GNSS Airborne Multipath Errors Distribution Using the High Resolution Aeronautical Channel Model and Comparison to SARPs Error Curve

Transcription

1 GNSS Arborne Multpath Errors Dstrbuton Usng the Hgh Resoluton Aeronautcal Channel Model and Comparson to SARPs Error Curve Chrstophe Macabau, Laetta Morella, Matheu Ramond, ENAC Cyrl Dupouy, STNA Alexander Stengass, Andreas Lehner, DLR BIOGRAPHY Chrstophe Macabau graduated as an electroncs engneer n 199 from ENAC (Ecole Natonale de l Avaton Cvle) n Toulouse, France. Snce 199, he has been workng on the applcaton of satellte navgaton technques to cvl avaton. He receved hs Ph.D. n 1997 and has been n charge of the sgnal processng lab of the ENAC snce. Laetta Morella wll graduate n 6 as an electroncs engneer from the Ecole Natonale de l Avaton Cvle (ENAC) n Toulouse, France. Matheu Ramond graduated n 5 as an electroncs engneer from the Ecole Natonale de l Avaton Cvle (ENAC) n Toulouse, France. He s currently a Ph.D. student nvolved n the ANASTASIA project. Cyrl Dupouy has been workng for STNA as a consultant engneer n GNSS snce 199. He graduated as an engneer n Aeronautcs from the French Natonal School of Cvl Avaton (ENAC) n 199. After ntally beng nvolved n a number of GNSS experments and studes for STNA, he joned n 1998 the New Landng Systems dvson where he was n charge of GBAS studes and the certfcaton process of GBAS ground equpment. Alexander Stengass was born n Mettmann, Germany n He receved hs Dpl. Ing. Dploma n Electrcal Engneerng n 1997 (Unversty of Ulm, Germany). Snce then he has been a research scentst at the German Aerospace Centre DLR - Insttute of Communcatons and Navgaton. He has been nvolved n several projects n the area of satellte navgaton and locaton dependent moble servces. In he was promoted Dr. Ing. at the Unversty of Essen. Homepage: Emal: alexander.stengass@dlr.de Andreas Lehner was born n Gmunden, Austra n 197. He receved hs dploma engneer degree n mechatroncs from the Unversty of Lnz n 1. Snce then he has been a research scentst at the German Aerospace centre DLR. Homepage: Emal: andreas.lehner@dlr.de ABSTRACT Because of ts coverage, GNSS s a very attractve mean to provde the navgaton servce at every stage of the flght of an arcraft. In ths purpose, the proposed system must comply wth ICAO requrements, whch nclude accuracy and ntegrty requrements. For example, durng the approach, the poston s hghly crtcal nformaton. The system performance durng ths phase of flght can be guaranteed through mtgaton of the error sources and through a relable estmaton of ther characterstcs to protect the users by delverng approprate ntegrty bounds. In the studed case, we are nterested n multpath durng arcraft approaches. Indeed, the sum of drect and reflected sgnals nduces a based measurement affectng the reported poston along the approach path. Ths bas may not be very large, but t needs to be approprately taken nto account n the error budget. Hence, t would be nterestng to compute the statstcs of the error due to multpath so as to predct adequately the measurement error standard devaton and then protect the user through pertnent ntegrty bounds. Ths work was already tackled by RTCA for GPS L1 C/A code users, and the fnal result was a standard curve adopted n the ICAO SARPs statng the standard devaton of the error due to multpath as a functon of the GPS satellte elevaton angle. In the framework of the European ANASTASIA project, whch ams at carryng out research, evaluaton and cost beneft analyss of communcaton and navgaton new technologes, the characterstcs of the error nduced by multpath needs to be determned for an arcraft usng new GNSS sgnals transmtted by future GPS and GALILEO constellatons. In ths purpose, t was decded to use an aeronautcal channel model developed for ESA, coupled to a generc recever smulator. The channel model was developed as a result of a measurement campagn carred out n by DLR, Joanneum Research, and the Unversty of Vgo for ESA. Two planes were used, one as a transmtter and the second as a recever. The second one was performng a landng procedure. Then, a model called hgh resoluton aeronautcal multpath navgaton channel was desgned. Presented at ION NTM 6, Monterey 1

2 Ths model completely descrbes the aeronautcal channel and calculates the characterstcs of the receved sgnal. It s assumed to be composed of a drect ray, and reflected rays from dfferent sources. The model separates the reflected rays n two dfferent knds: fuselage and ground echo. The parameters used n the mplemented channel model were determned thanks to the measurement campagn. The last nvestgated pont s the terran dependence. As explaned above, the parameters of the model were determned thanks to the measurements, so t s lkely that those parameters are not sutable for any other arport, partcularly the ground reflecton. Ths means that each arport wll have ts own parameters. As performng a measurement campagn on each and every arport s not bearable, the valdty of these results need to for any arport needs to be nvestgated. The am of ths paper s therefore to present the estmated standard devaton of the error due to multpath for a landng arcraft usng any new GNSS sgnal. Ths estmaton s provded by the overall conjuncton of the aeronautcal channel model and our GNSS recever smulator. 1. INTRODUCTION The man errors affectng the pseudorange measurements made by an arcraft durng a fnal approach are due to the onosphere, multpath, nterference troposphere and nose. One of the tasks of the ANASTASIA project s to characterze the threat represented by multpath durng the fnal approach for future GNSS recevers, trackng future GPS and GALILEO sgnals. A smlar work had been conducted wthn RTCA years ago for GBAS and SBAS dfferental GPS L1 C/A code users [Booth et al., ]. The man result had been a curve representng the standard devaton of the smoothed trackng errors due to multpath as a functon of the satellte elevaton, adopted by ICAO. To complete that task, t was agreed to use the Hgh Resoluton Aeronautcal channel model developed for ESA [Stengass et al., ], and nject the output multpath parameters nto a software recever smulatng the trackng process for the future GNSS sgnals. Ths multpath model s provded as a Matlab software package by DLR, and we used t as an nput of a GNSS recever smulator, comprsng code and phase trackng loops fed by correlator outputs affected by the multpath sgnals predcted by the channel model. We ran several smulatons along the same path n order to compute statstcs about the error due to multpath dependng on the elevaton. The model allows to compute multpath parameters and so the nvolved error. It s then compared to the ICAO SARPs curve for multpath standard devaton contrbuton. Those results are shown for dfferent recever confguratons (correlator wdth, flter bandwdth, etc.), and the nfluence of ground and fuselage reflectons are compared. The am of ths paper s therefore to present the estmated standard devaton of the error due to multpath for a landng arcraft usng any new GNSS sgnal. Ths estmaton s provded through smulaton by the overall conjuncton of the aeronautcal channel model and our GNSS recever smulator. The paper s organzed as follows: frst we present the ICAO multpath model for GPS L1 C/A. Then the model desgned from measurement at Graz Arport wll be depcted. Our generc GNSS recever smulator s then presented. Then, the modeled multpath errors standard devaton wll be presented for all GNSS sgnals, and contrbuton of each sgnal and recever feature wll be descrbed. Fnally, tests on the valdty of the ground reflecton power are presented.. SARPs ERROR CURVE As stated n [Booth et al., ], an arborne pseudorange accuracy allocaton for dfferental GPS L1 C/A systems was determned by RTCA. That allocaton ncludes the contrbuton of the arborne recever thermal nose and the arborne multpath. A standard model for the standard devaton of the arborne multpath was developed and valdated. The assumed sgma value s specfed to be ncluded n the term used n the weghtng matrx for the poston soluton and n the Protecton Level equatons. The adopted sgma model was proposed n [Murphy and Booth, 1999] and [Murphy and Booth, ], and valdated from efforts made by the FAA, Boeng and Honeywell, manly usng data collected for years durng normal producton flght testng. Through ths jont actvty, the data from 6 dfferent models of Boeng arplanes were collected and analyzed. The paper [Booth et al., ] presents nformaton regardng the work that has been done to valdate the standard multpath error expresson. The authors also stress the dffculty to assess the tals of the dstrbuton of the multpath errors. The study appeared to ndcate that the dstrbuton of arframe multpath errors does depend on the specfc arframe, but that the dstrbutons are smlar enough that a sngle curve may adequately cover all arframes. The adopted curve has the followng expresson, plotted n fgure 1: = exp 1 n meters. σ θ ( ) deg Presented at ION NTM 6, Monterey

3 ICAO STANDARD MULTIPATH SIGMA CURVE Measurement campagn SAT ( 1) σ = exp θdeg Fgure 1: ICAO arbone multpath sgma curve for dfferental GPS L1 C/A systems. Recently, a new measurement campagn was conducted n order to refne ths curve [Murphy et al., 5a], [Murphy et al., 5b]. Indeed, t s beleved that ths curve took nto account other error sources than rather just multpath, and thus a new campagn was launched to check that curve. Among the objectves, t was nterestng to check whether t s necessary to defne separate models for the arframe and ground multpath. As stated by the authors, the new flght test data seem to ndcate that the current arborne multpath model s a reasonable (f slghtly conservatve) representaton of the arframe and ground bounce multpath. It s beleved by the authors n [Murphy et al., 5b] that ther electromagnetc model results are probably a more accurate estmate of the true code phase multpath errors. Consequently, these authors thnk t should be possble to consder a somewhat tghter model. In addton, the new campagn seems to ndcate that the ground echo has a neglgble nfluence on the result. The channel characterstcs were measured usng a channel sounder durng standard ILS approaches, and statc measurements were made wth the arplane on the ground. The approaches were flown at Thalerhof arport of Graz, Austra usng an ATTAS VFW 61. Another arplane was used as the transmttng platform of a sgnal at 1.95 GHz usng a bandwdth of 1 MHz n order to measure the channel mpulse response. In a second step, a helcopter carryng the transmtter crcled the ATTAS VFW 61 plane parked on the ground, whle the reflectons on the plane were measured. To allow an extenson of the measurement results to larger arcrafts, the ground measurements were repeated wth an Arbus A. The channel mpulse response was observed n order to estmate the characterstcs of the dfferent multpath rays (tme delay, ampltude...). Then, these observatons were used to defne the channel model. Fgure s an llustraton of the measurements made.. HIGH RESOLUTION AERONAUTICAL CHANNEL MODEL Along wth the development of GALILEO t became necessary to mprove the knowledge about the aeronautcal channel. Especally the power, the orgn and the delay of the reflectons at the arcraft structure were a man topc n the scentfc dscussons. Durng ths exchange of opnons the lack of nformaton concernng the bandwdth of the reflectons became obvous. For that reason the European Space Agency (ESA) commssoned a contract about a measurement campagn on ths ssue n autumn to a research consortum, consstng of Joanneum Research (Austra), Unversty of Vgo (Span) and the German Aerospace Centre (Germany). The results of the nvestgaton carred out by ths consortum were presented n [Stengass et al., ]. Fgure : Channel mpulse response of the fnal approach n a large tme scale. In fgure, the Lne-Of-Sght sgnal can be seen at ns delay. The other ponts correspond to multpath: the reflected rays have a larger tme delay wth respect to the drect ray and have lower ampltude. The large delay ponts are related to ground reflecton. Ths delay s dependent on the arcraft alttude and s varyng between 9 and 1 ns. The ground reflecton power s varyng between the dfferent flghts but can be estmated n a range of -15 to -5 db. Presented at ION NTM 6, Monterey

4 The delay of the ground reflecton depends on the alttude of the arplane and the elevaton angle of the satellte as d = h sn( θ ). The fadng processes have nput parameters dependent on satellte elevaton and azmuth. The complete aeronautcal channel model s shown n fgure. Fgure : Measured mpulse response-short tme scale. As we can see n fgure, there s qute a strong reflecton very close to the drect sgnal at approxmately 1- ns delay wth a certan modulaton. It has been located on the fuselage near the antenna and called the fuselage echo. The power of ths echo s estmated to -1. db. The measurements do not show any wng reflecton. The results of the measurement campagn show that multpath error s almost due to the fuselage echo and the ground reflecton, and that a zero-delay replca s present, causng LOS sgnal fadng and phase dstorton. Adopted model From the results of the measurement campagn, t was decded that the model would be a drect path (Path ), a refractve component of the drect path (Path 1), an strong echo on the fuselage that s changng very slowly (Path ), and a quckly changng ground echo (Path). The output states of the model wll be the parameters of multpath: tme delay, ampltude and phase. We have seen n the precedent secton that, from measurements, values of tme delay and reflecton power for each ray of ther model were determned. But, the evoluton n tme of multpath parameters needs to be taken nto account. That s why smulatons were made by usng the recorded ptch, yaw and roll flght data to estmate the power spectrum. The ground echo s modulated by the reflectng terran structure. That s why the approach s dvded nto three dfferent zones of alttude (hgh, md and low alttude) n order to characterse the ground reflecton whch s characterzed n each zone by a Markov state. The Markov model descrbed here s specfc at Graz arport. The Markov parameters are the vector of the power values, and the transton matrx P contanng the probablty of changng from each power state determned for each alttude regon ndependently. Fgure : Complete aeronautcal channel model. The frst branch s the drect sgnal, followed by the refractve part modellng the modulaton. The thrd branch models the fuselage echo and the last branch s the ground echo. Examples of outputs The Matlab fles mplementng ths channel model and provded for download on DLR web ste are used n ths applcaton for an arcraft flyng a typcal approach wth an alttude profle as shown n fgure 5. The smulaton nterval s 5s, ncludng a frst s segment wth an alttude descendng rate of.5 m/s, followed by a s segment wth a descendng rate of.8 m/s. Ths profle smulates a generc A GNSS approach procedure ALTITUDE Fgure 5: Arcraft alttude profle. Wth such an alttude profle, the Hgh Resoluton Aeronautcal channel model s used to delver ground and fuselage echo characterstcs such as relatve Presented at ION NTM 6, Monterey

5 ampltude α, phase θ and delay τ w.r.t. the L.O.S. ray for an A. The satellte elevaton angle s assumed to be constant durng the approach, as durng the 5 seconds the satellte elevaton angle does not vary much. The default samplng rate for the output of the multpath parameters, used n ths project, s set to Fs=5. Hz n the channel model Matlab fles. Typcal outputs for elevaton angles of 1 and 7 are shown n the next fgures. SECONDS 6 x 1-6 RELATIVE DELAY OF MULTIPATH COMPONENTS 5 GROUND DELAY FUSELAGE REFR. DELAY FUSELAGE REFL. DELAY..5 RELATIVE AMPLITUDE OF MULTIPATH COMPONENTS GROUND AMP. FUSELAGE REFR. AMP. FUSELAGE REFL. AMP Fgure 9: Relatve delay of multpath components for a satellte angle of 7 (A) Fgure 6: Relatve ampltude of multpath components for a satellte angle of 1 (A). SECONDS x 1-6 RELATIVE DELAY OF MULTIPATH COMPONENTS GROUND DELAY FUSELAGE REFR. DELAY FUSELAGE REFL. DELAY Fgure 7: Relatve delay of multpath components for a satellte angle of 1 (A). RELATIVE AMPLITUDE OF MULTIPATH COMPONENTS GROUND AMP. FUSELAGE REFR. AMP. FUSELAGE REFL. AMP. We can see n fgures 6 and 8 that the relatve ampltude of each rays has dstnct behavours: the ground echo most of the tme has very small ampltude, but sudden hgh peaks (up to.) can be experenced. The fuselage reflecton ampltude s around., and has more fluctuatons for satelltes at low elevaton angles. The zero delay fuselage component has small ampltudes (lower than.5), and ts ampltude decreases qute well when the sat elevaton s ncreasng. As we can see from fgures 5, 7, 9, the delay of the ground reflecton vares lnearly as a functon of the arcraft alttude. It s roughly wthn one mcrosecond durng all the approach for a sat elevaton angle of 1, but at 7 the delay s larger and close to one mcrosecond only durng the last 5s of the approach. Therefore, ths ground reflecton echo may have an nfluence only at low elevaton angles for sgnals wth a chp rate Fc=1. MHz (GPS and GALILEO L1), but neglgble nfluence for hgh chp rate sgnals (GPS L5, GALILEO E5a/E5b) at hgh elevatons. In addton as seen prevously the ampltude varaton of the ground echo s rapd, thus t behaves lke nose. It s lkely to be fltered out by the code-carrer smoothng flter. The delay of the fuselage echoes s very small, set to 1.5 ns and s n the channel model as per the observatons.. RECEIVER SIMULATOR IMPLEMENTATION The multpath parameters generated by the Hgh Resoluton Aeronautcal channel model are then used to generate the correlator outputs usng the followng model: Ip = Qp = = = α K ~ c α K ~ ( ε + τ ) cos( ε + θ ) c τ ( ε + τ ) sn( ε + θ ) τ θ θ Fgure 8: Relatve ampltude of multpath components for a satellte angle of 7 (A). Presented at ION NTM 6, Monterey 5

6 I E = Q E = I L = Q L = = = = = α K ~ ( ε + C + τ ) cos( ε + θ ) c α K ~ α K ~ c c α K ~ ( ε + C + τ ) sn( ε + θ ) ( ε C + τ ) cos( ε + θ ) c τ τ τ ( ε C + τ ) sn( ε + θ ) τ S S S S ~ where Kc ( τ ) = ( h Kc )( τ ) s the fltered autocorrelaton functon of the PRN code. Ths fltered autocorrelaton functon s generated usng the ntal assumptons on the sgnal type (BPSK or BOC) and RF/IF flter characterstcs (flter type and bandwdth). Note that ths model assumes the multpath parameters are constant durng the ntegraton nterval. The code and phase trackng loops mplemented n the recever smulator have the followng parameters. The PLL s a rd order arctan loop wth a bandwdth equal to 1 Hz. The DLL s coupled to the PLL and s a 1 st order loop wth a bandwdth equal to 1 Hz. The DLL can have a dot-product or an Early- Mnus-Late Power dscrmnator. The correlator outputs are assumed to be affected by multpath only, we do not consder here the effect of nose Fgures 1 and 11 show examples of the code measurement errors observed n the recever smulator when njectng a sngle reflected ray wth a constant relatve ampltude equal to.5 and a relatve delay sweepng from to 1.6 chp GPS C/A code chps CODE TRACKING ERROR, GPS L1 C/A Cs=1, INF BW Fgure 1: Observed code trackng error plus theoretcal envelope (BPSK, nfnte bandwdth, wde correlator spacng Cs=1). θ θ θ θ CODE TRACKING ERROR, BOC(1,1) Cs=., INF BW Fgure 11: Observed code trackng error plus theoretcal envelope (BOC(1,1), nfnte bandwdth, narrow correlator spacng Cs=.). As we can see n fgures 1 and 11, the observed error fts wthn the theoretcal error envelope, plotted wth another tool. 5. SIMULATIONS CONFIGURATION The Hgh Resoluton Aeronautcal channel model and the recever smulator are used together to provde an ndcaton of what mpact the multpath has on the pseudorange measurements made by a future GPS/GALILEO recever onboard an arcraft flyng a fnal approach. To ths end, the Matlab mplementaton of the Hgh Resoluton Aeronautcal channel descrbed n secton s run wth the settngs presented here. The assumed arcraft s an A. The smulaton nterval s 5s. The nput alttude profle s as presented n fgure 15: t starts wth a frst s segment wth an alttude descendng rate of.5 m/s, followed by a s segment wth a descendng rate of.8 m/s. Ths profle smulates a generc A approach procedure. The parameters for the channel smulaton are then left unchanged as n the orgnal mplementaton. The propagaton channel s run 5 tmes per satellte elevaton value, from 1 to 7 per 1 steps. That results n 7*5=5 sets of multpath parameters, that are stored and then used dentcally for all the sgnal and trackng varatons presented below. Thus, all sgnals and trackng optons are tested aganst the same channel multpath confguraton. The recever smulator, descrbed n secton, s run wth the parameters presented here. For the results presented here, the DLL type s set to be a dot-product DLL. The sgnal type s frst set as BPSK, wth Fc=1. MHz, as for GPS L1 C/A code. The bandwdth s set to BW=MHz, for a chp spacng Cs=1 chp. Then, for the same sgnal we set BW=16MHz, for a chp spacng Cs=.1 chp. Then, we set Fc=1. MHz, as for GPS L5, GALILEO E5a and GALILEO E5b. The bandwdth s set to BW=MHz, for a chp spacng Cs=.5 chp. Presented at ION NTM 6, Monterey 6

7 Fnally, we set the sgnal type as BOC(1,1), wth Fc=1. MHz as for GALILEO L1. The bandwdth s set to BW=6MHz, for a chp spacng Cs=. chp. Then, the program stores the raw and 1s smoothed code and phase trackng errors at the end of the approach. Two ndependent samples are extracted from the smoothed code trackng error per approach. These two samples are taken separated by at least s, at random epochs n the nterval [s 6s-96s]. The frst nterval bound (s) s chosen so as to elmnate samples where the code-carrer smoothng flter dd not converge. The last nterval bound depends on the lowest alttude consdered for data analyss: 6s s the tme at whch the 5ft alttude s reached, 96s s the tme at whch the 5ft alttude s reached. Two types of results are presented here: statstcs of code trackng error for an arcraft alttude hgher than 5ft, statstcs of code trackng error for an arcraft alttude hgher than. Examples of observed raw and smoothed code trackng errors are shown n fgures 1, 1, 1, CODE TRACKING ERROR RAW SMOOTHED Fgure 1: Example smulated raw and smoothed code trackng error (GPS L5 GALILEO E5a/E5b, BW=MHz, Cs=.5, 1 sat) CODE TRACKING ERROR RAW SMOOTHED CODE TRACKING ERROR RAW SMOOTHED Fgure 1: Example smulated raw and smoothed code trackng error (GPS L1 C/A, BW=MHz, Cs=1, 1 sat) CODE TRACKING ERROR RAW SMOOTHED Fgure 15: Example smulated raw and smoothed code trackng error (GALILEO L1 BOC(1,1), BW=6MHz, Cs=., 1 sat). Fgures 1,1,1,15 show the nherent resstance of each recever confguraton to the same multpath. The observed error s reduced from the GPS L1 C/A wde chp spacng recever, to the BOC(1,1), narrow correlator and hgh chppng rate sgnal Fgure 1: Example smulated raw and smoothed code trackng error (GPS L1 C/A, BW=16MHz, Cs=.1, 1 sat). 6. VALIDITY: RESULTS FOR GPS L1 C/A The followng smulatons have been made wth GPS L1 C/A code (FC=1. MHz) to compare the results wth the ICAO SARPs curve. Fgure 16 shows the estmated standard devaton for a double sded bandwdth BW = MHz, a chp spacng C S =1, and trackng loops bandwdths such as B PLL =1 Hz, B DLL =1 Hz. Presented at ION NTM 6, Monterey 7

8 ESTIMATED STD OF MULTIPATH ERROR (1 s SMOOTHING) - GPS L1 C/A, BW=MHz, Cs=1 - ALT>5 ft ALT>= ICAO SPECS ALT>5 ft (99%) ALT>= (99%) Fgure 18 shows the observed dstrbuton of the smoothed code trackng errors for satellte elevatons 1 and ERROR HISTOGRAM (ELEVATION = 1 and 7 DEG) ALT>5 ft 1 ALT>= 1 ALT>5 ft 7 ALT>= OCCURENCE RATE.15.1 Fgure 16: Smoothed pseudorange error sgma compared to SARPS model (GPS L1 C/A, BW= MHz, C S =1 chp, 5 approaches per sat elevaton, A). As we can see n fgure 16, the resultng sgma s almost constant wth elevaton, between 6 cm and 7 cm, and s lower than SARPs curve. Ths s mostly explaned by the fact that the ground echo does not contrbute much to the fnal error, as t mostly behaves lke a hgh frequency error. Usng tradtonal confdence nterval theory on estmated varance wth unknown mean, 99% bounds are also plotted, takng nto account the fact that only 1 ndependent samples taken out of the smulator are consdered for each elevaton angle ( ndependent samples per smulated approach). Fgure 17 shows the rato between the standard devaton of the raw code trackng error and the standard devaton of the smoothed trackng error. Ths rato s labeled here the code-carrer smoothng effectveness factor, as n [Murphy and Booth, 5b]. 1 CODE-CARRIER SMOOTHING EFFECTIVENESS FACTOR ALT>5 ft ALT>= ERROR IN Fgure 18: Observed dstrbuton of smoothed code trackng errors for elevatons 1 and 7 (GPS L1 C/A, BW= MHz, C S =1 chp, ground reflecton ampltude, 5 approaches per sat elevaton, A). As we can see n fgure 18, the dstrbuton les roughly n [-.m.m] at 1 and les n [-.1m.1m] at 7. Also, ths dstrbuton does not look lke a Gaussan dstrbuton. For low elevaton angles, such as 1, the dstrbuton s skewed, and therefore the trackng error has a small bas of 1.5 cm. At hgh elevaton angles, the dstrbuton resembles a unform dstrbuton, wth peaks at both ends, stll exhbtng a bas smaller than mm. As an llustraton, fgure 19 shows the unsmoothed code trackng error dstrbuton..5. ERROR HISTOGRAM (ELEVATION = 1 and 7 DEG) ALT>5 ft 1 ALT>= 1 ALT>5 ft 7 ALT>= RATIO 8 OCCURENCE RATE Fgure 17: Code-carrer smoothng effectveness factor (GPS L1 C/A, BW= MHz, C S =1 chp, 5 approaches per sat elevaton, A). If the raw code trackng error was pure whte nose, ths rato should be close to We see n fgure 18 that the observed rato s close to 8 at 1, and decreases to at 7. Ths result shows that the raw code trackng error due to multpath exhbts a very hgh correlaton factor at hgh elevaton angles, and resembles whte nose at low elevaton angles ERROR IN Fgure 19: Unsmoothed code trackng error dstrbuton at 1 and 7 (GPS L1 C/A, BW= MHz, C S =1 chp, 5 approaches per sat elevaton, A). As we can see n fgure 19, the unsmoothed code trackng errors are mostly dstrbuted n [-.m.m], but many large errors do exst. Fgure shows the estmated standard devaton for a double sded bandwdth BW = MHz, C S =1, B_PLL=1 Hz, B_DLL=1 Hz, no ground reflecton: Presented at ION NTM 6, Monterey 8

9 .5 SMOOTHED ERROR HISTOGRAM (ELEVATION = 1 and 7 ) ALT>5 ft 1..5 ESTIMATED STD OF MULTIPATH ERROR (1 s SMOOTHING) - GPS L1 C/A, BW=MHz, Cs=1 - ALT>5 ft ALT>= ICAO SPECS ALT>5 ft (99%). ALT>= 1 ALT>5 ft 7 ALT>= 7 ALT>= (99%)..5. OCCURRENCE RATE Fgure : Smoothed pseudorange error sgma compared to SARPS model (GPS L1 C/A, BW= MHz, C S =1 chp, no ground reflecton, 5 approaches per sat elevaton, A). Resultng sgma s slghtly smaller, stll between 6 cm and 7 cm, smlar to prevous result wth all multpath components, so ground reflecton does not contrbute much: the man contrbutor s the fuselage echo. Fgure 1 shows the code-carrer smoothng effectveness factor n the case where no ground reflecton s present. 1 1 CODE-CARRIER SMOOTHING EFFECTIVENESS FACTOR ALT>5 ft ALT>= ERROR IN Fgure : Observed dstrbuton of smoothed code trackng errors for elevatons 1 and 7 (GPS L1 C/A, BW=16 MHz, C S =.1 chp, no ground reflecton, 5 approaches per sat elevaton, A). As we can see n fgure, the dstrbuton les roughly n [-.1m.15m]. Ths dstrbuton does not look lke a Gaussan dstrbuton and resembles more a unform dstrbuton, wth peaks at both ends, exhbtng a bas smaller than mm. Fgure shows the estmated standard devaton for a double sded bandwdth BW=16 MHz, CS=.1, B_PLL=1 Hz, B_DLL=1 Hz...5 ESTIMATED STD OF MULTIPATH ERROR (1 s SMOOTHING) - GPS L1 C/A, BW=MHz, Cs=1 GROUND AMP x - ALT>5 ft ALT>= ICAO SPECS ALT>5 ft (99%) ALT>= (99%) RATIO Fgure 1: Code-carrer smoothng effectveness factor (GPS L1 C/A, BW= MHz, C S =1, no ground reflecton, 5 approaches per sat elevaton, A). As we can see n fgure 1, smoothng does not mprove ths error at all because t mostly has behavour close to a bas n tme for each run. Ths can also be seen n the error dstrbuton, not shown here, that s very smlar to the smoothed code error dstrbuton, shown n fgure Fgure : Smoothed pseudorange error sgma compared to SARPS model (GPS L1 C/A, BW=16 MHz, C S =.1 chp, 5 trals per elevaton, A). As we can see n fgure, the resultng sgma s between 6 and 7 cm. Fgure shows the code-carrer smoothng effectveness factor. Presented at ION NTM 6, Monterey 9

10 CODE-CARRIER SMOOTHING EFFECTIVENESS FACTOR ALT>5 ft ALT>= Fgure 6 shows the code-carrer smoothng effectveness factor. 1 1 CODE-CARRIER SMOOTHING EFFECTIVENESS FACTOR ALT>5 ft ALT>= RATIO 6 8 RATIO 6 Fgure : Code-carrer smoothng effectveness factor (GPS L1 C/A, BW=16 MHz, C S =.1 chp, 5 approaches per sat elevaton, A). As we can see n fgure, smoothng does not mprove ths error very much because t mostly has behavour close to a bas n tme for each run. Ths can also be seen n the unsmoothed error dstrbuton, not shown here, that s very smlar to the smoothed code error dstrbuton. 7. RESULTS FOR L5, E5a, E5b The followng smulatons have been made wth GPS L5 or GALILEO E5a or GALILEO E5b code characterstcs (F C =1. MHz). Fgure 5 shows the estmated standard devaton for a double sded bandwdth BW = MHz, C S =.5, B_PLL=1 Hz, B_DLL=1 Hz.. ESTIMATED STD OF MULTIPATH ERROR (1 s SMOOTHING) - GPS L5, GALILEO E5a/E5b, BW=MHz, Cs= Fgure 6: Code-carrer smoothng effectveness factor (GPS L5, GALILEO E5a/E5b, BW= MHz, B_PLL=1 Hz, B_DLL=1 Hz, C S =1 chp, 5 approaches per sat elevaton, A). As we can see n fgure 6, smoothng does not mprove ths error at all because t mostly has a behavour close to a bas n tme for each run. Ths can also be seen n the unsmoothed code error dstrbuton, not shown here, that s very smlar to the smoothed code error dstrbuton, shown n fgure 7. Fgure 7 shows the smoothed pseudorange error dstrbuton..5. ERROR HISTOGRAM (ELEVATION = 1 and 7 DEG) ALT>5 ft 1 ALT>= 1 ALT>5 ft 7 ALT>= 7.5 ALT>5 ft ALT>= ICAO SPECS ALT>5 ft (99%) ALT>= (99%) OCCURENCE RATE Fgure 5: Smoothed pseudorange error sgma compared to SARPS model (GPS L5, GALILEO E5a/E5b, BW= MHz, B_PLL=1 Hz, B_DLL=1 Hz, C S =.5 chp, 5 approaches per sat elevaton, A). As we can see n fgure 5, the estmated sgma s of the same sze than for GPS L1 C/A code case, roughly constant between 6 and 7 cm. Other smulatons made n that case wth a reduced bandwdth BW=16MHz and Cs=.5, and generally wth a narrow chp spacng dd not show any notceable change n the results ERROR IN Fgure 7: Smoothed pseudorange error sgma compared to SARPS model (GPS L5, GALILEO E5a/E5b, BW= MHz, B_PLL=1 Hz, B_DLL=1 Hz, C S =.5 chp, 5 approaches per sat elevaton, A). As we can see n fgure 7, the dstrbuton les roughly n [-.1m.15m]. Ths dstrbuton does not look lke a Gaussan dstrbuton and resembles more a unform dstrbuton, wth peaks at both ends, exhbtng a bas smaller than mm. 8. RESULTS FOR GALILEO L1 BOC(1,1) Presented at ION NTM 6, Monterey 1

11 The followng smulatons have been made wth GALILEO L1 BOC(1,1) sgnal characterstcs (F C =1. MHz, Fs=1. MHz). Fgure 8 shows the estmated standard devaton for a double sded bandwdth BW =6 MHz, C S =., B_PLL=1 Hz, B_DLL=1 Hz. Fgure shows the smoothed code error dstrbuton for elevaton angles 1 and ERROR HISTOGRAM (ELEVATION = 1 and 7 DEG) ALT>5 ft 1 ALT>= 1 ALT>5 ft 7 ALT>= 7. ESTIMATED STD OF MULTIPATH ERROR (1 s SMOOTHING) - GALILEO L1 BOC(1,1), BW=6MHz, Cs= ALT>5 ft ALT>= ICAO SPECS ALT>5 ft (99%) ALT>= (99%) OCCURENCE RATE Fgure 8: Smoothed pseudorange error sgma compared to SARPS model (GALILEO BOC(1,1), BW=6 MHz, B_PLL=1 Hz, B_DLL=1 Hz, C S =. chp, 5 approaches per sat elevaton, A). Resultng sgma s smlar to GPS L1 C/A code case, as t s between 6 cm and 7 cm. Fgure 9 shows the code-carrer smoothng effectveness factor for GALILEO L1 BOC(1,1), BW =6 MHz, C S =.. RATIO CODE-CARRIER SMOOTHING EFFECTIVENESS FACTOR ALT>5 ft Fgure 9: Code-carrer smoothng effectveness factor (GALILEO L1 BOC(1,1), BW=6 MHz, C S =. chp, 5 approaches per sat elevaton, A). As we can see n fgure 9, the smoothng effectveness factor decreases as the elevaton angle ncreases. But ths factor s very small, only decreasng from to 1. Ths means that the GALILEO BOC(1,1) trackng error reducton factor s qute lmted, whch s an ndcaton that the error s hghly correlated. Ths s a general result already observed wth large bandwdth and narrow correlator recevers durng ths study. That seems to reflect the fact that rapdly changng errors are elmnated by the recever ALT>= ERROR IN Fgure : Smoothed pseudorange error dstrbuton for sat elevaton angles 1 and 7 (GALILEO BOC(1,1), BW=6 MHz, C S =. chp, 5 approaches per sat elevaton, A). As we can see n fgure, the dstrbuton of the smoothed code trackng errors les roughly n [-.1m.15m]. Ths dstrbuton does not look lke a Gaussan dstrbuton and resembles more a unform dstrbuton, wth peaks at both ends, exhbtng a bas smaller than mm. 9. GROUND REFLECTION POWER ADAPTATION In order to test the mportance of the ground reflecton power on the fnal estmated sgma, we have conducted several tests. The two man tests that were conducted conssted n multplyng the ampltude of the relatve ampltude of the ground reflecton by, and n amplfyng t n such a way that the GPS L1 C/A estmated sgma curve matches roughly the standard L1 sgma curve. Fgure 1 shows the estmated standard devaton for a double sded bandwdth BW= MHz, CS=1, B_PLL=1 Hz, B_DLL=1 Hz, ampltude of ground reflecton multpled by ESTIMATED STD OF MULTIPATH ERROR (1 s SMOOTHING) - GPS L1 C/A, BW=MHz, Cs=1 GROUND AMP x - ALT>5 ft ALT>= ICAO SPECS ALT>5 ft (99%) ALT>= (99%) Fgure 1: Smoothed pseudorange error sgma compared to SARPS model (GPS L1 C/A, BW= MHz, Presented at ION NTM 6, Monterey 11

12 C S =1 chp, ground reflecton ampltude, 5 approaches per sat elevaton, A). As we can see n fgure 1, the resultng sgma s stll lower than SARPs curve, but the observed value does ncrease at low elevaton angles compared to fgure 16 where the channel model s used wth ts ntal settngs. The maxmum value s 1 cm at 1. Ths s mostly explaned by the fact that the ground echo does not contrbute much to the fnal error, as t mostly behaves lke a hgh frequency error. We can also see n fgure 1 that the standard devaton of the smoothed code trackng error s smaller for samples taken when alttude s larger than 5 ft than for samples taken even when the arcraft s on the ground. Ths can be explaned by the fact that the GPS L1 ground echo has an ncreasng nfluence on the trackng error when the arcraft alttude s decreasng for a narrow bandwdth wde chp spacng GPS L1 C/A recever. Increasng the ground echo ampltude by a factor of causes the trackng loops to lose lock, and therefore ths ncrease by a factor s the maxmum reasonable ncrease whch s consdered. Another test was conducted to adapt ths ground reflecton power: the Markov state powers were ncreased n the model up to a level suffcent for the obtaned sgma curve for GPS L1 C/A wde chp spacng BW=Mhz to match the SARPs sgma curve. Ths enormous ncrease n ground power level had no notceable nfluence on the results obtaned for GPS L1 C/A narrow correlator, GPS L5 GALILEO E5a/E5b and GALILEO L1 BOC(1,1). Therefore, t was decded that no adaptaton of ground power echo was useful as ts nfluence s only notceable for GPS L1 C/A narrowband wde chp spacng recevers. Tests were also conducted wth nomnal channel settngs and a reduced DLL bandwdth n varous confguratons, that yelded exactly the same results: the ground contrbuton s so fast that t s wped out by the trackng loop and smoothng. 1. CONCLUSION A smulator usng the Hgh Resoluton Aeronautcal channel together wth a recever smulator has been bult and used to determne statstcs of the code trackng errors for GPS L1 C/A, GPS L5, GALILEO E5a, GALILEO E5b and GALILEO BOC(1,1) sgnals. The major contrbutor to the pseudorange error s n all cases the fuselage reflecton, although t has a very short delay (1.5 ns). Reducng the DLL chp spacng has a favourable mpact on the reducton of the measurement error for a chp rate of 1. MHz, but has no mpact for a chp rate of 1. MHz. Moreover, reducng the loops bandwdth seems useless because of the very slow varatons of ths fuselage echo. As only the arcraft structure has a sgnfcant effect, the relatve delay s very small and vares slowly, so a unque sgma curve can be proposed for all GNSS sgnals. Ths sgma curve s flat and can be assumed to be a constant standard devaton of 7 cm for any elevaton. We have notced that the computed sgma s smaller than SARPs curve for all the smulatons when usng the Hgh Resoluton Aeronautcal channel model wth ts default settngs. For GPS L1 C/A code, ths devaton s assumed to be due to the small effect of the ground reflecton power level, representatve of the Graz arport approach. The valdty of ths ground echo parameter has been nvestgated. Several optons were consdered, and t was fnally determned that when the ground echo characterstcs are set to match the L1 C/A SARPs error curve for wde chp spacng recevers, the observed error sgma for narrow correlator recevers, hgh chp rate sgnals and BOC(1,1) sgnal agan converges to the flat 7cm curve. It s however useful to note that the ground echo characterstcs has no nfluence on GPS L5, GALILEO E5a, GALILEO E5b sgnals because of ts very large relatve delay compared to the 1. MHz chp length. ACKNOWLEDGMENTS The authors want to acknowledge the help of all the people that supported or partcpated to the nvestgatons. Note: ANASTASIA Project (AIP-CT ) receves research fundng from the European Communty s 6th framework Programme (DG research). REFERENCES [Booth et al., ], J. Booth, T. Murphy, B. Clark, F. Lu, Valdaton of the Arframe Multpath Error Allocaton for Local Area Dfferental GPS, Proceedng of the IAIN/ION Meetng, June [Murphy and Booth, 1999], T. Murphy; J. Booth: GBAS SARPs Revew and Valdaton of Arborne Multpath Requrements, GNSSP WG B Toulouse 1/99 WP [Murphy and Booth, ], T. Murphy; J. Booth: GBAS SARPs Revew and Valdaton of Arborne Multpath Requrements, (Sectons B and B ), GNSSP WG B Canberra Jan [Murphy et al., 5a], T. Murphy, M. Harrs, J. Booth, P. Geren, T. Pankaske, B. Clark, J. Burns, T. Urda, Results from the Program for the Investgaton of Arborne Multpath Errors, Proceedngs of the ION Natonal Techncal Meetng Jan 5 [Murphy et al., 5b], T. Murphy, M. Harrs, P. Geren, T. Pankaske, B. Clark, J. Burns, More Results from the Investgaton of Arborne Multpath Errors, Proceedngs of the ION GNSS 5 [Stengass et al., ], A. Stengass, A. Lehner, F. Pérez Fontán, E. Kubsta, M. Jesús Martín and B. Arbesser-Rastburg, The Hgh Resoluton Aeronautcal Multpath Navgaton Channel, proceedngs of ION GPS. Presented at ION NTM 6, Monterey 1