Multipath Resistant Time of Arrival Estimation for Satellite Positioning

Transcription

1 EÜ nt Electron Commun (2003) No, 9 c Gustv Fischer Verlg en Multipth esistnt Time rrivl Estimtion f Stellite Positioning Bischf, Häb-Umbch, N Si mesh Dedicted to Pr Klus Meerkötter on the occsion his 0 th birthdy bstrct Stellite positioning systems, such s GPS the future Europen system Glileo, employ direct-sequence spredspectrum signls The positioning ccurcy is strongly ffected by the qulity the pseudo rnge mesurements These mesurements necessitte code crrier synchroniztion the received signl with the internlly generted reference signls n this type systems one mj err source is the multipth phenomenon, which results in sum delyed weighted copies the iginl signl to be present t the receiver input This cn result in systemtic err the code trcking loop resulting in rnge errs in the der severl tens meters n this pper we propose n etension the strd code trcking loop cpble estimting the prmeters the line-sight (LOS) signl seprting the LOS from the reflected signl ptions t is bsed on n nlysis the cross creltion the received signl with loclly generted code sequence in the vicinity the trcking point Dely-Locked Loop (DLL) F this reson, we cll this method Cross Creltion Function (CCF) nlysis The proposed method chieves considerbly me ccurte estimtes thn DLL ts perfmnce is comprble to the Multipth Estimting Dely-Locked Loop (MEDLL) which is considered to be the best method f reducing multipth inducederrs, so fr However, the computtionl compleity the CCF nlysis is by fct three smller compred to the MEDLL Etensive simultions hve been conducted f the proposed method the MEDLL in der to ssess the robustness the two pproches under vrious signl constelltions Keywds stellite nvigtion, multipth mitigtion, synchroniztion ntroduction Stellite positioning is bsed on the principle tht one s position cn be determined from distnces mesured to objects with known positions From the propgtion time mesurements to t lest four stellites the user s codintes in three-dimensionl spce cn be determined including n estimte the clock fset between user system clock [] With the spred spectrum signls used in the Globl Positioning System (GPS) the future Europen Glileo system time rrivl mesurements cn be obtined with high precision by conducting code crrier phse synchroniztion the received signl While mny sources err (eg ionospheric tmospheric propgtion delys, ephemeris errs) cn be eliminted by differentil eceived My, 2003 Bischf, Häb-Umbch, N Si mesh, University Pderbn, Deprtment Communictions Engineering, Pohlweg 4 49, D Pderbn, Germny techniques, ie by employing reference sttion close to the user s loction which sends crection signl to the user, this does not hold f errs due to multipth receiver noise [2] Errs in the code trcking loop due to reception the direct signl from the stellite one me reflections from the ground structures in the re, result in pseudnge errs t the meter tens meter level thus need ttention f high precision positioning nfluence multipth on the crrier phse is t the cm-level is therefe not considered in this pper [2] Mny pproches in literture ddress multipth t the signl processing level Code synchroniztion is typiclly done by DLL The pek trcking err due to multipth depends on the spcing between the erly lte crelt educing this spcing from one chip period to one tenth it in nrrow crelt DLL thus effectively combts multipth [4], t the epense incresed computtionl compleity, though Other pproches include the strobe edge crelt [], specil crelt reference wvefm design [], the Multipth Estimting Dely-Locked Loop (MEDLL) [8, 9] mong those the MEDLL is considered to be the best method to compenste multipth f stellite positioning However, its computtionl compleity is much higher thn tht DLL n this pper we propose new scheme nmed cross creltion function (CCF) nlysis f reducing multipth errs in positioning receiver with reduced compleity with perfmnce comprble to the MEDLL method t is bsed upon the nlysis cross creltion vlues the received signl with the locl code sequence in n intervl round the DLL trcking point The pper is gnized s follows n Section 2 we describe the stellite chnnel models used in our simultions Section 3 outlines DLL-bsed code synchroniztion illustrtes the multipth effect on trcking n the following section the MEDLL is described t serves s reference method f comprison to our proposed solution, which is presented in Section Section presents simultion results f perfmnce evlution 2 Chnnel Models 2 Simple Multipth Model n this pper we will consider two chnnel models The first one is simple ( ) pth model, in which the received signl is the sum the direct, ie line--sight (LOS) signl reflected rys The received signl in

2 b b replcements 2 Bischf, Häb Umbch, N Si mesh Multipth esistnt TO Estimtion f St Positioning # % () '& re the mplitude, phse dely re the spreding code the dt *) n Eq(), denotes dditive comple comple bseb hs the fm where 3 Code Synchroniztion with DLL the ( -th signl component, which re ll ssumed to be constnt 3 Principle Opertion signl, respectively n this pper we ssume f simplicity n spred spectrum systems code synchroniztion is typiclly two-stge process consisting cquisition tht vlued white Gussin noise n cse n infinite trnsmission bwidth trcking n the cquisition circuit code phse synchroniztion up to n err +, N is chieved is pulse trin consisting rec- The fine synchroniztion trcking is ten done with DLL with ST the block digrm depicted in Fig 2 Here, the received signl is crelted with the two shifted versions OEQP +,UN the code sequence is clled the crelt spcing, which is equl to in strd DLL Q f nrrow crelt Here,OP is the dely the loclly generted code sequence tngulr pulses durtion +-,, where +-, is the chip period, cn be epressed s ( +, (2) >=@?B +, < Here, BC is the pseudo-noise (PN) sequence Throughout this pper we will ssume chip period +, EDGFHF ns ( chipssecond), which is the vlue KBL HM used f the SPS Code GPS Becuse its simplicity, this chnnel model is ten used f theeticl perfmnce evlutions [2] 22 LMS Chnnel Model The L to Mobile Stellite (LMS) chnnel model is comple very relistic chnnel model, becuse it is bsed upon etensive helicopter mesurements [0] The received signl consists direct pth five reflected pths, ech them with dditionl diffuse multipth iginting from shdowing diffrction The mplitudes the diffuse multipth re yleigh distributed cn be pproimted by liner decrese s shown in [0] their delys re eponentilly distributed The reltive delys reltive mplitudes the reflected pths, s well s their Doppler bwidths were tken from [] mplitude [db] fst fding slow fding decreltion length slow fding very slow fding decreltion length very slow fding distnce [m] Fig mplitude the received signl versus driven distnce The mplitudes the respective pths ehibit three kinds EÜ nt Electron Commun (2003) No, 9 fding, s it is illustrted schemticlly in Fig F resons clrity the fst fding is only drwn f the first meters VXWZY\[ Power divider ]_^B` ]_^B` f'wgy hjikmln-oqp4rs tu[ f WZY hoikml4hqoqp r s tu[ f WZY hoikml [ Code genert Discrimint VCO Fig 2 Block digrm coherent DLL ced Loop filter Let us first ssume tht the received signl is simply delyed version the code sequence, ieg U v The purpose the DLL is to estimte the unknown dely The cross creltion wy the received signl with the erly lte version the code sequence yields w {z P +, +,~}~Q P +, w ƒ P S +, (3) < The integrtion intervl hs length +, w ƒ is the utocreltion function the code sequence which is ssumed to be idel (ie we neglect effects due to the finite length the PN sequence) w Šˆ Œ ŒQŽ +, (4) otherwise Due to this symmetry it follows tht the difference between erly lte creltion is zero f OP S, ie if the dely QP the locl code sequence is equl to the

3 z P P EÜ nt Electron Commun (2003) No, 9 Bischf, Häb Umbch, N Si mesh Multipth esistnt TO Estimtion f St Positioning 3 unknown s consequence, in DLL the estimte P <, ie if the locl dely is equl to the dely the f the unknown dely is set to be the zero crossing the LOS-pth, but rther t some dely bove discrimint v, ie in this cse OP The estimte, which is defined s the zero crossing is thus e The vlue this systemtic estimtion err depends on the dely the reflected pth compred to the, on Fig 3 S curve coherent DLL with crelt spcing Fig 3 shows the typicl S-curve shpe the discrimint The discrimint signl v QP is used in feedbck loop to trck the unknown code phse 32 Effect Multipth The presence multipth degrdes the trcking perfmnce the DLL becuse the locl signl is crelted with the composite signl (LOS plus multipth) insted the LOS signl only To illustrte the effect multipth on the DLL we ssume tht the received signl consists the direct LOS pth n dditionl reflected pth _ 2p _ () F positioning systems estimtes f code crrier phses & the LOS-pth hve to be determined F ese illustrtion we ssume& E& The creltions (3) now yield w ƒ P S z +, w ƒ P +, () s result the discrimint signl consists the superposition two S curves, one with zero crossing t OP the other with zero crossing top Fig 4 shows degenerted S curve (thick solid line) obtined s the superposition the S curve from the LOS-pth (thin solid line) the S curve from the reflected pth (dshed line) e { N +, Fig 4 Degenerted S curve The trcking curve does not hve zero crossing t direct pth, on the mplitude rtio N the phses & & Note tht this is systemtic err due to multipth, which even eists in the bsence dditive noise Fig 9 in Section shows the so clled err envelope nrrow crelt DLL, ie the systemtic rnge err s function f n mplitude rtio N ( Q speed light) The upper curve results if the direct reflected pth dd constructively (& & ), the lower cresponds to destructive composition f Œ Œ Œ Œ, the mimum err is Œ O Œ +,, cresponding to [2, 4] 4 MEDLL The MEDLL, which ws introduced by Vn Nee [8, 9], computes the Mimum Likelihood estimtes the prmeters '& the individul components the received signl The likelihood function is given by '& P P U % () where Š }~Q Œ UŠ Œ 4 _ P - (8) n vn Nee s pproch the number pths the received signl is estimted once t the beginning periodiclly fter specified time intervls, wheres the prmeters &, (, re estimted in ech trcking step Setting the prtil derivtives () wrt ll unknowns to zero yields set coupled nonliner equtions [8] With the received signl ccding to Eq () ssuming bsence noise we cn write f the CCF wy w (9) where w is the component w coming from the ( -th ry, cf Eq () Knowledge w is required to solve the ML-equtions n the MEDLL pprochw QP P is computed t delys in prllel bnk crelts, s shown in Fig Note tht in prctice the input signl is smpled with some smpling period + the integrl hs to be replced by sum The cross creltion vlues wy re the input to the DSP process, which solves the MEDLL equtions The itertive lgithm proposed by vn Nee ttempts to estimte ll unknowns &, (, such tht w cn be decomposed into its constituents 4 ccding to Eq (9) Since the nlytic fm w ƒ is known from Eq (4), w cn be reconstructed thus the loction

4 b b Gold8 & plcements Code genert Crrier genert 4 Bischf, Häb Umbch, N Si mesh Multipth esistnt TO Estimtion f St Positioning cresponding to the mimum the the mimum w cn be obtined, s opposed to just the dely wy sequence ] ` ] ` DSP ] b` Fig Block digrm MEDLL However, very smll delys cnnot be discerned, resulting in residul code trcking err This will be nlyzed in me detil in Section +, ccding to section 32 Furtherme, we will lwys ssume tht The CCF nlysis is crried out in the \ intervl \ # % Q '&U (0) which is symmetric to # Subsequently, the intervl width is subdivided into the five intervls ( *)\ 9 Q '+, U 4 Q () Thus, lies in the middle Furtherme, we choose spcing * KHL +, Due to this choice the mimum errœ X Œ derived bove it is gurnteed tht lies in ( t the edges the intervls we compute the creltion coefficients (CC) (0 w- wy 9, v (2) 4 L Finlly, the comple nmlized slopes re computed by ( (04 32 ( w % -, e 4 (3) where denotes the nmlizing fct Gold depends on the vlue the CF the pplied Gold sequence t +-, Fig illustrtes the defined vlues 9 EÜ nt Electron Commun (2003) No, 9 Fig Emple illustrting the used nottion Due to noise the finite signl bwidth two slopes re usully not totlly identicl, F this reson, we introduced tolernce vlue tol n the rest this re sid to be (un)equl if section, two slopes Œ Œ=< (4) tol CCF nlysis From the bove definitions we cn deduce the following four fcts i) The CF the i-th signl component hs slope Preliminry emrks Definitions chnges t +, Since lies in, there n this section we present novel method, clled CCF is no other slope chnge w # in Likewise, there nlysis, f code synchroniztion in the presence multipth ts perfmnce is similr to the MEDLL, howond pth,w # cn be most one slope chnge the CF the sec-, in ever t reduced computtionl compleity The proposed ii) f? = the intervl contins no slope chnge the respective slope must be one the following method is bsed upon n nlysis the cross creltion function the received signl the internlly generted % code sequence round the zero crossing the trcking C Fig shows typicl CCF f two rriving pths with the cresponding curve nrrow crelt DLL t is ssumed tht the slopes in the different intervls received signl nvigtion receiver cn be modeled s consisting two pths []w * w ew ssuming Œ Œ Œ Œ, we hve mimum dely err # FCED B >@ >? > Fig llustrtion the different slopes the CCF iii) f the slopes in two neighbing intervls re different, t lest one two intervls must contin slope chnge one the CFs iv) f is less thn+,, the slope the CCF in the intervl +,, & hs the negtive vlue the slope in the intervl, +, & The reverse is lso vlid f f two slopes with(gh we obtin, then must lie left right from ll the mim the CFs Net, the CCF nlysis is presented s stepwise procedure F simplicity we ssume rel vlued signls ( creltions) The generliztion to comple signls is re compred conclusions re drwn from equlity inequlity these slopes mimum five comprisons is required to obtin two linerly independent equtions f the two unknowns done lter on n ech step two slopes

5 EÜ nt Electron Commun (2003) No, 9 Bischf, Häb Umbch, N Si mesh Multipth esistnt TO Estimtion f St Positioning n the following, ech step is introduced by digrm The line t the top summrizes the conclusions drwn so fr The rhombus in the middle shows the investigted slope comprison The boes t the left the right show the consequences in cse n equlity inequlity, respectively f nother comprison is required, the number in the circle denotes the number the step with which the CCF nlysis continues Since it hs to be dmitted tht replcements the resoning is firly complicted (though not relly difficult), the method will be further illustrted by n emple in Sec 3 component n cse only one rriving pth it yields, since there is no multipth err 2 lgithm f CCF nlysis n this cse the CCF nlysis termintes The CCF nlysis strts with comprison the slopes in the intervls, which lie left from here nequlity n cse inequlity we cn drw the conclusion tht there eists reflected pth (cse () step cn be ecluded) tht cn not be right no infmtion yet from the mimum the CF the reflected pth This 2 mens, tht lies right from the intervl n cse tht Compute CC lies in, the slope would hve the sme vlue s Check equlity Check equlity no yes n der to check this, the CCF nlysis continues tol? with step 3, compring the slopes ) )+*,* ) )-* 0 ) 3 Equlity n cse equlity und one the 4 following three cses is possible lgithm f () There is only one relevnt pth Check equlity t follows ' pth seprtion no yes tol? lredy obtined infmtion (modified version) () Both re due to rising edge w w S () The slope is due to the rising edge w only, becuse the second pth is delyed such tht +, is () ll other equtions, respectively, re linerly dependent on Eq () n der to check, if there is only one pth two pths with very There my eist second pth, which is, however, sufficiently delyed ( err, see Fig 9 b #%'&( ) therefe doesn t introduce n smll reltive dely, specil seprtion lgithm ws developed This lgithm t first computes n dditionl CC t the two dditionl slopes - 2 w- w- - 2 () Bsed on these two slopes the lgithm clcultes estimtes f the mplitudes the dely the direct is set to Equlity n equlity mens, tht is right from ll mim the CFs Becuse the inequlity in step 2, cn not be left replcements from, hence, must contin the slope chnge t right from fter this, the CCF nlysis continues with step 2 comprison gin, there is only one independent eqution slightly modified version the seprtion lgithm is pplied This lgithm gin yields n estimtion vlue f nequlity Since lies right from, in cse inequlity +q, the CCF nlysis is terminted must be contined in nequlity n inequlity cn on one h men tht The CCF nlysis continues with step 2 S 32 lies in right from nother possibility is tht , lies in n der to check, which the cses is vlid, comprison is perfmed in step 4 3 Compute CC t Check equlity %) )+*,* %) )+* )4 0 0 ) lgithm f 4 2 no tol? yes infmtion pth seprtion Equlity n cse n equlity 4 Compute CC Compute mpl Check equlity )+*,* the intervl no tol? yes )-* * lredy obtined infmtion must be right from the mim the CFs ll contributing pths, ie there is only one pth two pths re very close together We now only hve the linerly independent eqution Equlity n cse equlity due to the dditionl inequlity we cn con- clude tht either () to lie between () +, lies in n both cses there is no slope jump in we obtin the eqution () n der to determine whether () () holds we compute n dditionl CC t dd> D +, the cresponding slope 32 (dd) dd w (8)

6 9 L + EÜ nt Electron Commun (2003) No, 9 Bischf, Häb Umbch, N Si mesh Multipth esistnt TO Estimtion f St Positioning f dd is not equl to there must be slope chnge between (dd) w +, must be left from We obtin Compute mpl Compute mpl (9) )+*,* )+* )4 *,* no tol? yes ) *,* the mplitudes cn be computed lredy byobtined infmtion 4 (20) f re unequl, either must contin the slope jump t +, n der to check, which f dd, then there cn be no slope chnge between dd +, these two intervls contins the slope jump, the dditionl must lie in creltion coefficient 9 t n this cse we hve (2) 9 T Š +, 0 (28) the mplitudes cn be computed ccding to the dditionl slope (22) 9 2 nequlity f is not equl to, it follows tht either () must contin the slope jump t w- w- 9 (29) re computed Then 9 () must contin the slope chnge t +, +, is compred to Equlity n cse n equlity, the intervl cn not lie in, becuse in this cse we would hve n equlity 9 must contin the slope jump t +, Thus, both re left Furtherme, the intervl cn not contin, since if it would contin, we would hve n equlity 9 from +,, such tht both intervls only contin ption the CF the direct pth is vlid Using Eq () we obtin replcements n der to find out, which these both cses is vlid, n dditionl CC 9 t LQ +, n dditionl slope (30) infmtion must be computed Compute mpl )+*,* )4 *,* 2 9 ) )-*,* ) )+* ) 0 ) 0 0 no tol? yes ) Compute mpl )+* )4 *,* (23) Equlity n cse n equlity, we cn 9 conclude tht +, must lie in dditionlly to we obtin the eqution (24) the mplitudes cn be computed by (2) nequlity n cse inequlity must lie in Thus, the intervl lies between we obtin (2) (2) gin we hve two linerly independent equtions re ble to compute the mplitudes ccding to Eq (20) the mplitude vect nequlity n cse n inequlity, Then +, lies left from (3) +, must lie in (32) is vlid From the equtions () (32) we obtin _ (33) the mplitude vect ccding to Eq (20) Now, f ll possible constelltions the mplitudes both pths re determined The procedure cn be redily etended to comple-vlued signls, where we compute the slopes (, ) from the rel (, ) from the imginry prt the creltion function n the net step the phses &, ( the phse difference & diff re clculted X3% X3% & & diff & ) +B ) (34) Now, the prmeters '&, ( diff hve been determined (t lest pproimtely), the finl step is to obtin n estimte the bis O# from the err envelope 3 & diff diff & diff (3)

7 3 3 9 = rg replcements EÜ nt Electron Commun (2003) No, 9 Bischf, Häb Umbch, N Si mesh Multipth esistnt TO Estimtion f St Positioning diff & diff is defined by upper prt the err envelope if diff & diffu sgn lower prt the err envelope if sgn & diff ' Ž (3) Becuse the DLL err envelope is constnt to lrge etent, we only need to know the ect dely difference diff & diff ' Gold f very smll vlues f vlues in the vicinity +, Gold F diff the seprtion lgithm directly computes n estimtef Gold so tht this cse is not criticl n the other Gold cse we computed the dditionl CC 9 in step 4 obtined n equlity Gold dd diff is then between Q D +, +, n this cse we ssume n verge vlue diff +, red the cresponding bis from the err envelope Me ect results could be obtined if me creltions were computed n the following section the CCF nlysis is illustrted by mens n emple 3 Emple f the CCF nlysis F the following emple we ssume rel vlued signls f the direct pth the reflected pth with mplitudes Q ( # ) ws chosen to K +, The resulting CCF the computed slopes re shown in Fig 8 The slopes re nmlized f clrity Under the given ssumptions the nrrow-crelt DLL multipth err is QK F +,, which cresponds to N ) b )4 ) b ) ) b 0 ) Fig 8 Smple CCF with ssumed vlues First (step ) the slopes re compred From the equlity we cn follow tht there is no jump in, ie one the three cses given bove in step is given This mens there is () only one pth () lies right from +q, is left from () +, lies right from n the net step (step 2) Q if re compred n the cse only one pth the pek the second pth lies right from both slopes would be equl n our emple we hve n inequlity both slopes so tht there is t lest one reflected pth either () must lie between +, () +, is right from Now (step 3) re compred n equlity would men tht the intervl must lie right from ll the mim the CFs (see fct (iv) in Sec) However, in our emple we obtin n inequlity This mens tht either () lie between +q, () +, must lie in right from n der to find out which these cses is vlid, comprison the slopes is perfmed (step 4) n our emple this comprison yields n inequlity we cn conclude tht there must be slope jump in either, so tht only two cses re possible Either () +, lies in () lies in The other cses cn be ruled out F emple, +, cn not lie right from, since if it lied right from, the slopes would be equl Meover, +, cn not be contined in, becuse otherwise there would be no slope chnge in Note tht the constelltion with +, right from is considered s sitution with only one pth, becuse the second pth does not ffect the DLL in this cse n dditionl CC 9 t LQ +, the dditionl slope must be computed The slope 9 9 S is subsequently compred with n our emple this comprison yields n inequlity We cn conclude tht there is slope jump in one these two intervls From the inequlity we lredy know tht either # must contin slope jump Becuse there re t most two jumps in, the intervl must contin the slope jump t We cn now conclude tht lies right from left from, such tht must be equl to Q Furtherme, we know tht must be equl to, becuse lies between +, We now hve the two equtions cn compute the mplitude vect Q (3) (38) Q fter tht, the phses (&,& ) would hve to be computed n this emple we ssumed rel-vlued signls, so& diff Furtherme, we know tht the dely is greter thn less thn L n this region the err envelope is constnt using Eq (3) we cn estimte the multipth err by 3 S Q +, Š F (39) +, Perfmnce nlysis Err Envelopes G Q the reflected pth to Fig 9 compres the systemtic rnge err s function the dely the direct pth f nrrow crelt DLL (, MEDLL, CCF nlysis Here we ssumed 2 ry chnnel model (ie ) without dditive noise The curves bove the bsciss crespond to & & the curves below the bsciss to& &, respectively F ll other phse vlues the err lies within this err envelope n this figure we ssumed signl-to-multipth (SM) rtio, ie db F the MEDLL N

8 D 8 Bischf, Häb Umbch, N Si mesh Multipth esistnt TO Estimtion f St Positioning CCF results we chose to Q KHL +, The signl bwidth ws chosen to 204 MHz cresponding to the bwidth the C code signl chip rte 023 Mchips ws ssumed F wide rnge dely differences, both MEDLL CCF nlysis perfm virtully bisfree The err envelope the CCF nlysis ehibits two regions residul systemtic errs On one h reflected pths with delys less thn +, cn not be perfectly seprted by the seprtion 00 lgithm The other region is round +-, f both pths 00 re 0bout one chip durtion prt (decresingincresing 00 edge the err curve), we cn only determine tht the dely is in the intervl +,, +, & [m] rnge err DLL MEDLL CCF-nlysis >? >@ Fig 9 Err envelopes f the CCF nlysis, the MEDLL the conventionl DLL F this reson, the estimted multipth err is fflicted with n err Overll, the perfmnce the CCF nlysis is similr to the perfmnce the MEDLL F smll delys the CCF nlysis even outperfms the MEDLL if the sme number smples per chip is used F both methods, errs f smll reltive delys cn be reduced if is reduced, ie if me vlues the creltion functionw re computed F the MEDLL perfmnce given in Fig 9 ten creltion vlues per chip were used 2 Perfmnce in WGN Fig 0 compres the perfmnce MEDLL CCF nlysis in the presence dditive white gussin noise (WGN) F both methods we ssumed n integrtion time 00 ms, which cresponds to the durtion 30 dt bit in GPS This long creltion time yields to SN higher thn 30 db fter creltion, such tht the creltion coefficients, thus, the slopes cn be computed with sufficient ccurcy F the multipth-free cse both methods deliver bis free estimtion Fig 0 shows the vrince the estimted trcking err < ~ s function the signl-to-noise rtio t the input stellite nvigtion receiver SNs between db re typicl vlues t the input stellite nvigtion receiver [2], the SN becomes positive fter despreding t cn be seen tht the vrinces f both methods re nerly identicl f ll SN vlues The two other curves show the trcking err vrince both methods in cse n dditionl reflected pth delyed by Qg +, n SM db The vrince obtined from the CCF nlysis is gin in the sme region s the vrince f the F D CED EÜ nt Electron Commun (2003) No, 9 MEDLL f the me comple relistic LMS chnnel model WGN is employed, the trcking err vrince is incresed f both methods, see Fig One reson f this is the fst fding which ffects the perfmnce both methods nother reson is the diffuse multipth spred, which cn not be compensted by mens either MEDLL CCF nlysis ] [m MEDLL (only noise) MEDLL (SM= db) CCF nlysis (only noise) CCF nlysis (SM= db) SN [db] Fig 0 Trcking err vrinces f different scenrios ] [m MEDLL CCF nlysis SN [db] Fig Trcking err vrinces f the relistic LMS chnnel model F this relistic scenrio both methods show pproimtely the sme perfmnce The good perfmnce the CCF nlysis is remrkble, since we ssumed in the derivtion, tht the received signl consists direct one reflected component only lso f the MEDLL we hd set in ll simultions Overll, the perfmnce the CCF nlysis is comprble to the MEDLL perfmnce n some scenrios it even outperfms the MEDLL 3 Computtionl Costs The computtionl compleity the MEDLL is minly determined by the number creltions, since the itertive solution the ML equtions cn be done on DSP is not the computtionl bottleneck Note tht the crelt spcing is independent the smpling period +, lthough it my ten be chosen equl The systemtic err seen in Fig 9 cn be reduced by incresing, the number creltion vlues per chip, however, t the cost incresed computtionl compleity Creltion vlues hve to be computed f the whole dely rnge where w hs vlues different from zero This rnge is size LQ +, ( +, left from

9 L EÜ nt Electron Commun (2003) No, 9 Bischf, Häb Umbch, N Si mesh Multipth esistnt TO Estimtion f St Positioning 9 Q +, to the right ) This mens pproimtely vlues Becuse the lrge number creltions the MEDLL is only implemented in moniting sttions in DGPS sttions One creltion vlue is computed by multiplying the smpled input signl with the loclly generted code sequence over n intervl chips The number multiplictions dditions is thus, where +N + is the number smples per chip F MEDLL n integrtion time +-, eceeding one second should be used [9] Tble Comprison the computtionl costs DLL MEDLL CCF nl # creltions L LK Ž D ntegrtion Time &( 0 s s G 0 s F the CCF nlysis the computtionl compleity is lso minly determined by the number creltions t first, two creltions re required to find the zero crossing the S-curve Furtherme, si seven creltions re needed to determine the mplitudes the delys (if required) the respective pths Hence, t most nine creltions re needed to obtin the perfmnce given in the figures n comprison to this, conventionl DLL requires two creltions (erly, lte), depending on the kind discrimint, third (on-time) one Tble compres the number creltion vlues to be computed to obtin n estimte the code dely The tble lso contins typicl vlues f the integrtion times used f the computtion the creltion vlues Conclusions Outlook [] L Grin, -M ousseu, Enhnced Strobe Crelt Multipth Mitigtion f Code Crrier, Proc the # t nt Technicl Meeting the Stellite Division the nstitute Nvigtion, ON-GPS-9, Vol, pp 9 8 [] L Weill, GPS Multipth Mitigtion by Mens Crelt eference Wvefm Design, Proc nstitute Nvigtion Nt Tech Meeting, n 99, pp 9-20 [] C Mcbiu, B oturier, Benhllm, Perfmnce GPS eceivers with me thn one Multipth, Proc the ON GPS99, Nshville, 999 [8] vn Nee, The Multipth Estimting Dely Locked Loop, Proc 2nd EEE Symp on Spred Spectrum Techniques pplictions, Yokohm, 992, pp [9] vn Nee, Multipth Multi-Trnsmitter nterference in Spred-Spectrum Communiction Nvigtion Systems, PhD Disserttion, Delft Univ Techn, Delft, 99 [0] F P Fontn, M Vzquez-Cstro, C E Cbdo, P Grci, E Kubist, Sttisticl Modeling the LMS Chnnel, EEE Trnsctions on Veh Techn, Vol 0, No, Nov 200 [] Glileo Phse B2, User Segment equirements Document, DD 033, QS GL 00-GL, ssue, Mrch 2002 [2] Prkinson, Brdfd W mes Spilker eds 99 GPS They Prctice Volumes Wshington DC mericn nstitute eronutics stronutics, nc enke Bischf received his Dipl-Mth degree in Technomthemtics in 999 from the University Pderbn Since 999 he wks s reserch scientist t the Dept Communictions Engineering t the University Pderbn, Germny He wks in the re f receiver structures modern stellite nvigtion systems His specil interest is the multipth mitigtion in stellite nvigtion receivers He is now wking towrds his PHD n this pper we proposed new method cpble compensting f multipth errs in stellite nvigtion systems t is bsed upon n nlysis the cross creltion function the received signl the internlly generted code sequence in n intervl round the DLL trcking point n comprison to MEDLL, which is nowdys regrded s the method with the best perfmnce, the computtionl cost is reduced by pproimtely fct three Simultneously, simultion results showed tht the perfmnce the CCF nlysis is comprble to in some cses even better thn the perfmnce the MEDLL This is lso vlid f relistic LMS chnnel model, comprising si pths dditionl diffuse multipth spred n future we hve to emine, in how fr the bit resolution the pplied DC will ffect the method eferences [] P Misr, BP Burke, MM Prtt, GPS perfmnce in Nvigtion, Proc the EEE, Vol 8, No, n 99, pp 8 [2] MS Brsch, vn Dierendonck, GPS eceiver rchitectures Mesurements, Proc the EEE, vol 8, no, n 99, pp 48 4 [3] CC Counselmn, Multipth-ejecting GPS ntenns, Proc the EEE, vol 8, no, n 99, pp 8 9 [4] vn Dierendonck, P Fenton, T Fd, They Perfmnce Nrrow Crelt Spcing in GPS eceiver, NVGTON, ournl the nstitute Nvigtion, Vol 39, No 3, Fll 992, pp einhold Häb Umbch obtined Dipl-ng Dr-ng degree in Electricl Engineering from chen University Technology in , respectively From 983 to 988 he ws with the Lehrstuhl fuer Elektrische egelungstechnik, chen University Technology, wking on digitl receiver design From 988 to 989 he ws postdoctl fellow t the BM lmden eserch Center, Sn ose, C, conducting reserch on coding signl processing f recding chnnels s reserch stff member Philips eserch he wked on vrious spects utomtic speech recognition from 990 to 200 Since 200 he is full press in communictions engineering t the University Pderbn, Germny Si mesh Nmmi received his Mster Technology in Communiction Systems from ndin nstitute Technology, Mdrs in 2000 He ws with Motol ndi Electronics Limted Hyderbd ndi f 2 yers Since 2002 he is wking s reserch stff member t the Dept Communictions Engineering t the University Pderbn, Germny His reserch interests re minly in reducing multipth mitigtion f nvigtion receivers reducing multi trnsmitter interference f communiction receivers