Airport Multipath Simulation for Siting DGPS Reference Stations

Transcription

1 Airport Multipath Simulatio for Sitig DGPS Referece Statios Christophe Macabiau ad Beoît Roturier CNS Research Laboratory of the ENAC Eric Chatre STNA Alai Reard SETANT AVIONIQUE Preseted at ION NTM 99 o Jauary 5th, 1999 BIOGRAPHY Christophe Macabiau is a Post-Doctoral researcher at the Ecole Natioale de l Aviatio Civile (ENAC) i Toulouse, Frace. After workig i 1993 for the MLS Project Office i Ottawa, Caada, he received his Ph.D. from the Laboratoire de Traitemet du Sigal et des Télécommuicatios of the ENAC i He is curretly workig o the applicatio of code ad phase LADGPS positioig techiques to aeroautics. Beoît Roturier graduated as a electroics egieer i 195 from the Ecole Natioale de l Aviatio Civile (ENAC), Toulouse, Frace. After workig for 1 moths at Tahiti Faaa airport, Frech Polyesia, he led the Istrumet Ladig Team at the Service Techique de la Navigatio Aériee (STNA) i Paris from 197 to 199. Sice 199, he has bee teachig ad doig research at the ENAC, he is curretly i charge of the CNS Research Laboratory. He obtaied his Ph.D. i 1995 from the Istitut Natioal Polytechique de Toulouse (INPT). His curret research area is propagatio modelig for aeroautical telecommuicatio systems. Eric Chatre graduated as a electroics egieer i 199 from the ENAC (Ecole Natioale de l Aviatio Civile), Toulouse, Frace. Sice 1994, he has bee workig with the Service Techique de la Navigatio Aériee (STNA) i Toulouse. He is ivolved i GNSS stadardizatio activities i ICAO GNSSP ad EUROCAE, RTCA forums. Alai Reard is a GPS expert i the Advaced Studies divisio of the Navigatio Departmet of SETANT AVIONIQUE. After graduatig i 197 as a egieer from the Ecole Natioale Supérieure d Electroique et de Radioélectricité of Greoble, he worked o radioavigatio systems for commercial aircraft from 1973 to 197. The, he developed radioavigatio systems based o OMEGA util 19. Sice 19, he has bee desigig GPS ad GLONASS avigatio uits. ABSTRACT 1 The sitig of a GPS referece statio o a airport is achieved by miimizig the ifluece of the eviromet o the pseudorage measuremets, while complyig with the practical operatioal istallatio costraits. The CNS Research Laboratory (URE-CNS) of the ENAC, i collaboratio with the STNA ad SETANT AVION- IQUE, has started a study that aims at providig sitig guidelies for the Frech Civil Aviatio Authority. As a result, a tool is developed, based o computed error predictios usig mathematical models, ad o sigal disturbace measuremets at preselected locatios. The first part of this tool is a ed-to-ed GPS simulator that is used to establish the mai basic rules for the choice of the best locatio of the statio o a airport with regards to multipath effects. Its goal is to aalyse the measuremet errors iduced by simple obstacles. The aim of the proposed paper is to preset the simulatio software which was developed ad some examples of the results it ca provide. The simulator is comprised of three cascaded modules. The first module computes the positio of the satellites with a time step larger tha the time of coherece of the propagatio chael. The secod module simulates the propagatio chael. It is derived from the raytracig MUSICA tool (MUltipath SImulatio for Civil Aviatio) that was previously developed by the ENAC for classical avaids multipath simulatio. Usig the chael trasfer fuctio determied through the Uiform Theory pof Diffractio, it geerates the disturbed sigal delivered by the atea of the statio to its receiver frot-ed. The, this sigal is haded to the last module, that simulates a geeric GPS receiver ad delivers the rage measuremet errors iduced by the perturbatios itroduced i the whole propagatio chael. The examples chose show the ability to predict the ifluece of reflectig ad diffractig objects, such as the groud ad buildigs o the code ad phase measuremet errors. I. INTRODUCTION The pseudorage measuremets made by a GPS receiver are disturbed by a combiatio of differet errors such as satellite clock bias ad SA, atmospheric propagatio errors, trackig loop oise, ad errors iduced by the multipath propagatio of the sigal. The amplitude

2 ad phase of the reflected ad diffracted sigals reachig the atea deped o a high umber of factors. Amog them are the ature ad size of the diffractig obstacles, the relative locatio ad orietatio of the receivig atea with respect to these obstacles, the patter ad polarizatio of the atea, ad the processig operatios performed withi the receiver. Therefore, the multipath-iduced errors affectig the measuremets made by two distat receivers are differet. As a cosequece, the pseudorage correctios broadcast by a Local Area DGPS referece statio ca cotamiate the measuremets made by the user receiver with multipath errors that are proper to the referece statio. The multipath errors affectig the pseudorage correctios trasmitted by the referece statio ca be reduced i several ways, icludig careful sitig, good atea desig, ad adequate sigal processig. The study reported i this paper is focused o the selectio of the sitig locatio of the receivig ateas of a LADGPS referece statio. The perturbatios caused by a complex airport eviromet o the pseudorage correctios trasmitted by a Local Area DGPS referece statio are difficult to determie because the trasmittig satellites are i costat movemet ad because small obstacles ca geerate sigificatly disturbig sigals. Therefore, it is ecessary to elaborate a powerful tool to help the civil aviatio authorities to select the best locatios to istall the referece statios. The fuctioal priciple of the sitig tool ca either be based o sigal disturbace measuremets at preselected locatios or o computed error predictios based o mathematical models. Although both tools have major drawbacks, they are complemetary. Ideed, while the actual measuremets correspod to real life situatios, the variety of the field observatios is restraied by physical costraits, ad the assessmet of all the safety critical situatios is ot possible i practice. O the other had, the coformace of the simulatios to reality is limited by the adequacy of the mathematical models, but iitial results ca be obtaied faster for a very high umber of represetative situatios, ivolvig typical simple objects. Therefore, the complete sitig tool is built i two steps: first, a simulator is implemeted, the a measurig istrumet is developed, ad both compoets are used i parallel to achieve our goal. Several papers were published to report the work carried out o the predictio of evirometal effects o GPS measuremets, ad the defiitio of obstacle clearace areas. [Gomez S. et al, 1995] ad [Lippicott et al., 1996] have used the Uiform Theory of Diffractio to model GPS sigal stregth ad phase shift geerated by the obstacles, while [Walker R. et al, 1996] have used a parabolic equatio techique. [Perez Fota F. et al, 199] applied their aalysis to civil aviatio, ad [Braasch M., 199], [Weiser M., 199] have focused o airport operatio. Our software combies propagatio simulatio ad receiver simulatio to provide straight predictios of measuremet errors. The program, iitially preseted i [Macabiau et al., 199], treats multipath as a perturbatio of the whole trasfer fuctio of the propagatio chael. The sigal is ot modeled as a discrete sum of delayed ad atteuated replicas, but as a trasmitted sigal modified by the trasfer fuctio of a global propagatio chael. Therefore, our program takes ito accout most of the effects degradig the pseudorage measuremets. The validatio of this simulatio software is a importat step. It is doe i two stages. First, the results obtaied from the simulatios are compared with the theoretical results correspodig to the simulated situatios, i order to check for flaws i the desig ad i the implemetatio of the algorithms. Next, measuremet errors obtaied i particular situatios are compared to the errors predicted by the simulator for the same situatios, as modeled by the users. The choice of the situatios is critical, as they must be modeled as precisely as possible i order to be simulated with our software, ad theoretical results must be available for these situatios. I this paper, we first describe the mai poits of the simulatio software, such as its architecture ad the uderlyig theoretical priciples of the propagatio ad receiver modules. Next, we make a short itroductio of the examples preseted i this paper. The, we show some examples of the results obtaied usig the software i differet situatios, like reflectio from a groud plate, ad diffractios from complex obstacles like buildig walls ad edges. Fially, a coclusio is draw from this study. II. PRESENTATION OF SIMULATION SOFTWARE The ed-to-ed GPS simulator is software that simulates the effect of multipath o a GPS receiver. The iput data is the positio of the satellites at various epochs. The output data are the GPS observatio errors, such as the pseudorage measuremet errors. Time Almaac Sigal fed to satellite atea CONSTELLATION Receiver Positio Satellites positios Obstacle Parameters PROPAGATION Samplig Frequecy Ateas Parameters R.F. frot-ed Received sigal Loops Parameters RECEIVER Noise Bits/ Model sample Figure 1: Data ow i the simulator. Measuremet Errors

3 The simulatio is doe usig three processig modules writte i MATLAB 5., that exchage data as illustrated i figure 1: The costellatio module determies the positios of the GPS satellites i the WGS-4 referece frame usig the iput almaac file ad the specified trasmissio time. The period used to sample the positio of the satellites is equal to the samplig period of the trasfer fuctio of the propagatio chael. The propagatio module combies ray-tracig software based o the Uiform Theory of Diffractio adapted to GPS sigals, ad a sigal geerator that computes the basebad equivalet spectrum of the disturbed sigal received from a particular satellite by the receivig atea. The received sigal is computed by filterig the sigal fed to the trasmittig atea of the satellite by the calculated trasfer fuctio of the chael. The receiver module cotais a model of a GPS receiver that simulates the operatios performed by a receiver, i order to determie the measuremet errors iduced by multipath. The program computes the code ad phase trackig errors by searchig for the code ad phase delay estimates that cacel the PLL ad DLL cotrol sigals. Specific models of the propagatio chael ad of the receiver processig operatios were developed ad iserted i the simulator. The propagatio chael is modeled as a liear time variat filter c, as preseted i equatio (1): Z +1 r(t) = e(t ; )c( t)d (1) ;1 e is the sigal fed to the trasmittig atea of the satellite. I our case, e is the power wave set to the atea. r is the sigal delivered by the receivig atea. I our case, r is the power wave set to the receiver frot-ed. is the argumet of the weightig fuctio c used to compute the filter output r. t is the time at which the trasfer fuctio of the chael is applied. I order to reduce the computatio time, the propagatio chael is sampled with a time iterval larger tha the iteral samplig period of the receiver. As explaied i [Macabiau et al., 199], the trasfer fuctio is determied with a period lower tha the time of coherece of the chael, which is of the order of a few secods. At 3 each oe of these samplig epochs, the characteristics of the chael are assumed to be costat, ad a short slice of the received sigal is geerated. Therefore, for each of the samplig epochs p of the trasfer fuctio of the chael, the received sigal (1) ca be expressed as: +1 r p () = e( ; m)c p (m) () m=;1 p represets the time at which the trasfer fuctio of the chael is sampled. describes the time evolutio of the received sigal. m is the argumet of the filter memory c The frequecy domai equivalet of () is R p (k) =C p (k)e(k) (3) The trasfer fuctio R p (k) is determied by the propagatio module for each frequecy kf aroud L1. The Shao theorem states that a sigal must be sampled at a rate larger tha twice the badwidth of its Fourier trasform. As recalled i [Macabiau et al., 199], the badwidth of the Fourier trasform of the trasfer fuctio of the chael is the multipath delay spread of the chael. Therefore, the trasfer fuctio of the chael is sampled with a frequecy step f lower or equal to half the coherece badwidth f c of the chael. f < 1 f c (4) The trasfer fuctio R p (k) is determied by the ray-tracig software. The kerel of this software, called MUSICA (MUltipath SImulatio for Civil Aviatio) was developed by the ENAC for classical avaids [Roturier B., 1996]. This part of the software is based o the Uiform Theory of Diffractio (UTD). The electromagetic field radiated by the satellite atea i ay poit of polar coordiates [r '] ca be modeled as preseted i equatio (5). e ~E(r ')= p6p ;ikr T G Tmax F T ( ') r ITx j I ~ ~ T j Tx + ITy ~ j I ~ T j Ty + ITz j I ~ ~ T j Tz (5) P T is the power of the sigal fed to the atea. k = f c wave. is the waveumber of the trasmitted G Tmax is the maximum field gai of the trasmittig atea.

4 F T is the ormalized field radiatio patter of the trasmittig atea. ~ I T is the complex curret vector of the trasmittig atea. Its complex compoets [I Tx I Ty I Tz ] are as depicted i figure. ~ Tx, ~ Ty, ~ Tz are uit vectors defiig the polarizatio of the radiated field, all orthogoal to the directio of propagatio. For example, The vector ~ Tx is defied as ~ Tx = (~ U x^~r)^~r j I ~, U ~ T ^~rj x is the vector defiig the x axis. F R is the ormalized field radiatio patter of the receivig atea. ~ I R is the complex curret vector of the receivig atea. Its complex compoets [I Rx I Ry I Rz ] are as depicted i figure 3. ~ Rx, ~ Ry, ~ Rz are uit vectors defiig the polarizatio of the icomig field, all orthogoal to the directio of propagatio. For example, the vector ~ Rx is defied as ~ Rx = (~ U x^~r)^~r j I ~, U ~ x is R^~rj the vector defiig the x axis. z θ r z θ Phase ceter of Trasmittig atea x O I T x I T z I T y ϕ r θ R x Figure : Polarizatio of the trasmitted wave w.r.t the orietatio of the trasimittig atea. The computatio of the electric field compoet is based o the ray theory. The electromagetic ray is the portio of space that cotributes sigificatly to the trasport of the electromagetic eergy. This volume ca be assimilated to the first Fresel zoe. There are 5 types of rays, sorted by decreasig power: the direct ray, the reflected rays, the kife-edge diffracted rays, the corer diffracted rays ad the creepig rays. The rays that reach the receiver ca have followed a complex path, resultig from several successive iteractios with obstacles. The iteractio betwee the electromagetic wave ad a object is computed i two steps: first the rays are traced, the the reflexio ad diffractio coefficiets are computed. The complex power wave R i delivered by the icidet ray i is modeled as i equatio (6): 1 R i (f )= k p G R max F R ( ') 1 IRx j ~ I Rj ~ Rxi : ~ E i + IRy j ~ I Rj ~ Ryi : ~ E i + IRz j ~ I Rj ~ Rzi : ~ E i (6) G Rmax is the maximum field gai of the receivig atea. y Phase ceter of receivig atea x ri I R x I R z O θ R x ϕ I R y Figure 3: Polarizatio of the received wave w.r.t the orietatio of the receivig atea. The trasmitted power P T, ad the maximum field gais G Tmax ad G Rmax are costat throughout the simulatio. For each ray i, for each positio of the satellites, ad for each evaluatio frequecy kf, MUSICA uses F T, F R, I ~ T, ad I ~ R, to compute the icidet field ~E i, as well as the resultig power wave R i (kf ) delivered by the atea. The total P power wave delivered by N(t) the atea is R(kf )= i= R i(kf ). The trasfer fuctio of the propagatio chael is the defied as: N(t) R i (k) i= C p (k) = p (7) PT The sigal eterig the receiver frot-ed is the result of the filterig of the iput sigal e by the propagatio chael c. The sigal fed to the satellite atea is modeled as: p e(t) = P T C(t)D(t)cos(f t ; ) () C is the C/A code of the trasmittig satellite. D is the avigatio message. f is the omial L1 frequecy. is a iitial radom phase. y 4

5 This sigal is a arrow bad sigal that ca be modeled usig the equivalet low pass sigal e LP such as e(t) =< e LP (t)e ift (9) <fg is the real part operator. We ca see that the equivalet low pass sigal is ecessarily complex: p e LP (t) = P T C(t)D(t)e ;i (1) Similarly, the received sigal r(t) is also a arrow bad sigal. Therefore, we ca defie r LP (t) such that r(t) =< r LP (t)e ift (11) The operatios performed withi the RF frot ed are modeled as ideal amplificatio, frequecy traspositio, samplig ad quatizatio, as depicted i figure 4. f Atea r(t) Amplifier IF f - f I Receiver h IF Pre-correlatio Filter V() f s Samplig ad quatizatio to sigal ad data processig Figure 4: Model of the RF frot-ed used i the receiver simulator. The digital sigal delivered by the RF frot-ed is the modeled as V () =Q < V LP (T s )e ifi Ts (1) Q fg is the quatizatio operator. V LP is the equivalet low-pass sigal resultig from the amplificatio ad the filterig of r LP by the RF frot-ed pre-correlatio filter h IF. We ca write V LP (t) = ; h IF (t)e ;ifi t?e LP (t). T s is the samplig period. f I is the itermediate frequecy. Usig these models, we ca see that the equivalet low pass sigal V LP is such that V LP (t)= ;; h IF (u)e ;ifi u? ; c(u)e ;ifu?e LP (t) (13) The digital sigal V () eters all the trackig chaels of the receiver. I the followig, we aalyze the processig operatios of oe sigle trackig chael. The receiver model used for this study is preseted i figure 5. 5 V() V OI DCO V OQ I cos si Q P P E-L Code Gee E-L I&D 1 ms I&D 1 ms I&D 1 ms I&D 1 ms ASIC (hardware) DCO BUS I D Q D I P Q P + discrimiators Loop Filter + Code ad phase Loop Filter CPU (software) Figure 5: Mai architecture of a GPS receiver trackig chael. Courtesy of SETANT AVIONIQUE [Reard A., 1997]. This iput sigal is coverted ito the I ad Q chaels, by mixig this sigal with the DCO outputs V OI ad V OQ such that < : :154 V DLL V PLL V OI () =cos f I T s ; ^() V OQ () =si f I T s ; ^() (14) ^() is the estimate of the icomig carrier phase. The samples used by the phase trackig loop discrimiator are I P (k) ad Q P (k) as preseted i equatio (15). >< >: I P (k)=k Q P (k)=k ms = ms [V ()V OI ()C(T s ; ^ (k))] V ()VOQ ()C(T s ; ^ (k)) = K is the gai of the I ad Q mixers. (15) The sigals used by the code trackig loop are I DE;L (k) ad Q DE;L (k). >< >: ms I DE;L (k)=k [V ()V OI () ; = C(Ts ; ^ (k) ; );C(T s ; ^ (k) + ) ms Q DE;L (k)= K V ()VOQ () ; = C(Ts ; ^ (k) ; );C(T s ; ^ (k) + ) (16) ^ () is the code delay estimate ad is the Early mius Late chip spacig. Usig the low-pass equivalet model preseted i (1), the expressio of the I ad Q samples ca be sim-

6 plified ito: ms h >< I P (k) K Q < = ms h >: Q P (k) K Q < = >< >: K I DE;L (k) ms = V LP ()e i^(k) oo iv LP ()e i^(k) h Q oo C(T s ;^ (k)) i C(T s ;^ (k)) oo < V LP ()e i^(k) (17) ; C(T s ; ^ (k); ) ; C(T s ; ^ (k)+ ) ms oo K Q DE;L (k) = h Q < iv LP ()e i^(k) ; C(T s ; ^ (k); ) ; C(T s ; ^ (k)+ ) (1) The PLL ad DLL cotrol sigals are computed usig I P (k), Q P (k), I DE;L (k) ad Q D E;L (k). I the case of a arctaget PLL ad a o-coheret dot-product DLL, for example, the PLL ad DLL cotrol sigals are ( VPLL (k) = arcta QP (k) I P (k) (k)qp (k) V DLL (k) = ID E;L (k)ip (k)+qd E;L IP (k)+q P (k) (19) The PLL ad the DLL are closed loop trackig devices that reach stable lock poits i steady state if the sigal to oise ratio is sufficiet. These stable lock poits are such that the discrimiatio fuctio is caceled o a stable slope. Therefore, the determied trackig errors are the predicted values of ^(k) ad ^ (k) such that the PLL ad DLL error sigals reach a stable zero-crossig poit, as idicated i (). VPLL (k) = ^(k) ad ^ (k) are such that () V DLL (k) = A few precautios have to be take whe computig the fial trackig error usig this techique: The trackig error due to oise ca ot be observed directly, istead its level has to be determied usig classical equatios. The sigal to oise ratio has to be moitored to detect the situatios the loops lose track of the sigal. Whe the error sigals show several stable zerocrossig values, like for example whe the direct ad the reflected sigal are separated by a time delay greater tha the chip legth plus half the Early-Late gate delay, the simulated result may ot correspod to reality as the actual loops may lock o the reflected sigal. This situatio has to be flagged to the user. These predicted errors are raw trackig errors that do t take ito accout the other processig operatios, such as code-phase smoothig for example. Further processig operatios have to be reproduced o these predicted errors. i 6 This techique does ot allow to simulate the trasiet trackig errors. III. PRESENTATION OF EAMPLES The software was tested i a umber of classical cofiguratios, ad the output was chaecked agaist theoretical results. The examples preseted i this paper are the output values at two stages of the simulator. This comprises the trasfer fuctio delivered by the propagatio simulator, ad the measuremet errors provided by the receiver simulator. The output values are compared with the theoretical values as much as possible. The trasfer fuctio is sampled every 5 secods, with a frequecy step f=5 khz, 3.5 MHz aroud L1. Although all sorts of radiatio patters ca be used by the simulator, i these examples, the simulated receivig atea is a omidirectioal atea. This is doe to emphasize the ifluece of multipath, ad to allow quick verificatio of the results. The measuremet errors delivered by the receiver simulator are the code ad phase trackig errors. The simulated receiver is a arrow correlator receiver, with a chip spacig =:65Tc. The PLL is a arctaget costas loop, ad the DLL is a o-coheret ormalized dot-product trackig loop. The code ad phase estimates are such that the DLL ad PLL cotrol sigals are caceled. The upper ad lower bouds of the code trackig error " D (k) i the case of oe sigle diffracted ray are plotted i figure 6 for a relative amplitude =.57 ad =.4, as these values are ecoutered i upcomig sectios IV ad V. CODE MEASUREMENT ERROR IN CHIPS MAIMUM CODE MEASUREMENT ERROR FOR Dc=.65 Tc RELATIVE DELAY OF REFLECTED RAY IN CHIPS Figure 6: Evelope of code measuremet error for D c =:65Tc ad =:57 ad =:4 (see sectios IV ad V). I the case of oe sigle diffracted ray, the phase

7 trackig error ca be approximated as: PHASE SHIFT OF TRANSFER FUNCTION AFTER REMOVAL OF DIRECT RAY PHASE SHIFT si '(k) " P (k) = arcta 1+si '(k) (1).6.4 is the relative amplitude of both carriers eterig the PLL after uspreadig by the puctual code replica. '(k) is the relative phase shift betwee both carriers. PHASE SHIFT IN RADIANS...4 Two examples are preseted i order to show the capability of the simulator. I sectio IV, a omidirectioal atea is simply placed above wet soil. The height of the atea is chaged from 5 m to 5 m. The results are show for a high elevatio satellite ad for a low elevatio satellite. The results obtaied ca be easily checked with classical results about oe specular reflectio. I sectio V, the omidirectioal atea is placed 5 m above the groud ad close to a metallic buildig. The distace to the buildig is 1 m whe trackig a high elevatio satellite, ad 1 m whe trackig a low elevatio satellite. IV. ANTENNA ABOVE WET SOIL Reflectio off a groud plate gives place to a direct sigal ad a reflected sigal. 11 x 1 1 MODULE OF TRANSFER FUNCTION SIMULATED THEORY FREQUENCY IN Hz x 1 9 Figure : Phase of the trasfer fuctio 3.5 MHz aroud L1. Figures 7 ad show the module ad the phase shift of the trasfer fuctio at a particular epoch for a atea located 5 m above a wet soil groud plate, ad a satellite with a approximate elevatio agle of 76 degrees. The magitude of the soil reflectio coefficiet at L1 for this elevatio agle is approximately.57. These plots show the fadig that will occur at some specific frequecies. Figure 9(b) shows the deformatio of the spectrum of the received sigal at a particular epoch. This figure is to be compared with figure 9(a). It is visible that the cetral frequecy compoets are severely affected by the trasfer fuctio plotted i figures 7 ad. 5 MAGNITUDE OF INPUT SIGNAL.9 1 x 1 6 MAGNITUDE OF RECEIVED SIGNAL SPECTRUM MAGNITUDE IN W 15 1 MAGNITUDE IN W MODULE FREQUENCY IN Hz x FREQUENCY IN Hz x (a) Spectrum of E(k). (b) Spectrum of R(k). Figure 9: Compariso of spectrum of sigal fed to satellite atea E(k) ad received sigal R(k) FREQUENCY IN Hz x 1 9 Figure 7: Module of the trasfer fuctio 3.5 MHz aroud L (a) PLL (" P = ;:197 rad.). (b) DLL (" D = ;:17Tc). Figure 1: PLL ad DLL discrimiators at a particular epoch. 7

8 Figures 1(a) ad 1(b) show the PLL ad DLL error sigals V PLL ad V DLL for the arctaget PLL discrimiator ad the dot-product DLL discrimiator. As we ca see, the stable lock poits are ot cetered, as the multipath drives the loops away from the direct sigal trackig. The PLL error sigal cacels for " P = ;:197 radias. The DLL error sigal cacels with a trackig error " D = ;:17T c. CHIPS.1.1. CODE TRACKING ERROR Figures 11 ad 1 show the code ad phase trackig error i the situatio depicted i figures 7 ad, over a period of 5 miutes. The propagatio chael is sampled with a 5 secod period. The elevatio agle of the satellite goes from 76.5 o to 74.3 o. The relative delay of the reflected ray goes from 97. m to 96.3 m, which is roughly.33 Tc. As we ca see, the code trackig error show i figure 11 is a periodic fuctio. Its values are bouded by -.1 Tc ad.1 Tc, or equivaletly -53 m ad 35 m. These are the maximum values of the code trackig errors i this situatio for this type of receiver, as idicated i figure 6. The phase trackig error show i figure 1 is a periodic fuctio as well, as expressed i (1). The total amplitude of the trackig error is compatible with (1), takig ito accout the additioal atteuatio of the reflected ray due to uspreadig x 1 4 Figure 13: Code trackig error over 1 miutes for a omidirectioal atea 5 m above wet soil. RADIANS PHASE TRACKING ERROR.15 CODE TRACKING ERROR CHIPS x 1 Figure 11: Code trackig error over 5 miutes for a omidirectioal atea 5 m above wet soil. RADIANS PHASE TRACKING ERROR x 1 4 Figure 14: Phase trackig error over 1 miutes for a omidirectioal atea 5 m above wet soil. Figures 13 ad 14 show the code ad phase trackig errors i the case the atea is located 5 m above wet soil, for a period of 1 miutes i the same coditios. The relative delay of the reflected ray is ow divided by 1, goig from 9.7 m to 9.6 m, which is roughly.3 Tc. I that case, we ca see that the period of the code ad phase trackig error is much loger. I additio, the amplitude of the code trackig error is bouded with.1 Tcad -.4 Tc, or equivaletly.9 m ad -1.3 m, which are the predicted values from figure 6. This is due to the fact that the relative delay of the reflected ray is shorter, therefore ot perturbig much the DLL. The total amplitude of the phase trackig error, oly drive by the relative atteuatio of the icomig reflected carrier after uspreadig is slightly icreased. This is due to the fact that the reflected ray is less atteuated by the uspreadig operatio x 1 4 Figure 1: Phase trackig error over 5 miutes for a omidirectioal atea 5 m above wet soil.

9 4 x 1 3 CODE TRACKING ERROR Figures 17 ad 1 show the code ad phase trackig error i the case the atea is located 1 m from the buildig, for a period of 1 miutes. The elevatio agle of the satellite goes from 7.6 o to 74.3 o. CHIPS CODE TRACKING ERROR x 1 4 Figure 15: Code trackig error over 15 miutes for a omidirectioal atea 5 m above wet soil. CHIPS..3.4 Figure 15 shows the code trackig error i the case the atea is located 5 m above wet soil, for a period of 15 miutes, trackig the sigal from a low elevatio satellite. The elevatio agle of the satellite goes from 14.7 o to 9.7 o. The amplitude of the wet soil reflectio coefficiet at this elevatio agle is roughly.4. The relative delay of the reflected ray goes from.5 m to 1.7 m. The code trackig error is a periodic fuctio, with a period larger tha i the previous case due to the fast rotatio of the phase as the satellite is goig dow. We ca see that the amplitude of the code trackig error is much smaller, bouded by. Tcad -.14 Tc,or equivaletly.6 m ad -4.1 m. This is due to the fact that the relative delay of the reflected ray is shorter, therefore ot perturbig much the DLL. V. ANTENNA CLOSE TO BUILDING x 1 4 Figure 17: Code trackig error over 1 miutes for a omidirectioal atea located 1 m away form a metallic buildig. The vertical lie shows the time at which the wall relfects a ray that hits the atea. RADIANS PHASE TRACKING ERROR.4 REFLECTED OFF THE WALL REFLECTED OFF THE GROUND DIRECT REFLECTED BY THE GROUND AND DIFFRACTED BY THE ROOF DIFFRACTED BY THE ROOF EDGE DIFFRACTED BY THE WALL CORNERS REFLECTED OFF THE WALL AND OFF THE GROUND ANTENNA Figure 16: Ray-tracig for the atea 5 m above wet soil, close to a metallic hagar. I this example, the omidirectioal atea is placed 5 m above wet soil, close to a metallic hagar. The atea is hit by the direct ray, the ray reflected by the groud, ad several reflected ad diffracted rays comig from the hagar, as idicated i figure x 1 4 Figure 1: Phase trackig error over 1 miutes for a omidirectioal atea located 1 m away form a metallic buildig. The vertical lie shows the time at which the wall relfects a ray that hits the atea. As we ca see, the evolutio of the code trackig error has a overall appearace which is similar to the evolutio plotted i figure 13. This idicates that the mai disturbig ray is the ray reflected by the groud. However, small perturbatios of the code trackig error ca be see o top of this mea value, which represet the cotributio of the hagar to the trackig error. These small disturbaces do ot chage whe the ray reflected by the buildig wall hits the atea, as idicated by the straight lie i this figure. The perturbatio due to the wall o the code trackig error is ot sigificat, compared with the perturbatio due to the ray reflected by the groud. This is due to the fact that the relative delays of the rays diffracted by the hagar are smaller tha the relative delay of the ray reflected by the groud. 9

10 Figure 19 shows the code trackig error i the case the atea is located 1 m from the buildig, for a period of 15 miutes. The elevatio agle of the satellite goes from 14.7 o to 9.7 o. We ca see that the trackig error is ot similar to the error plotted i figure 15. This is due to the fact that the mai perturbig factor is the buildig, ad ot the groud i that case, as all the rays comig from the hagar have a large relative delay. The small oscillatios are due to a ray diffracted by the buildig edges, ad the ifluece of the ray reflected by the wall is very large, as the error icreases up to.3 Tc or 9 m after this ray hits the atea, as idicated by the straight lie. CHIPS CODE TRACKING ERROR x 1 4 Figure 19: Code trackig error over 15 miutes for a omidirectioal atea located 1 m away form a metallic buildig. The vertical lie shows the time at which the wall relfects a ray that hits the atea. VI. CONCLUSION The software was checked agaist theoretical results i classical situatios, ad will udergo practical validatio agaist real-life measuremets durig the ext weeks. The simulator ca be used to aalyze the impact of multipath i various cofiguratios (obstacles, atea, RF frot-ed, sigal processig). This simulator will be completed with a measurig tool to determie sitig criteria i typical airport eviromets. The simulator ca also be used to characterize other effects i the trasmissio lik (impact of satellite failure modes o receiver measuremets for example). ACKNOWLEDGEMENTS Braasch M. (199) Characterizatio of GPS Multipath Errors i the Fial Approach Eviromet, proceedigs of ION GPS-9, The Istitute of Navigatio, Kasas City, Sept Gomez S., Paeto R., Sauders P., Hwu S. ad Lu B. (1995) GPS Multipath Modelig ad Verificatio Usig Geometrical Theory of Diffractio, proceedigs of ION GPS-95, Palm Sprigs, September Lippicott W., Milliga T. ad Igli D. (1996) Method for Calculatig Multipath Eviromet ad Impact o GPS Receiver Solutio Accuracy, proceedigs of ION Natioal Techical Meetig, Sata Moica, Jauary -4. Macabiau C., Roturier B., Behallam A., ad Reard A. (199) Developmet of a Edto-Ed GPS Simulator as a Tool for Sitig GPS Referece Statios o Airport Platforms, proceedigs of ION GPS-9, Nashville, September Perez Fota J., Vazquez Castro M. A., Kubista E., Paraboi A., Arbesser-Rastburg B., Buoomo S., ad Poiares Baptista J. (199) A Methodology for the Characterizatio of Evirometal Effects o GNSS Propagatio, Iteratioal Joural of Satellite Commuicatios, Vol 16, pages 1-. Reard A. (199), persoal coversatios with the authors. Roturier B. (1996) Modélisatio de multitrajets par l UTD pour les systèmes de radioavigatio et commuicatio de l aviatio civile, proceedigs of JINA 1996, 1-14 November, pages 6-9. Walker R. ad Kubik K. (1996) Numerical Modelig of GPS Sigal Propagatio, proceedigs of ION GPS-96, Kasas City, September 17-. Weiser M. (199) Ifluece of GNSS Groud Statio Sitig o Multipath Errors, Workig paper 16, ICAO GNSSP Workig Group B meetig, Welligto, 3 February - 6 March. The authors wish to thak the compay SETANT AVIONIQUE for providig advice ad techical assistace, as well as the techical services brach of the frech civil aviatio authority, the STNA, for supportig this research. REFERENCES 1