton of vsble satelltes GPS GPS & Galleo Grey: rural envronment Black: urban envronment X (meters) 100 X (meters) L1 C/A (16 MHz) + SBAS Grey: rural envronment L1/E1 BOC(1,1) + SBAS Black: urban envronment L1/E1 MBOC + L5/E5a BPSK(10) Fg 9 CDF of the HPL obtaned wth the cvl avaton WLSR RAIM wth the followng constant parameters: P FA = and = Trajectory duraton (seconds) a) Wdeband L1 C/A + SBAS users, HPL = 50 meters Trajectory duraton (seconds) b) L1/E1 MBOC & L5/E5a BPSK(10) users, HPL = 50 meters N X WLSR RAIM (P FA =5 ) Grey: rural envronment WLSR RAIM (P FA = ) Black: urban envronment WLSR RAIM modfed for ETC Fg 10 CDF of the number of postons declared vald by the RAIM n a trajectory of 30 seconds for L1/E1 MBOC & L5/E5a BPSK(10) users ( =5, T c =5 s, HAL=5 m) Trajectory duraton (seconds) c) L1/E1 MBOC & L5/E5a BPSK(10) users, HPL = 5 meters WLSR RAIM (P FA =5 ) WLSR RAIM (P FA = ) WLSR RAIM modfed for ETC Grey: rural envronment Black: urban envronment Fg 11 Probablty that any of the postons estmated durng the user trajectory through a geo-object s not valdated by the RAIM ( =5 ) Let us consder an ETC system that charges a road segment when there s at least one vald poston nsde the geo-object, that s, N Th =1 n (1) Ths threshold has been proved to meet the overchargng requrement provdng the lowest probablty of mssed geo-object [14] Fg 11 shows the probablty of not

11 10 chargng a user that has drven through a road segment as a functon of the trajectory duraton, a tme between ndependent postons (T c ) of 5 s, and varous recever and RAIM confguratons Both GPS & Galleo recevers have smlar performance, so for the sake of clarty only the dual frequency results are plotted The novel algorthm always provdes the best results, reachng a dfference of more than one order of magntude wth respect to the classc WLSR RAIM n the dual constellaton case for duratons longer than 0 s The classc WLSR RAIM has better performance wth a P FA of than of 5, whch means that n ths case the gan n the avalablty rate compensates the loss n the false alarm rate The reduced vsblty penalzes the sngle constellaton performance: whle the probablty of not chargng the road segment wth a HAL of 50 m and after 5 s of trajectory s for GPS & Galleo users, t s stll over 01 for GPS-only users VII CONCLUSION GNSS-based ETC systems need to montor the postonng ntegrty n order to control the effects of underchargng and overchargng due to postonng falures Wth ths purpose, two RAIM algorthms have been studed: the WLSR RAIM used n cvl avaton and a modfed algorthm that, mantanng the, maxmzes the number of vald postons (that s, avalable RAIM and no fault detected) The am of the proposed algorthm s to decrease the rate of underchargng n reduced vsblty scenaros lke urban envronments, assurng the same maxmum allowed overchargng rsk as the cvl avaton RAIM procedure Ths objectve has been demonstrated by smulatons It has also been shown the mprovement of dual constellaton recevers n urban envronments, whch provde underchargng rates several orders of magntude lower than GPS-only ones The proposed desgn wth a varable P FA and a fxed HPL can be extended to other exstng RAIM algorthms REFERENCES [1] Internatonal Cvl Avaton Organzaton (ICAO), Internatonal Standards and Recommended Practces, Annex 10 to the Conventon on Internatonal Cvl Avaton, Aeronautcal Telecommuncatons, Volume I, Rado Navgaton Ads, 6th Edton, July 006 [] RTCA, Inc, Mnmum Operatonal Performance Standards for Global Postonng System / Wde Area Augmentaton System Arborne Equpment, DO-9, Dec 006 [3] Department of Defense USA, "Global Postonng Servce Standard Postonng Servce Performance Standard", 4th Edton, Sept 008 [4] J Cosmen-Schortmann, M Azaola-Saenz, M A Martnez-Olague, M Toledo-Lopez, Integrty n Urban and Road Envronments and ts use n Lablty Crtcal Applcatons, Proceedngs of IEEE/ION PLANS 008, Monterey, CA, May 008, pp [5] Racal Tracs Ltd, Galleo Overall Archtecture Defnton (GALA) Defnton and Szng For The Safety of Lfe Market, 6 October 000 [6] Drectve 004/5/EC of the European parlament and the councl on the nteroperablty of electronc road toll systems n the Communty, Apr 9, 004 [7] B Pftznger, T Baumann, T Jestädt, Analyss and Evaluaton of the German Toll System Usng a Holstc Executable Specfcaton, hcss, pp , 01 45th Hawa Internatonal Conference on System Scences, 01 [8] R Vargc, M Buncak J Kacur, On self-smlarty n servce trggerng n NGN networks usng satellte based tollng systems, ELMAR, 011 Proceedngs, vol, no, pp , Sept 011 [9] Velaga, NR; Quddus, MA; Brstow, AL; Yuheng Zheng;, "Map- Aded Integrty Montorng of a Land Vehcle Navgaton System," Intellgent Transportaton Systems, IEEE Transactons on, vol13, no, pp , June 01 [10] Toledo-Moreo, R; Betalle, D; Peyret, F;, "Lane-Level Integrty Provson for Navgaton and Map Matchng Wth GNSS, Dead Reckonng, and Enhanced Maps," Intellgent Transportaton Systems, IEEE Transactons on, vol11, no1, pp100-11, March 010 [11] Toledo-Moreo, R; Zamora-Izquerdo, MA; Ubeda-Marro, B; Gomez- Skarmeta, AF;, "Hgh-Integrty IMM-EKF-Based Road Vehcle Navgaton Wth Low-Cost GPS/SBAS/INS," Intellgent Transportaton Systems, IEEE Transactons on, vol8, no3, pp , Sept 007 [1] F van Graas, J L Farrell, Baselne Fault Detecton and Excluson Algorthm, Proceedngs of the 49th Annual Meetng of The Insttute of Navgaton, Cambrdge, MA, June 1993, pp [13] Internatonal Organzaton for Standardzaton (ISO), Electronc fee collecton Chargng performance Part 1: Metrcs, ISO/TS , Frst Edton, 01 [14] D Salós, Integrty montorng appled to the recepton of GNSS sgnals n urban envronments, PhD thess, Insttut Natonal Polytechnque de Toulouse, 01 [15] B W Parknson, P Axelrad, Autonomous GPS Integrty Montorng usng the Pseudorange Resdual, NAVIGATION, Vol 35, No, Summer 1988, pp [16] R G Brown, P McBurney, Self-Contaned GPS Integrty Check Usng Maxmum Soluton Separaton, Navgaton: Journal of the Insttute of navgaton, Vol 35, No 1, Sprng 1988, pp [17] M A Sturza, Navgaton System Integrty Montorng usng Redundant Measurements, NAVIGATION, Vol 35, No 4, Wnter , pp [18] YC Lee, Analyss of range and poston comparson methods as a means to provde GPS ntegrty n the user recever, Proceedngs of the Annual Meetng of The Insttute of Navgaton, June, 1986 [19] R G Grover Brown, A Baselne GPS RAIM Scheme and a Note on the Equvalence of Three RAIM Methods, NAVIGATION, Vol 39, No 3, Fall 199, pp [0] T Walter, P Enge, Weghted RAIM for Precson Approach, Proceedngs of the 8th Internatonal Techncal Meetng of the Satellte Dvson of The Insttute of Navgaton (ION GPS 1995), Palm Sprngs, CA, September 1995, pp [1] Ober, PB, "Ways to Improve RAIM/AAIM Avalablty Usng Poston Doman Performance Computatons," Proceedngs of the 1997 Natonal Techncal Meetng of The Insttute of Navgaton, Santa Monca, CA, January 1997, pp [] R G Brown, G Y Chn, GPS RAIM: Calculaton of Thresholds and Protecton Radus Usng Ch-Square Methods-A Geometrc Approach, Global Postonng System: Papers Publshed n NAVIGATION Volume V, 1998, pp [3] MA Sturza, AK Brown, "Comparson of Fxed and Varable Threshold RAIM Algorthms," Proceedngs of the 3rd Internatonal Techncal Meetng of the Satellte Dvson of The Insttute of Navgaton (ION GPS 1990), Colorado Sprng, CO, September 1990, pp [4] S Feng, WY Ocheng, D Walsh, R Ioanndes, "A measurement doman recever autonomous ntegrty montorng algorthm", GPS Solutons, 006, vol10, no, pp85-96 [5] O Julen, Desgn of Galleo L1F trackng loops, PhD thess, Unversty of Calgary, Department of Geomatcs Engneerng, 005 [6] D Salós, C Macabau, A Martneau, B Bonhoure, D Kubrak, "Nomnal GNSS Pseudorange Measurement Model for Vehcular Urban Applcatons," Proceedngs of IEEE/ION PLANS 010, Indan Wells, CA, May 010, pp

12 11 Danel Salós graduated as a telecommuncaton engneer n 006 from the Unversty of Saragossa, Span, and receved hs PhD n 01 from the Unversty of Toulouse, France Snce 008, he has been workng n the telecom lab at the ENAC, France Hs feld of nterest s sgnal processng appled to satellte navgaton systems, ncludng GNSS ntegrty montorng Anaïs Martneau s the head of the Electroncs, Electromagnetsm and Sgnal dvson of ENAC She graduated n 005 as an electroncs engneer from the ENAC and she receved her PhD n 008 from the Unversty of Toulouse Snce 005, she has been workng at the Sgnal Processng and Navgaton (SIGNAV) research group of the TELECOM lab of ENAC where she carres out research on ntegrty montorng technques Chrstophe Macabau graduated as an electroncs engneer n 199 from the ENAC (Ecole Natonale de l Avaton Cvle) n Toulouse, France Snce 1994, he has been workng on the applcaton of satellte navgaton technques to cvl avaton He receved hs PhD n 1997 and has been n charge of the sgnal processng lab of ENAC snce 000, where he also started dealng wth navgaton technques for urban navgaton He s currently the head of the TELECOM lab of ENAC, that ncludes research groups on sgnal processng and navgaton, electromagnetcs and data communcaton networks Bernard Bonhoure graduated as an aeronautc engneer from ENSICA n Toulouse (ISAE) He joned CNES n 1989, he has worked on several successful space programmes such as TOPEX/POSEIDON, SPOT, ENVISAT, JASON As a navgaton system expert, he s now nvolved n many actvtes lnked to GNSS satellte postonng and performances Damen Kubrak graduated n 00 as an electroncs engneer from ENAC, Toulouse, FranceHe receved hs PhD n 007 from ENST Pars, France Snce 006, he s workng at Thales Alena Space, Toulouse, France, where he s nvolved n land vehcle navgaton, GNSS sgnal processng and hybrdzaton for seamless postonng, asssted GNSS and moble phones performance assessment