Aalyses of Iterty Motor echques for a Global Navato Satellte System (GNSS-) heodor Z ad Berd Essfeller Isttute of Geodesy ad Navato (IfEN), Uversty FAF Much D-85577 Neubber, Germay Erw Löhert ad Robert Wolf IfEN Gesellschaft für Satellteavato mbh (IfEN GmbH) D-85579 Neubber, Germay BIOGRAHIES heodor Z s Research Assocate at the Isttute of Geodesy ad Navato at the Uversty of Federal Armed Forces Much. I 1995 he receved a dploma Electrcal Eeer from the Uversty of Erlae- Nurember. He s curretly cocered wth research the felds of GS/GLONASS RAIM ad of EGNOS/GNSS terty. Dr. Berd Essfeller s full rofessor of Navato ad Vce-Drector of the Isttute of Geodesy ad Navato at the Uversty of Federal Armed Forces Much. He s resposble for the operato of the laboratory, for teach ad research avato ad sal process. ll the ed of 1993 he wored dustry as a project maaer the developmet of GS/INS avato systems. He receved the Habltato (vea leed) Navato ad hyscal Geodesy 1996. Erw Löhert receved a dploma Aerospace Eeer 1993 from the Much Uversty of echoloy. I 1994 he joed the Isttute of Geodesy ad Navato as a Research Assocate, wor maly the research areas of aeroravmetry ad GS/INS terato. Sce March 000 he s a project maaer at IfEN GmbH wor the feld of terty determato. Robert Wolf receved a dploma Aeroautcal Eeer 1995. He wored as a research assocate at the Isttute of Geodesy ad Navato of the Uversty of the Federal Armed Forces, Germay. Hs ma actvtes were the feld of GS/INS hybrdzato, Kalma flter ad orbt determato. Sce 1999 he s wor for IfEN GmbH, were he s volved the terty alorthm developmet for the Idepedet Chec Set of the EGNOS system. ABSRAC A GNSS- has to overcome the basc defceces,.e. the lac of terty, avalablty, cotuty ad accuracy the Sal-I-Space (SIS), of preset satellte avato systems as the U.S. Global osto System (GS) ad the Russa Global Navato Satellte System (GLONASS). hus, the Europea cotrbuto to GNSS- (Galleo) wth the curret basele of reus the Europea Geostatoary Navato Overlay Servce (EGNOS) requres that the SIS provdes already terty for Cateory I (CA I) precso approach ad lad. he terty of a system refers to the assurace that all fuctos of ths system perform wth the operatoal lmts where the terty rs s the probablty of udetected falures result the loss of specfed accuracy. Aalyses of approprate terty motor techques for a GNSS- must be performed order to demostrate whether or ot ths performace requremet ca be met by the proposed GNSS- archtectures. I addto to ths, these aalyses have to show the advataes ad lmtatos of these techques as well as the achevable servce terty motor levels for the dfferet terty motor cocepts. he paper dscusses basc terty motor cocepts as Recever Autoomous Iterty Motor (RAIM) le methods for the Galleo users ad the cotrbuto of the Galleo roud-based terty motor as well as the frst results of a adapted RAIM alorthm avalablty smulato. hs dscusso taes also several Galleo hybrdzato techques, e.. the combato of Galleo wth other avato systems (GS, LORAN-C, etc.) ad/or wth further sesors (barometrc altmeter, etc.), to accout. INRODUCION he eeral purpose of terty motor s the protecto of a servce provded by a system aast errors, whch exceed a specfed boud. hs protecto of a system servce ca be acheved by several methods, where redudat formato s used by ether a sle depedet autoomous subsystem or by a combato of depedet autoomous subsystems order to chec
the correctess of ths servce ad/or the total system s motored by a exteral depedet motor system. he objectve of the depedet autoomous terty motor, whch s performed by a Galleo user recever, s the protecto of the avato soluto provded by ths user recever aast posto errors exceed the alarm lmt. For ths reaso, the terty motor of a user recever must provde a tmely war whe a falure exsts (.e. whe a posto error exceeds the alarm lmt). I addto to ths, f a user recever utlzes addtoal formato from the Groud Iterty Chael (GIC) of Galleo, from further avato systems ad/or from other sesors, the the terty of the avato soluto, whch s provded by ths user recever, creases. he follow dscusso wth reard to the avato soluto terty motor by the user recever ves a frst prelmary qualtatve assessmet of the terty motor level, whch ca be acheved at user level, as well as of the mpact of the GIC o the terty motor level. Moreover, the hybrdzato of Galleo wth other avato systems ad/or wth further sesors s cosdered too. USER AUONOMOUS INEGRIY MONIORING BASICS All measuremets, whch are used by the user recever for the determato of the avato soluto, are also used by the terty motor of ths user recever order to chec the cosstecy of ths avato soluto. I eeral, the depedet autoomous terty motor, whch s performed by a Galleo user recever, s structured as follows: () User terty motor avalablty chec (checs whether or ot the umber of used measuremets as well as the relatve eometry of the user recever posto ad the satellte postos are suffcet for the determato of a correct avato soluto, whch meets the user performace requremets) () Hypothess test (checs whether or ot oe of the measuremets, whch are used by the user recever, s correct whe the terty motor of ths user recever s avalable where t s assumed that oly oe of these measuremets s correct at a tme) If the terty motor of a user recever s ot avalable (e.., due to suffcet relatve eometry of the user recever posto ad the satellte postos), the the user performace requremets caot be met by the terty motor performed by ths user recever. herefore, the avato soluto cosstecy chec,.e. the hypothess test, caot be performed by the terty motor of a user recever whe ths user terty motor s ot avalable. he user has to use measuremets from other avato systems or sesors order to determe a correct avato soluto, whch meets the user performace requremets, ths case. Note that the user caot compute a correct avato soluto meet the user performace requremets whe the terty motor of the Galleo user recever s ot avalable ad whe o measuremets from other avato systems or sesors are avalable. O the other had, a hypothess test (.e. the calculato of a test statstc ad the subsequet comparso of ths test statstc wth the cocer threshold) s performed by the terty motor of a user recever order to decde whether or ot a correct measuremet exsts whe ths user terty motor s avalable. If o correct measuremet s thereby detected (.e. ths test statstc s smaller tha or equal to ths threshold), the t s assumed that the avato soluto calculated by the user s a correct avato soluto, whch meets the user performace requremets. Otherwse a correct measuremet s detected (.e. ths test statstc s reater tha ths threshold) ad the avato soluto computed by the user s assessed as correct. he user has to perform further operatos order to obta a correct avato soluto meet the user performace requremets ths case. After the detecto of a correct measuremet, a user ca proceed as follows: () Determato of a correct avato soluto, whch meets the user performace requremets, by us oly measuremets, whch are ot used by the user for the determato of the avato soluto that s assessed as correct, from other avato systems or sesors () Isolato,.e. detfcato, ad/or excluso of the correct measuremet from the avato soluto, whch s assessed as correct It must be oted that fault solato/excluso s oly requred for prmary meas of avato as well as for sole meas of avato. Moreover, the relatve eometry of the user recever posto ad the satellte postos s ot always suffcet for the fault solato/excluso purpose. herefore, the user caot compute a correct avato soluto meet the user performace requremets whe a correct measuremet s detected ad whe fault solato/excluso caot be performed as well as whe o other measuremets tha those used by the user for the determato of the avato soluto, whch s assessed as correct, are avalable. ADAED RAIM ALGORIHM Several methods ca be used for the terty motor at user level where RAIM le techques, whch chec the correctess of the avato soluto provded by the user recever, are usable for the terty motor performed by ths user recever. Assum that the least squares
adjustmet s used by the user recever order to determe the avato soluto, the the RAIM method proposed by Breer [1] ca be modfed order to obta a adapted RAIM alorthm, whch ca be used by the terty motor of ths user recever ad whch s also applcable whe Galleo s hybrdzed wth other avato systems ad/or wth further sesors. hs adapted RAIM alorthm s the bass for the follow aalyses of the avato soluto terty motor performed by the user recever ad s deoted as the party method wth aled coordate systems. Mathematcal Model he mathematcal model, whch s used by the adapted RAIM alorthm (.e. by the party method wth aled coordate systems), bases o the assumpto that at a ve pot of tme measuremets are avalable at the user recever. It s addtoally assumed that > m for fault detecto as well as > m+1 for fault detecto ad solato/excluso, where m s the umber of uows. he uows are the three user recever posto coordates ad the user recever cloc offset wth respect to the Galleo etwor tme (.e. the umber of uows s equal to four whe the user recever uses oly Galleo satellte measuremets). Note that the hybrdzato of Galleo wth other avato systems ad/or wth further sesors eerally results addtoal uows (e.. user recever cloc offsets wth respect to the etwor tmes of other avato systems whe Galleo s hybrdzed wth further avato systems). he learzato of the olear fuctos, whch belo to the measuremets, of the uows yelds the relatoshps betwee these measuremets ad the uows the form of the follow system of lear alebrac equatos: wth y M G M x ε M y = G x + ε (1) M M 1 resdual vector m des matrx wth ra(g M ) = m m 1 vector of the devatos of the uows from the predcted values of the uows 1 error vector he resdual vector cossts of the dffereces betwee the values of these olear fuctos at the uows ad the values of these olear fuctos at the predcted values of the uows. Furthermore, the elemets each row of the des matrx are the frst order partal dervatves of the correspod olear fucto at the predcted values of the uows. he frst order partal dervatves, whch are the elemets of a row of the des matrx, are thereby obtaed by the aylor seres expaso of the correspod olear fucto yeld the lear alebrac equato, whch belos to ths row of the des matrx. It must be oted that the frst M three compoets of x are the three compoets of the user recever posto devato from the predcted user recever posto. Moreover, the error vector s Gaussa wth zero mea vector ad wth costat postve defte covarace matrx R,.e. ε M N(0, R). he matrx R s specfed by R = (W W) -1 wth the daoal matrx 1 1 W da( σ,, σ ) () = 1 where σ s the stadard devato of the th compoet of the error vector (σ > 0 {1,..., }). If the th compoet of the error vector belos to a Galleo satellte measuremet, the the varace σ of ths compoet of ε M s specfed as follows [5]: wth σ UIVE, σ m45 σ trv σ = σ SISA, + + σ SNR, + + (3) R E E ecose ta s 1 Re h + I σ σ SISA, σ UIVE, R e E h I σ SNR, σ m45 σ trv Stadard devato of the th compoet of ε M Stadard devato of the combed satellte ephemers ad cloc error cotrbuto Stadard devato of the vertcal oospherc error cotrbuto Mea radus of the earth Elevato ale of the satellte Heht of the maxmum electro desty Stadard devato of the user recever ose cotrbuto Stadard devato of the multpath error cotrbuto at 45 derees Stadard devato of the vertcal tropospherc error cotrbuto Note that the stadard devato σ SISA, of the combed satellte ephemers ad cloc error cotrbuto s determed by the Sal I Space Accuracy (SISA), whch s provded by Galleo to the users, of the correspod satellte sce the SISA of a satellte s a σ boud of the correspod measuremet error compoet, whch s caused by the combed ephemers ad cloc error of ths satellte (.e. σ SISA, = SISA / where SISA s the Sal I Space Accuracy of the correspod satellte). I addto to ths, the stadard devato σ UIVE, of the vertcal oospherc error cotrbuto s approxmately equal to zero whe a Galleo user recever uses two sals wth dfferet carrer frequeces for the determato of the avato soluto. Now, the substtutos y = Wy M, G = WG M ad ε = Wε M are used order to obta the follow system of ormalzed lear alebrac equatos:
where y = Gx + ε (4) fa r fa t C False alarm probablty False alarm rate Correlato tme of the measuremet errors y G x ε 1 ormalzed resdual vector m ormalzed des matrx m 1 vector of the devatos of the uows from the predcted values of the uows 1 ormalzed error vector Furthermore, t s addtoally assumed that o more tha oe of the measuremets s correct ad that a correct measuremet s represeted by the correspod compoet, whch has a mea that s ot equal to zero, of the ormalzed error vector. Adapted RAIM Alorthm Avalablty he avalablty of the terty motor of a user recever must be checed order to decde whether or ot the terty motor, whch s performed by ths user recever, meets the user performace requremets. he user terty motor avalablty chec of the party method wth aled coordate systems bases o the QR decomposto G = QR of G where the matrx Q s a orthooal matrx ad the m matrx R has zeros row m+1 to ad a upper traular m m matrx R x row 1 to m. Moreover, Q = ( Q x, Q ) s parttoed to the m matrx Q x ad the (-m) matrx p Q p. I addto to ths, a orthooal (-m) (-m) matrx A s chose so that the frst elemet of the th colum of the (-m) matrx = A Q p s p 1 ad all other elemets of the th colum of are zero. Us the complemetary error fucto F CEF ( t) = 1 π t the the threshold s determed by wth d F 1 CEF fa d e y / dy, (5) 1 = F CEF ( / ) (6) fa hreshold ( t ) Iverse fucto of the complemetary error fucto False alarm probablty Number of measuremets he false alarm probablty s thereby specfed as follows: where = r t (7) fa fa C If the stadard devato of oe of the measuremet error compoets of the used sesors ad avato systems s sfcatly reater tha the stadard devatos of all other measuremet error compoets of the used sesors ad avato systems, the the correlato tme t C of ths measuremet error compoet, whch has ths reatest stadard devato, s used for the computato of the false alarm probablty fa. Otherwse oe of the measuremet error compoets of the used sesors ad avato systems has the reatest stadard devato ad ths reatest stadard devato s of the same order of matude as the stadard devatos of some other measuremet error compoets of the used sesors ad avato systems so that the larest correlato tme t C of these measuremet error compoets, whch have these reatest stadard devatos, s used for the calculato of the false alarm probablty fa. hus, f the m m matrx C L represets the lear trasformato that trasforms the three user recever posto devato compoets of x to the topocetrc local Cartesa coordate system wth ts axes alo the local orth, local east ad local vertcal dow at the user recever posto whereas the rema compoets of x are ot chaed by ths lear trasformato, the the Horzotal rotecto Level (HL) as well as the Vertcal rotecto Level (VL) are ve as follows: where HL VL d F 1 CEF md p 1 b 1 b b 3 d HL = Max =,, + F p 1 CEF 1 1 ( md ) b 1 + b 1 d + FCEF (md ) VL = Max b3 = 1,, p1 (8) (9) Horzotal rotecto Level Vertcal rotecto Level hreshold ( t ) Iverse fucto of the complemetary error fucto Mssed detecto probablty Frst elemet of th colum of Frst elemet of the th colum of the m matrx B = C L (G G) -1 G Secod elemet of the th colum of the m matrx B = C L (G G) -1 G hrd elemet of the th colum of the m matrx B = C L (G G) -1 G he mssed detecto probablty s at ths defed by = r t (10) md md C
wth md r md t C Mssed detecto probablty Mssed detecto rate Correlato tme of the measuremet errors hs adapted RAIM alorthm s avalable for horzotal avato whe the HL s smaller tha or equal to the Horzotal Alarm Lmt (HAL). Otherwse the HL s reater tha the HAL ad ths adapted RAIM alorthm s ot avalable for horzotal avato. I addto to ths, f the VL s smaller tha or equal to the Vertcal Alarm Lmt (VAL), the ths adapted RAIM alorthm s avalable for vertcal avato. Note that ths adapted RAIM alorthm s ot avalable for vertcal avato whe the VL s reater tha the VAL. Fault Detecto Method he fault detecto alorthm of the party method wth aled coordate systems bases o the matrces too. If p ( = 1,..., ) are the frst rows of these matrces, the the test statstcs are ve as follows: d = y (11) hs adapted RAIM alorthm decdes that o correct measuremet exsts whe d d for all = 1,..., where d s the threshold specfed by equato (6). Otherwse ths adapted RAIM alorthm decdes that a correct measuremet exsts. Fault Idetfcato Method If a correct measuremet s detected by the fault detecto alorthm, the the fault detfcato alorthm of the party method wth aled coordate systems also uses the matrces for the detfcato of ths correct measuremet. he removal of the frst row of a matrx yelds the (-m-1) matrx L. Furthermore, a orthooal (-m-1) (-m-1) matrx F, q s chose so that the frst elemet of the qth colum of the (-m-1) matrx ( ) Z, q = F, q L s equal to z 1q ad all other elemets of the qth colum of Z, q are equal to zero except for the th colum of Z, q (.e. q N q wth N = {1,..., }). If z, q ( = 1,..., ; q = 1,..., -1, +1,..., ) are the frst rows of the matrces Z, q, the the detfcato values are ve as follows: p h z q, q, = y (1) he threshold d, whch s specfed by equato (6), s used by ths fault detfcato alorthm, too. If o subscrpt j, whch fulfls the codto { N j} h d q { q N q j} h, j > d j, q, (13) exsts wth j N, the ths fault detfcato alorthm s ot avalable. Otherwse ths codto s fulflled by a subscrpt j ad ths fault detfcato alorthm s avalable. he measuremet, whch belos to ths uque subscrpt j, s detfed by ths fault detfcato alorthm as the correct measuremet ths case. GIC CONRIBUION O USER INEGRIY MONIORING he falure sources, whch affect the Galleo satellte measuremets of a user recever, are multfarous where the GIC ca oly motor a part of these falure sources. For stace, local falure sources, whch oly corrupt the measuremets of the user recevers located close to these local falure sources, as extreme multpath (e.., due to satellte sal reflectos o the surface of a arcraft,.e. o the surface of the user tself), extreme oosphere, poor user/satellte eometry (e.., due to arcraft ba maeuvers), satellte sal terfereces ad/or jammer sals are ot observable by the GIC. Note that the falure sources of the user recevers caot be motored by the GIC, too. herefore, the GIC caot chec the (full) terty o user level so that the users have ay case to apply RAIM le techques. hs meas that the GIC ca oly verfy the (partal) terty of the roud cotrol ad space semets (.e. the GIC ca oly motor each dvdual measuremet error compoet, whch s caused by the combed ephemers ad cloc error of the correspod Galleo satellte). O the other had, a user recever ca detect at maxmum -m correct measuremets amo the used measuremets so that the terty of the avato soluto, whch s provded by ths user recever, creases whe ths user recever utlzes the terty formato provded by the GIC. he eeral purpose of the roud-based terty motor, whch s performed by the GIC, s the verfcato of the SISA values, whch are provded by Galleo to the users. hs SISA verfcato s performed by chec whether or ot the SISA of each dvdual satellte bouds the correspod measuremet error compoet, whch s caused by the combed ephemers ad cloc error of the correspod satellte, at all user locatos, whch le wth the Galleo servce area, wth a specfed probablty SISA, whch s ether derved from the user performace requremets or a approprate value defed by Galleo. hs meas that the roud-based terty motor oly checs whether or ot the codto SISA ( X < SISA ) = F (SISA ) F ( SISA ) (14) holds at the worst user locato for each dvdual SISA where SISA deotes the SISA of the th satellte ad
F (x ) = (X < x ) s the actual probablty dstrbuto fucto of the actual measuremet error compoet X, whch belos to the th satellte ad whch s caused by the combed ephemers ad cloc error of the th satellte, at the worst user locato for SISA. he curret Galleo basele specfes the subdvso of the world to reos. I addto to ths, the curret Galleo basele also defes the trasmsso of oe lobal SISA for each dvdual satellte (.e. world-wde servce area for the SISA of each dvdual satellte) ad of oe reoal terty fla for each dvdual satellte as well as for each dvdual reo, whch s the servce area for the correspod terty fla. Each of these reoal terty flas cossts of two bts wth the formato Not Motored, Do't Use or Usable. If a Galleo satellte caot be motored by the roudbased terty motor of a reo (e.., due to the suffcet umber of avalable measuremets for ths satellte reard ths reo), the the correspod terty fla s set to Not Motored. Otherwse ths satellte ca be motored by the roud-based terty motor of ths reo ad the correspod terty fla s set to Usable whe the SISA of ths satellte bouds the correspod measuremet error compoet, whch s caused by the combed ephemers ad cloc error of ths satellte, at all user locatos, whch le wth ths reo, wth the specfed probablty SISA. Moreover, f the roud-based terty motor of ths reo ca motor ths satellte ad f the measuremet error compoet, whch s caused by the combed ephemers ad cloc error of ths satellte, at the worst user locato for the SISA of ths satellte reard ths reo s ot bouded by ths SISA wth the specfed probablty SISA, the the correspod terty fla s set to Do't Use. It must be oted that a Galleo satellte measuremet, whch belos to a satellte wth a reoal terty fla set to Not Motored or to Do't Use, s ot used by a user recever, whch s located wth the correspod reo ad whch apples the terty formato (.e. the SISA values of the Galleo satelltes as well as the reoal terty flas of the Galleo satelltes) provded by Galleo. Assum that each satellte falure results a posto soluto error, whch exceeds the alarm lmt, of a user recever wth a probablty, whch s equal to oe, as well as that the probabltes of avalable ad wth the specfed accuracy operat terty motor fuctos (.e. GIC as well as user terty motor) are also equal to oe, the the probablty of at least oe udetected falure (.e. the terty rs) wth respect to a user recever ad the probablty of loss-of-fucto (.e. the cotuty rs) reard ths user recever are ve as follows: uf uf = 1 (1 F md, G F md, G md, U md, U ) (15) where uf lof = fa, U + (1 fa, U ) = m+ 1 lof F md,g md,u lof fa,u fa,g m fa, U fa, G (1 ) fa, G (16) robablty of at least oe udetected falure (.e. terty rs) at user robablty of a Galleo satellte falure Codtoal probablty of mssed detecto for the GIC o the codto that a Galleo satellte has faled Codtoal probablty of mssed detecto for the user o the codto that a Galleo satellte has faled ad that ths faulty satellte has ot bee detected by the GIC robablty of loss-of-fucto (.e. cotuty rs) at user robablty of false alarm for the user robablty of false alarm for the GIC Number of user measuremets Number of uows at user It must be oted that F s the relablty fure (falure probablty) of Galleo. GALILEO HYBRIDIZAION WIH OHER NAVIGAION SYSEMS AND/OR SENSORS Several methods ca be used for the avato soluto terty motor at user level where RAIM le techques are applcable for the terty motor, whch s performed by the user recever, whe Galleo s hybrdzed wth other avato systems, e.. wth GS ad/or wth LORAN-C, ad/or wth further sesors, e.. wth a Iertal Navato System (INS) ad/or wth a barometrc altmeter. he addto of the measuremets from further avato systems ad/or from other sesors to the Galleo satellte measuremets eerally creases the user terty motor avalablty sce the umber of avalable measuremets at the user recever sfcatly creases. Note that the adapted RAIM alorthm, whch s brefly descrbed above ad whch s obtaed by the modfcato of the RAIM method proposed by Breer [1], ca also be used by a user terty motor whe Galleo s hybrdzed wth other avato systems (e.. GS, LORAN-C, etc.) ad/or wth further sesors (e.. INS, barometrc altmeter, etc.). If a user recever uses measuremets from further avato systems as GS ad/or LORAN-C addto to the Galleo satellte measuremets, the the uows are the three user recever posto coordates ad the user recever cloc offsets wth respect to the Galleo etwor tme as well as to the etwor tmes of these other avato systems. hus, the frst three compoets of the m 1 vector x, whch s specfed by equatos (1) ad (4),
are the three compoets of the user recever posto devato from the predcted user recever posto ad the rema compoets of ths vector x are the user recever cloc offset devatos from the predcted user recever cloc offsets. For stace, the umber of uows s equal to fve ad the des matrx G M, whch s defed by equato (1), s of the form 1,1 1, 1,3 1 0 m m m m m,1 1 0 1, 1 1,3 G M = ~ ~ ~ (17) + 1,1 + 1, + 1,3 0 1 1 1 1 m m m m m ~ ~ ~ +,1 +, +,3 0 1 1 1 1 whe Galleo s oly hybrdzed wth GS ad whe the umber of Galleo satellte measuremets s equal to 1 wth 1 > 0 as well as whe the umber of GS satellte measuremets s equal to wth = 1 > 0. he frst three elemets, j ( = 1,..., 1 ; j = 1,, 3) of the th row of G M are the compoets of the 3 1 ut vector pot from the correspod Galleo satellte posto to the predcted user recever posto ad the frst three elemets ~, j ( = 1 +1,..., 1 + ; j = 1,, 3) of the th row of G M are the compoets of the 3 1 ut vector pot from the correspod GS satellte posto to the predcted user recever posto ths case. O the other had, f Galleo s hybrdzed wth a barometrc altmeter, the oly oe addtoal measuremet s avalable at the user recever where the uows are the three user recever posto coordates ad the user recever cloc offset wth respect to the Galleo etwor tme (.e. the umber of uows s equal to four). he thrd elemet of the row, whch belos to ths barometrc altmeter measuremet, of the des matrx specfed by equato (1) s equal to oe ad all other elemets of ths row are equal to zero. ADAED RAIM ALGORIHM AVAILABILIY SIMULAION A frst prelmary qualtatve assessmet of the terty motor level, whch ca be acheved at user level, was performed by a adapted RAIM alorthm avalablty smulato. he adapted RAIM alorthm, whch s brefly descrbed above ad whch results from the modfcato of the RAIM method proposed by Breer [1], was thereby used for ths smulato. Smulato Assumptos able 1 shows the Galleo costellato parameters used for the adapted RAIM alorthm avalablty smulato. able 1. Galleo Satellte Costellato arameters [] arameter Smulato Assumpto Waler Costellato 30/3/0 Alttude 33.371 m Iclato 54 Eccetrcty 0 Moreover, the Optmzed 4 GS Costellato, whch s specfed by the RCA Specal Commttee 159 documet RCA/DO-9B [6], was used for ths smulato. Istead of us the ephemers referece epoch of the Galleo satellte costellato specfed by the erformace Budet Fle [] ad the ephemers referece epoch of the Optmzed 4 GS Costellato defed by the RCA Specal Commttee 159 documet RCA/DO-9B [6] for ths smulato, the ephemers referece epoch of the Galleo satellte costellato ad the ephemers referece epoch of the Optmzed 4 GS Costellato were set to the 4th of Jue 000 (000, 6, 4, 00:00:00) for the adapted RAIM alorthm avalablty smulato. I addto to ths, the LORAN-C statos specfed by the Lora-C Cha Iformato documet [4] were used for ths smulato too. Furthermore, the adapted RAIM alorthm avalablty smulato was performed world-wde for the 9th of Jue 000 over 4 hours wth a sampl tme of 600 s as well as wth a rd spac of 1. he CA I user performace requremets, whch were used for the adapted RAIM alorthm avalablty smulato, are show the follow table. able. CA I User erformace Requremets [3] arameter Smulato Assumpto Cotuty Rs 10-5 per Approach Iterty Rs 4 10-8 per Approach Vertcal Alarm Lmt (VAL) 10 m me o Alarm (A) 6 s For the adapted RAIM alorthm avalablty smulato, t was addtoally assumed that the HAL s equal to 10 m, that the elevato mas ale s equal to 5, that the correlato tme t C of the measuremet errors s equal to 360 s, that the stadard devato of the GS measuremet errors (wthout selectve avalablty) s equal to 8 m, that the stadard devato of the barometrc altmeter measuremet errors s equal to 50 m, that the omal stadard devato of the LORAN-C measuremet errors s equal to 61.5 m as well as that the stadard devato of the measuremet errors of accurate LORAN-C measuremets s equal to 4 m. Moreover, stead of us the Galleo measuremet error stadard devato specfed by equato (3) for the adapted RAIM alorthm avalablty smulato, a elevato depedet stadard devato (1.1 m - 4.3 m) of the Galleo measuremet errors was used for ths smulato. It was also assumed reard ths smulato that the durato of a CA I approach s equal to 150 s ad that oly oe user, whch coducts a CA I approach, s affected by a satellte
Fure 1. Galleo Satellte ad/or LORAN-C Stato Vsblty at 9th of Jue 000, 01:00:00 (Left: Galleo Satellte Vsblty; Ceter: LORAN-C Stato Vsblty; Rht: Combed Galleo Satellte ad LORAN-C Stato Vsblty) falure, whch s ot detected by the GIC, at a tme. herefore, the CA I cotuty rs rate r CR, whch s - equal to 6.67 10 8 /s, ad the CA I terty rs rate r IR, whch s equal to.67 10-10 /s, were used for the adapted RAIM alorthm avalablty smulato so that the probablty of at least oe udetected falure ( uf ) -8 reard a user recever s ve by uf = r IR t C = 9.6 10 ad the probablty of loss-of-fucto ( lof ) wth respect to ths user recever s determed by lof = r CR t C =.4 10-5. A vsblty smulato for the used Galleo satellte costellato, for the used LORAN-C statos ad for the hybrdzato of Galleo wth LORAN-C showed that the umber of vsble Galleo satelltes s, o averae, equal to 10 at user level,.e. = 10 for Galleo (see Fure 1). hus, the adapted RAIM alorthm avalablty smulato was performed for the follow two cases where t was also tae to accout that md,u (.e. the codtoal probablty of mssed detecto for the user o the codto that a Galleo satellte has faled ad that ths faulty satellte has ot bee detected by the GIC) s determed by equato (15). () Worst case: F = 10-1, md,g = 1 (.e. low Galleo relablty, o roud-based terty motor -8 by the GIC) md,u = 9.6 10 () Good case: F = 10-4, md,g = 9.6 10 - (.e. hher Galleo relablty, roud-based terty -3 motor by the GIC) md,u = 10 Smulato Results he follow fures show the HL, the VL as well as the adapted RAIM alorthm avalablty wth respect to horzotal/vertcal avato at the rd pots of a worldwde rd for the worst case ad for the ood case where t s also cosdered that a user recever uses ether oly Galleo measuremets or Galleo measuremets combato wth GS, LORAN-C ad/or barometrc altmeter measuremets. Fure. Horzotal rotecto Level [m] for Galleo at 9th of Jue 000, 01:00:00 (Left: Worst Case; Rht: Good Case) Fure 3. Vertcal rotecto Level [m] for Galleo at 9th of Jue 000, 01:00:00 (Left: Worst Case; Rht: Good Case)
Fure 4. Adapted RAIM Alorthm Avalablty [%] for Galleo reard Horzotal Navato (Left: Worst Case; Rht: Good Case) Fure 5. Adapted RAIM Alorthm Avalablty [%] for Galleo reard Vertcal Navato (Left: Worst Case; Rht: Good Case) Fure 6. Horzotal rotecto Level [m] for Galleo hybrdzed wth GS at 9th of Jue 000, 01:00:00 (Left: Worst Case; Rht: Good Case) Fure 7. Adapted RAIM Alorthm Avalablty [%] for Galleo hybrdzed wth GS reard Horzotal Navato (Left: Worst Case; Rht: Good Case)
Fure 8. Adapted RAIM Alorthm Avalablty [%] for Galleo hybrdzed wth LORAN-C ad wth Barometrc Altmeter reard Horzotal Navato (σ LORAN-C = 61.5 m; Left: Worst Case; Rht: Good Case) Fure 9. Adapted RAIM Alorthm Avalablty [%] for Galleo hybrdzed wth LORAN-C ad wth Barometrc Altmeter reard Horzotal Navato (σ LORAN-C = 4 m; Left: Worst Case; Rht: Good Case) CONCLUSIONS he curret Galleo basele satellte costellato causes two strpes (world-wde) of poor user terty motor avalablty wth respect to horzotal avato due to sx dyamc areas wth deraded Galleo satellte vsblty,.e. wth oly 8 vsble Galleo satelltes, at user level (see Fure 1 ad Fure 4). Moreover, the fures above also show that the CA I user performace requremets, partcular for vertcal avato, caot be met worldwde ad all the tme. If the GIC cotrbutes to the chec of the (partal) terty of the roud cotrol ad space semets by perform roud-based terty motor, the the user terty motor avalablty reard horzotal avato creases as ca be see from Fure 4. Furthermore, the hybrdzato of Galleo wth GS ehaces the user terty motor avalablty wth respect to horzotal avato too (see Fure 4 ad Fure 7). O the other had, the hybrdzato of Galleo wth LORAN-C ad wth a barometrc altmeter oly sfcatly creases the user terty motor avalablty wth reard to horzotal avato whe a user recever uses accurate LORAN-C measuremets,.e. whe σ LORAN-C = 4 m as ca be see from Fure 4, Fure 8 ad Fure 9. ACKNOWLEDGMENS he authors acowlede the support ad co-operato of the Deutsches Zetrum für Luft ud Raumfahrt e.v. (DLR) wth the project `GNSS- Itertät uter besoderer Berücschtu der Sesorterato m Nutzersemet (Cotract No. FKZ:50 NA 991). REFERENCES [1] Breer, M., Implemetato of a RAIM Motor a GS Recever ad a Iterated GS/IRS, roceeds of he hrd Iteratoal echcal Meet of he Satellte Dvso of he Isttute of Navato, ION GS-90, Colorado Sprs, CO, September 19-1, 1990, pp. 397-406 [] Galleo Overall Archtecture (GALA) Defto Study: erformace Budet Fle, Documet Referece No. GALA-ASI-DD036, Issue No. 1.1, May 5, 000 [3] Global Navato Satellte System ael (GNSS): Local Area Aumetato of GS for the recso Approach of Arcraft, GNSS/WG-D/W-113, Wor Group A, B, C, D, Meet, reseted by Jeff Wllams, Gold Coast, Australa, February 17-8, 1997 [4] LORAN: Lora-C Cha Iformato WGS 84 Coordates, Iteret Ste: http://www.meapulse.com/table.html, Meapulse, Ic., N. Bllerca, MA, 1999 [5] Mmum Operatoal erformace Stadards For Global osto System/Wde Area Aumetato System Arbore Equpmet, RCA Documet No. RCA/DO-9, repared by RCA Specal Commttee 159 (RCA SC-159), RCA, Ic., Washto, D.C., Jauary 16, 1996 [6] Mmum Operatoal erformace Stadards For Global osto System/Wde Area Aumetato System Arbore Equpmet, RCA Documet No. RCA/DO-9B, repared by RCA Specal Commttee 159 (RCA SC-159), RCA, Ic., Washto, D.C., October 6, 1999