COMPARION OF C/A C COMBINE ACQUIITION TECHNIQUE Cyrll Grnot, Kyl O Kf and Gérard achapll Poston, ocaton and Navgaton PAN Rsarch Group partmnt of Gomatcs Engnrng, Unvrsty of Calgary chulch chool of Engnrng 5 Unvrsty rv NW Calgary, Albrta, Canada TN N CANAA BIOGRAPHY Cyrll Grnot s a Ph. studnt n th partmnt of Gomatcs Engnrng at th Unvrsty Of Calgary chulch chool of Engnrng. H arrvd n Calgary n arly 6 to prform a s month ntrnshp n th PAN Group undr th suprvson of r. Grard achapll. Ths tranng prod concludd 5 yars of gnral ngnrng ducaton wth yars of prparaton school and 3 yars at Tlcom INT and vntually ndd up wth a proposton to stay n Calgary as an Mc. studnt. Aftr a fw months n th PAN Group, h fnally transfrrd from Mc. to Ph. at th bgnnng of May 7. H pcts to complt hs Ph. n ptmbr 9. Kyl O Kf s an Assstant Profssor of Gomatcs Engnrng at th Unvrsty of Calgary. H compltd Ph and Bc. dgrs n th sam dpartmnt n and. H has workd n postonng and navgaton rsarch snc 996 and n satllt navgaton snc 998. Hs major rsarch ntrsts hav bn n GN systm smulaton and assssmnt, spac applcatons of GN, carrr phas postonng, and local and ndoor postonng wth ground basd rangng systms. Profssor Gérard achapll holds a CRC/CORE Char n Wrlss ocaton n th partmnt of Gomatcs Engnrng at th Unvrsty of Calgary, whr h also hads th PAN Group. H has bn nvolvd wth GP dvlopmnts and applcatons snc 98. Mor nformaton s avalabl at http://plan.gomatcs.ucalgary.ca. ABTRACT gradd sgnal nvronmnts such as ndoors and n urban canyons typcally lmt th scop of GP rcvr opraton. GP sgnals can b attnuatd by db or mor undr ths advrs condtons. In dgradd sgnal nvronmnts, nhancng th procssng gan by db or mor rqurs a sgnfcant ncras n cohrnt ntgraton tm. Howvr, th cohrnt ntgraton tm ndd can b rducd f on wr to combn th nrgy of sgnals transmttd from th sam satllt but on dffrnt frquncs. Wth th launch of th latst Block IIR-M satllt, thr ar now four GP C capabl satllts. Though th C sgnal s transmttd.5 db lowr than C/A and acquston usng zro-paddng rsults n an addtonal 3 db loss, mprovd acquston rlatv to C/A s possbl f C and ar usd togthr. Th purpos of ths papr s to ntroduc th lmtatons of common acquston on or C and nvstgat four dffrnt combnd acquston mthods cratd to ovrcom ths lmtatons. Each mthod ams to prform a jont stmaton of th cod dlays and opplr frquncs on and whl kpng th cohrnt ntgraton tm as low as possbl and thrfor avodng a dcras n frquncy bn sz. Th rsults of ach mthod ar assssd n trms of probablty of dtcton and fals alarm and compard to on anothr as wll as to common non-cohrnt acquston of C/A only. Th frst mthod nvolvs th summaton of non-cohrnt acqustons on and. Th scond nvstgats th summaton of both non-cohrnt and dffrntal acqustons on and. Th thrd uss th noncohrnt summaton of th multplcaton of th C/A and C post-corrlaton outputs. Th fnal tchnqu uss non-cohrnt summaton of th C/A plus th C post-corrlaton outputs. Th ffcts of opplr rrors, / phas dffrncs and cohrnt ntgraton tms ar analyzd and dscussd. Prlmnary rsults show that th summaton of non-cohrnt and dffrntal acqustons rsult n a substantal mprovmnt n th probablty of dtcton compard to th non-cohrnt only cas and outprforms as wll all of th othr mthods tstd. INTROUCTION Urban canyons and ndoor nvronmnts can prov trmly dffcult n trms of GN rcvr prformanc. Undr ths advrs condtons, sgnals dgradaton can cd db. To ovrcom ths problm, currnt solutons rqur a consdrabl ncras n th cohrnt ntgraton tm usd durng th acquston procss Watson t al 7. Common tchnqus nclud th us of Hgh nstvty GP H GP rcvrs rlyng on data bt stmaton and Assstd-GP rcvrs makng us of trnal nformaton to prform data wp-off tchnqus. Howvr, th avalablty and th rlablty of assstanc data or data bt stmaton tchnqus stll rmans a problm. Fortunatly, th GP systm s currntly bng modrnzd through th addton of two nw cvl sgnals Europan Navgaton Confrnc 8 Toulous, Franc Apr3-5, 8 /9
namly C and 5. Rspctvly for cvlans and avaton purposs, thy ar dsgnd to ovrcom th lmtatons of lgacy C/A GP. For nstanc, th nw C sgnal carrs a plot channl n addton to th usual data channl. Ths nw channl s modulatd by a long rangng cod C cod of 767,5 chps, clockd at 5.5 khz and dos not carry any navgaton data thrfor allowng for longr cohrnt ntgraton wthout th nd for trnal adng. Morovr, du to ts trmly long lngth.5 s, t offrs about 5 db cross corrlaton protcton. Manwhl, th data channl conssts of a modrat rangng cod CM cod of,3 chps also clockd at 5.5 khz but s furthr modulatd by th navgaton mssag transmttd at 5 Hz. Ths last pont s spcally mportant as t undrlns th fact that data bt transtons and CM cod boundars ar synchronzd thrfor rmovng th ncssty of data bt synchronzaton aftr th acquston. Howvr, as th C sgnal shars th frquncy wth th mltary PY sgnal, t rmans lmtd to a sngl b-phas carrr. As such, th two channls ar tm multpld at,3 MHz and th total sgnal powr s shard btwn thm both. Th transmt sgnal bng alrady.5 db lowr than C/A GP, ths lads to th fact that ach channl s ndvdually.5 db lowr than C/A. Nvrthlss, th C sgnal s stll vry attractv both n trms of acquston and trackng du to th prsnc of th plot channl and th ms CM cod of th data channl synchronzd wth data bt transtons. Howvr, f on wr to us drctly th CM cod or th C cod, th sgnfcant ncras of th cohrnt ntgraton tm usd would also rqur that th sz of th opplr bns sz s rducd. As such, th total numbr of opplr bns s multpld and so s th rqurd procssng tm to covr th tndd spac sarch. A wll known formula rlatng th opplr bn sz to th cohrnt ntgraton tm s th followng: bn 3T wth bn bng th opplr bns sz n Hrtz and T th cohrnt ntgraton tm n sconds. As llustratd n Fgur, a 33.33 Hz opplr bn sz s ncssary to us th CM cod drctly and no lss than opplr bns ar ndd to covr th ntr opplr frquncy rang - Hz to Hz. If on wr to gnor th data channl and consdr only th plot, th lngth of th cod mpls that mor than 75 bns ar rqurd to swp th ntr opplr frquncy rang whn usng a cohrnt acquston schm. Morovr, a.5 scond cohrnt acquston would call for a farly stabl oscllator, no usr dynamcs and an accurat opplr modl for th satllt. On th othr hand, usng a sub-scton of th C cod would prov to b dffcult wthout trnal tmng nformaton to algn th local cod wth th ncomng sgnal. Thrfor, th C cod s nvr usd durng th acquston procss and as such s commonly zro-paddd. To ovrcom ths problm, svral solutons wr rcntly proposd. For nstanc, Psak proposd a FFT-basd CM / C acquston mthod for wak sgnal condtons; m t al 6 dvlopd a fast acquston schm basd on adng to prform th CM cod phas and carrr opplr stmatons. On th othr hand, complt combnd / acquston takng advantag of th powr duplcaton was proposd by Grnot t al 7. Rgardng trackng algorthms, th combnaton of th C plot and data channl and assssmnt of prformanc has bn proposd by Muthuraman t al 7. Fnally, othr sgnal combnatons across frquncs whr consdrd by Ioannds t al 7 for combnd acquston of GP and 5. In ths papr, th assssmnt of ntr-frquncy combnd acquston prformanc s furthr nvstgatd through four dffrnt combnd acquston tchnqus. Indd, snc both C/A and C ar transmttd from th sam satllt and synchronzd n trms of tmng, t can b assum that th opplr frquncs ar rlatd by th rato f / f and th rlatv cod dlay btwn th two sgnals s small Grnot t al 7, Ioannds t al 7 vn though prsnt du to th dffrnt onosphrc and nstrumntal dlays. POT-CORREATION METHO PROPOE All th proposd mthods ar post-corrlaton mthods, manng that any dffrnc btwn thm taks plac aftr th ntgrat and dump procss Fgur. Fgur : Frquncy bn sz rqurd as a functon of cohrnt ntgraton tm usd Fgur : Common parts of th acquston: opplr rmoval, cod rmoval, and ntgrat and dump procss Europan Navgaton Confrnc 8 Toulous, Franc Apr3-5, 8 /9
Not that rprsnts th cohrnt ntgraton tm consdrd. Onc th cohrnt summaton ovr has takn plac on both and sgnals, four dffrnt post-corrlaton procsss ar appld. Th frst mthod NC nvolvs th summaton of non-cohrnt acquston on and Fgur 3. Th scond NCff nvstgats th summaton of both non-cohrnt and dffrntal acquston on and Fgur. Th thrd NCM uss th non-cohrnt summaton of th multplcaton of th C/A and C post-corrlaton outputs Fgur 5. Th fnal tchnqu COH uss non-cohrnt summaton of th C/A post-corrlaton output addd cohrntly th C post-corrlaton output Fgur 6. Fgur 6: Non-cohrnt summaton of th C/A plus th C ovr M post-corrlaton outputs METHOOOGY In ordr to nvstgat th prformanc of ach mthod and compar thm to th common non-cohrnt acquston mthod of C/A only, a statstcal analyss has bn conductd. As ach mthod dffrs from th othrs only aftr th ntgrat and dump procss of and sgnals, spcal consdraton was gvn toward th possblty to smulat drctly th and corrlator outputs. Fgur 3: ummaton of th non-cohrnt acqustons of and ovr M post-corrlatons outputs Gvn a samplng frquncy F and so a samplng tm T such that ach cohrnt ntgraton tm ovr scond contans N sampls, w can prss th k th sampl of th n th cohrnt ntgraton aftr th opplr rmoval as follows: y k Cd k c k πfkt θ j w k wth C bng th carrr powr, dk bng th data bt of th ncomng sgnal of th k th sampl, ck bng th cod chp of ncomng sgnal of th k th sampl, F bng th carrr frquncy, θ bng th orgnal phas rror and wk bng th nos trm of th k th sampl. Not that n th cas of GP n a multpath fr nvronmnt, all th wk ar ndpndnt. Thrfor, th output of th ntgrat and dump procss of n th cohrnt ntgraton s: Fgur : ummaton of th non-cohrnt and dffrntal acqustons on and ovr M post-corrlatons outputs Not that n th abov fgur, rprsnts th dlay appld to th post-corrlaton outputs as wll as th cohrnt ntgraton tm usd durng th ntgrat and dump procss and th star * stands for th compl conjugat of th ncomng sgnal. nn s n N s Cdkck jπ FkT θ c local k l k n N s jπ FkT w k clocal k l whr c local s th local cod of th rcvr and F s th rsdual frquncy aftr th opplr rmoval procss. Assumng that th local cod s algnd wth th ncomng cod wth an rror of dt and that th ntgrat and dump s prformd ovr a full cod prod only n th cas of C/A, ms, w can appromat th abov quaton as: nns n Cd n R dt N k n Ns j π FkT θ W n 3 Fgur 5: Non-cohrnt summaton of th multplcaton of th C/A and C post-corrlaton outputs ovr M post-corrlaton outputs whr R s th auto-corrlaton functon and Wn s th rsultng nos aftr summaton whch mans that th varanc of W s qual to th varanc of w dvdd by N. Ths last pont s du to th normalzaton trm n front of th summaton n quaton. Europan Navgaton Confrnc 8 Toulous, Franc Apr3-5, 8 3/9
Notcng that N tms T s quals to, th summaton trm of quaton 3 can thn b rarrangd as: nn jπ FkT θ s k n N s N jπ FT n θ s k jπ FkT From abov quaton, t s clarly vdnt that th summaton trm s a gomtrc progrsson and as such can b rducd to: N s k jπ FkT sn π FT sn π FT jπ FT jπ FT j π F T T 5 Not that th dnomnator can b prssd as: π F sn π FT π FT as π FT << F And as F s th samplng frquncy, t s far largr than th rsdual frquncy rror thrfor rducng 5 to: sn π FT sn π FT N sn π FT π FT j π F T T j π F T T Fnally, rplacng th summaton trm of quaton 3 by quaton 6 and notcng that >> T, t can b shown that: n W n sn π FT Cd n R dt π FT 6 j π FT n θ From quaton 7, t s clarly shown that th corrlator output s functon of th known paramtrs ms and th sgnal powr and th unknown paramtrs dt whch rprsnt th tm rror durng th corrlaton of th cod, dn th data bt of th n th mllscond, F th rsdual frquncy rror and θ th ntal phas rror of th frst mllscond. In ordr to stmat th prformanc of ach postcorrlaton mthod, th output of th corrlators wr frst smulatd for as shown n Tabl. 7 Tabl : Paramtrs usd to smulat th outputs of th corrlators for Known Paramtrs fnd by usr ms Unknown paramtrs d n Random or - dt Unformly dstrbutd F Unformly dstrbutd Unformly dstrbutd C/N θ Not that dt and F ar random procss unformly dstrbutd and bound rspctvly by th cod stp sz as such f th cod stp sz s of.5 chp, dt vars btwn -.5 and.5 chps and th cohrnt ntgraton tm s formula rlatng cohrnt ntgraton tm to opplr bn sz, th mamum rror bng th opplr bn sz ovr two. θ bng th ntal phas rror, t s unformly dstrbutd btwn and π. Not that corrlator s rlatd to th corrlator output as th C/N of data channl s.5 db lowr than C/A and th rsdual opplr frquncy rror on s drctly rlatd to th on on by th rato f / f. Tabl : Paramtrs usd to smulat th outputs of th corrlators for Known Paramtrs C/N C/N.5 ms Unknown paramtrs d n Random or - dt dt d ono d ono pndnt on VTEC and Map VTEC Unformly dstrbutd Map Unformly dstrbutd F F f / f θ Unformly dstrbutd Morovr, dt s not anymor only dpndnt on th cod stp sz du to possbl rlatv onosphrc dlay btwn and. As t s assumd that both sgnals ar synchronzd, dt must b qual to dt on plus th onosphrc dlay. Undr common onosphrc condton, th Vrtcal Total Elctron Contnt VTEC vars btwn VTEC and 3 VTEC durng daylght. Howvr, as th sgnal path through th onosphr dpnds on th satllt lvaton, a mappng functon varyng btwn for 9 lvaton and 3 for lvaton must multply th VTEC n ordr to obtan th lant TEC TEC. Fnally th rlatv tm dlay btwn and sgnal can b prssd as: t 7.3 f f VTEC Map 8 f f As such, dt s now dpndnt on two unknown paramtrs namly th VTEC and th mappng factor. Both ths paramtrs whr smulatd usng a unform Europan Navgaton Confrnc 8 Toulous, Franc Apr3-5, 8 /9
Europan Navgaton Confrnc 8 Toulous, Franc Apr3-5, 8 5/9 dstrbuton varyng rspctvly btwn VTEC and 3 VTEC and and 3. IMUATION PROCE ETAI Frst of all, th smulaton prformd amd to assss th prformanc of th combnd acquston tchnqus usng ms cohrnt ntgraton wth four non-cohrnt summatons M. Consdrng th vctor of corrlator output on and on as: [ ] 3 3 X Th output of ach combnd acqustons s dnotd as. For all th combnd ths can thn b prssd through a quadratc form: AX X H 9 H standng for Hrmtan conjugat. As such, th NC mthod can b prssd as NC and has a dsgn matr A NC as follows: A NC Th NCff mthod can b prssd as NCff and has a dsgn matr : A NCff Th COH mthod can b prssd as COH and has a dsgn matr: A NCff Fnally, th last mthod NCM bng prssd as NC nds a slght modfcaton of th X vctor as X m : [ ] 3 3 m X As such, w can now apply th quadratc form wth A NCM as follows: A NC Not that th combnd acquston proposd wr thn compard to th common C/A non-cohrnt acquston whch can b prssd as: NC Thrfor, th quadratc form can also b usd drctly wth X wth A NC prssd as: A NC
REUT Frst th ovrall prformanc of th proposd acqustons ar nvstgatd usng th smulaton paramtrs dscrbd n Tabl 3. Tabl 3: Paramtrs usd to assss th post-corrlaton mthods prformanc C/N 3 db-hz C/N 5.5 db-hz ms Cod phas stp.5 chp F Unform on [ ; 333.33] Hz F F f / f θ θ Unformly dstrbutd on [ π] Numbr of trals, As mntond arlr n ths papr, th sgnal powr of C/A s.5 db abov that of CM channl whch s commonly usd n th acquston procss, wth th plot channl bng zro-paddd. Thrfor, on has to b carful whn tryng to combn C/A and CM sgnals. Indd as mor sgnal powr s prsnt on C/A than CM, th lattr should hav lss wght that th formr. Assumng a wght of on C/A, th thortcal CM wght to apply s drctly rlatd to th rlatv powr R C/N of th two sgnals as follows: smallr wght than th synchronzd and sgnals cas. Not that th optmal wght s thrfor dpndnt of th onosphr actvty. Onc th optmal wght of.5 has bn dtrmnd, th ovrall prformanc of all th proposd mthods ar assssd usng th sam paramtrs than th on prsntd n Tabl 3. Rsults ar prsntd through th Rcvr Opratng Curv ROC whch s bascally th probablty of dtcton as a functon of th probablty of fals alarm. Not that th ROC curv obtand s th quvalnt of th on a rcvr would hav f t had no accss to any trnal nformaton. Fgur 8 llustrats th rsults obtand for ach acquston mthods. It clarly shows th advantag of combnng and sgnal usng th NC or th NCff mthods. Indd, both of ths mthods provd to outprform th probablty of dtcton obtand usng a non-cohrnt acquston on only. W R C / N /.6 Th ffct of applyng a dffrnt wght to th output of th corrlators s llustratd n Fgur 7. Not that n ths fgur, th probablty of dtcton s gvn for th NC mthod. Fgur 8: Rcvr Opratng Curv ROC for th dffrnt mthods proposd. Howvr, th COH and th NCM hav an ovrall probablty of dtcton wors than that obtand usng th NC mthod. Fgur 7: Probablty of dtcton obtand by applyng dffrnt wghts to th post-corrlaton outputs As clarly shown n Fgur 7, th thortcal wght of.6 dos not corrspond to th optmal on whch s.5. Indd, th probablty of dtcton obsrvd usng a wght of.5 s abov all th ons obtand wth a dffrnt wght. Ths can b asly plan by th fact that th thortcal wght found was not takng nto account th onosphrc dlay whch bhavs n ths cas lk a sgnal attnuaton on and as such calls for a In th cas of th COH mthod, th dgradaton obsrvd s pland by th fact that no nformaton on th sgnal phass or th data bts was avalabl to th rcvr. As such, f both sgnals had th sam ntal phas but th data bt transmttd on wr of th oppost sgn than th on transmttd on, addng th two sgnals cohrntly wll dstroy th sgnal componnt. mlarly, f both sgnals hav th sam data bt sgn but ar out of phas by π, th cohrnt summaton wll rsult n a dgradaton of th total sgnal powr. Fnally, vn f both sgnals hav th sam data bt and ntal phas rror, th dffrnt rsdual opplr frquncy wll rsult n a phas shft btwn th two sgnals ovr tm whch tslf wll rsult n a sgnal dgradaton durng th cohrnt summaton of th and corrlator outputs. Fgur 9 llustrats th dgradaton that wll b obsrvd for ach non-cohrnt summaton M as a functon of th rsdual opplr frquncy rror. Not that th rlatv ntal phas dffrnc btwn and sgnals was st to zro. Europan Navgaton Confrnc 8 Toulous, Franc Apr3-5, 8 6/9
rarrangmnt of th NCff quaton can asly plan ths bhavour: NCff Fgur 9: gradaton obsrvd on th cohrnt summaton of and post-corrlaton outputs for ach mllscond as a functon of opplr rsdual On th othr hand, th NCM mthod s obvously also dpndnt on th frquncy rror through th multplcaton of th two snc functons. Howvr, th gratst bottl nck of ths mthod dos not com from any rmanng rrors on th sgnals. Indd, du to th multplcaton, wghtng th post-corrlaton output s uslss thrfor t can not consdr th fact that th sgnal has a sgnal powr.5 db lowr than C/A. From th abov quaton, t s clarly vdnt that th NCff mpls a cohrnt summaton of two succssv post-corrlaton outputs on th sam frquncy. As such, th cohrnt ntgraton tm for ths summaton s ms and so th rsultng opplr bn sz must b dvdd by two compard to th on mllscond cas to avod larg sgnal dgradaton. Th mamum opplr rsdual rror should thn b rducd to about 65 Hz to consrv farly good prformanc. Not that at ths pont, th opplr rror of s only of 8 Hz and that th corrspondng boundars for th opplr rror to b 65 Hz s a opplr rror of Hz. At ths pont, both and cohrnt summatons show a strong dgradaton rsultng from th combnd acquston proposd. Fgur clarly llustrats ths ffct as th NCff mthod bgns to prnc th strongst dgradaton n th probablty of dtcton and prforms wors than th NC onc th rsdual opplr rror of s about 5 Hz In ordr to confrm th abov rsults and planatons, anothr srs of smulaton was prformd usng th followng paramtrs Tabl. In ths cas, assssng th ffct of th rsdual opplr frquncy on th acquston schms was attmptd. In ordr to do so, all of th data bt transtons wr manually rmovd as wll as any ntal phas rrors. Tabl : mulaton paramtrs usd to assss th ffct of th frquncy rror on th acquston schms C/N C/N 3 db-hz 5.5 db-hz ms.5 chp From to 333.33 Hz Cod phas stp F F F f / f θ θ Pfa. Numbr of trals, Fgur llustrats th rsults obtand as a functon of th rsdual opplr frquncy rror on. Not that as mntond arlr, th opplr rrors on ar rlatd to th opplr rrors on by th rato f / f. It s obsrvd that th two mthods th most affctd by a rsdual opplr rror ar th COH as pctd and th NCff. Ths last pont can b rathr surprsng as both th non-cohrnt mthod and dffrntal mthod takn sparatly am to gt rd of th rsdual dynamcs. As such, thy ar only dpndnt on th opplr rror trm through th snc functon. Howvr, a smpl Fgur : Effct of rsdual opplr rrors on th dffrnt acquston mthods On th othr hand, t has bn mntond that th rlatv phas offst would affct th COH mthod. In ordr to vrfy ths last pont and confrm that t dos not affct any of th othr mthods, a fnal smulaton was prformd usng th followng paramtrs. Not that n ordr to analyz th ffct of th rlatv phas offst only, rsdual opplr rrors and data bts wr rmovd from th smulaton. Europan Navgaton Confrnc 8 Toulous, Franc Apr3-5, 8 7/9
Europan Navgaton Confrnc 8 Toulous, Franc Apr3-5, 8 8/9 Tabl 5: mulaton paramtrs usd to assss th ffct of th ntal rlatv phas rror btwn and on th acquston schms C/N 3 db-hz C/N 5.5 db-hz ms Cod phas stp.5 chp F F F f / f θ θ From to π Pfa. Numbr of trals, Fgur : Effct of th rlatv phas offst btwn and sgnals on th dffrnt acquston mthods Rsults obtand ar shown n Fgur. As was pctd and pland prvously, th COH mthod s strongly affctd by th rlatv phas offst as t mpls th cohrnt summaton of th post-corrlaton outputs of th and sgnals. On th othr hand, non of th othr mthods nvolvd such a summaton and thy ar not affctd by th rlatv phas offst btwn th sgnals. Fnally, a last st of data was smulatd to assss th prformanc of ach acquston n cas of a ms cohrnt ntgraton. Tabl 6: Paramtrs usd to assss th post-corrlaton mthods prformanc C/N 3 db-hz C/N 5.5 db-hz ms Cod phas stp.5 chp F Unform on [ ; 66.66] Hz F F f / f θ θ Unformly dstrbutd on [ π] Numbr of tral, Not that th output of th corrlators s stll smulatd ovr ms n ordr to assss for possbl data bt transtons on C/A or CM. As such th dsgn matr usd for ach mthod must b modfd. Th NC mthod can now b prssd as NC and has a dsgn matr A NC as follows: A NC Th NCff mthod can b prssd as 3 3 NCff and has th followng dsgn matr: A NCff Th COH mthod can b prssd as NCff and has th followng dsgn matr: A NCff Fnally, th last mthod NCM bng prssd as NC and th followng dsgn matr s usd: NC A
wth X m bng a vctor of two lmnts such as: X m Th ovrall prformanc of ach mthod for a ms cohrnt acquston s shown n Fgur. Th NCff mthod s stll prformng wll but s now undr th NC mthod. Onc agan, ths s du to th cohrnt summaton carrd by th NCff tchnqu and callng for a smallr opplr frquncy bn sz. of Navgaton, Cambrdg Unvrsty Prss, 6, 3, 97-55. m,.w.,.w. Moon, C. Park,.J. 6 /C GP Rcvr Implmntaton wth Fast Acquston chm, Poston, ocaton, And Navgaton ymposum, 6 IEEE/ION, 5-7 Aprl, pp 8-8. Muthuraman, K.,.K. hanmugam and G. achapll 7 Evaluaton of ata/plot Trackng Algorthms for GP C gnals Usng oftwar Rcvr, n Procdngs of GN 7, 5-8 ptmbr, Fort Worth TX, Insttut of Navgaton. Psak, M..,. Wntrntz, M. Morau FFT- Basd Acquston of GP Cvlan CM and C gnals, n Procdngs of th ION GN, ong Bach, ptmbr, Insttut of Navgaton. Watson, R., G. achapll, R. Klukas,. Turunn,. Ptlä and I. Halvaara 6 Invstgatng GP gnals Indoors wth Etrm Hgh-nstvty tcton Tchnqus. Navgaton, Journal of th Insttut of Navgaton, 5,, 99-3. Fgur : Prformanc of ach mthod usng a two ms cohrnt ntgraton tm On th othr hand, th COH mthod havng no nformaton about th rlatv phas offst and th data As to th mthod nvolvng th summaton of both noncohrnt and dffrntal acquston on and, t was provd that vn though th dffrntal or non-cohrnt tchnqu ar ndpndnt of th carrr frquncy rror but for th snc trm, t s not th cas for th NCff mthod. Fnally, th NC mthod rprsntng th summaton of non-cohrnt on and non-cohrnt on rmans th bst mthod as t s ndpndnt of th rsdual opplr frquncy rror and th rlatv phas offst btwn th sgnal and provd to outprform th non-cohrnt acquston of only. Yang, C. 5 Jont Acquston of CM and C Cods for GP C, n Procdngs of ION GN 5, ong Bach, Calforna, ptmbr 5, Insttut of Navgaton ACKNOWEGEMENT Th frst author would lk to thank Flornc Macch, Ph studnt n Gomatcs Engnrng, for hr constant hlp and support, as wll as th Informatcs Crcl Of Rsarch Ecllnc CORE and th GEOIE Ntworks of Cntrs of Ecllnc for thr fnancal support. REFERENCE Grnot, C.,.K. hanmugam, K. O Kf and G. achapll 7 A Novl and C Combnd tcton chm for Enhancd GP Acquston, n Procdngs of GN 7, 5-8 ptmbr, Fort Worth TX, U.. Insttut of Navgaton. Ioannds R. T.,.E. Aguado and G. Brodn, vrs gnals Combnatons for Hgh-nstvty GN, Journal Europan Navgaton Confrnc 8 Toulous, Franc Apr3-5, 8 9/9