A Self-adaptive open loop architecture for weak GNSS signal tracking

Transcription

1 NTERNATONAL JOURNAL OF CRCUTS, SYSTEMS AND SGNAL PROCESSNG Volum 8, 014 A Slf-adaptv opn loop archtctur for wa GNSS sgnal tracng Ao Png, Gang Ou, Janghong Sh Abstract An FFT-basd opn loop carrr tracng archtctur for wa GNSS (Global Navgaton Satllt Systm) sgnal s ntroducd n ths papr, as wll as a slf-adaptv mthod whch s dvlopd to mprov th stablty and rlablty of th archtctur. Prformanc of th proposd archtctur s analyzd thortcally. Smulaton rsults show th proposd archtctur s mor stabl and rlabl n wa sgnal nvronmnts, compard wth tradtonal clos loop archtctur. Kywords GNSS, carrr tracng, wa sgnal, opn loop, slf adaptv.. NTRODUCTON HE Global Navgaton Satllt Systm (GNSS) provds Taccurat postonng and tmng srvc basd on xtrmly accurat dstanc masurmnts from satllts to rcvr. Tang GPS for nstanc, sgnal transmsson tm from dffrnt satllts to a spcfd rcvr s masurd through a long prodcal bnary psudo-random gold cod, C/A cod for cvlan and P(Y) cod for mltary[1]. Th rcvr rqurs a stabl carrr tracng mchansm to obtan C/A cod nformaton and navgaton bts. Most tradtonal rcvrs us clos-loop archtcturs to mplmnt th carrr tracng archtctur. Thy nclud phas loc loop (PLL), whch s popular n commrcal rcvrs for ts low cost and hgh stablty, and xtndd Kalman fltr basd tracng loop[], whch can wor undr lowr sgnal-to-nos rato nvronmnt than PLL. Many wor[3-5] hav bn don on clos-loop tracng soluton to mprov th loop prformanc by choosng approprat ntgraton tm[3] or by usng othr adaptv and probablstc mthods[5]. But a drawbac stll xsts that whn th carrr-to-nos rato (CNR) dtrorats th clos-loop archtcturs bcom lss stabl. Onc a rcvr loss loc, t wll ta a long tm to dscovr th loss of loc and fx t. n comparson wth clos-loop archtcturs, opn-loop archtcturs manly basd on FFT algorthm hav a sgnfcant advantag on rlablty and robustnss. Th carrr frquncy can b drctly obtand through th FFT algorthm wthout a Ao Png s wth School of nformaton Scnc and Engnrng, Xamn Unvrsty, Xamn, Chna; (-mal: pa@xmu.du.cn). Gang Ou s wth School of nformaton Scnc and Engnrng, Xamn Unvrsty, Xamn, Chna; (corrspondng author to provd -mal: ougang@xmu.du.cn). Janghong Sh s wth School of nformaton Scnc and Engnrng, Xamn Unvrsty, Xamn, Chna; (-mal: shjh@xmu.du.cn). long tm fd-bac adjustng procss, n contrast wth clos-loop solutons. Ths long tm fd-bac procss may lad to loss of loc, spcally n wa sgnal condtons. What s mor, FFT-basd opn loop archtctur can obtan th ntr mag of sgnal by computng th powr spctrum. Th sgnal-to-nos rato of vry obsrvaton can b drvd from FFT rsult, wth whch th rcvr can dcd to gv out vald carrr frquncy stmaton or ma a furthr procssng. Mor dffrncs btwn clos-loop and opn-loop archtcturs can b sn n [6]. Th man wor of ths papr s to dvlop a FFT basd opn loop GNSS carrr tracng archtctur. Th FFT calculaton lngth n th proposd archtctur s lmtd so that th mplmntal complxty s accptabl. Bsds, a lngth-adaptv ntgraton mthod s also ntroducd to obtan a bttr prformanc undr vry low CNR condtons. Th rst of ths papr s organzd as follows: w start wth th sgnal modl n scton. n Scton 3, w prsnt th opn loop tracng archtctur. Th prformanc of th proposd archtctur s thn analyzd thortcally n Scton 4. Smulaton and analyss ar prformd n Scton 5. Fnally, conclusons ar drawn n Scton 6.. SGNAL MODE GPS s a Drct-Squnc cod dvson multpl accss systm. ts L1C sgnal uss a 1.03MHz psudo-random gold cod calld C/A cod. Th navgaton data bts ar BPSK modulatd, and th data rat s 50Hz. Th rcvd GPS sgnal s down convrtd to ntrmdat frquncy and sampld to a srs of dscrt valu s[] gvn by s[ ] = Ad[ ] C[ ]xp{ j[ π( ff + fd ) Ts + θ0]} + n0[ ] (1) whr A s th rcvd sgnal magntud, d[] s navgaton data bt, C[] s th GPS L1 C/A cod, f d s th Dopplr frquncy causd by rlatv moton btwn satllt and rcvr, n 0 s addtv wht Gaussan nos wth zro man and varanc σ. A rcvr gnrats two orthogonal carrr rplcas and a C/A cod rplca. Assum C/A cod has bn roughly synchronzd n a stabl tracng cas, whch mans th cod phas dffrnc btwn rcvd sgnal and local rplca dos not xcd 1 chp lngth. Th frquncy of ths two orthogonal carrr rplcas s an stmatd valu gvn by th rcvr, wth an stmaton rror dnotd as f. Hr w us short tm cohrnt SSN:

2 NTERNATONAL JOURNAL OF CRCUTS, SYSTEMS AND SGNAL PROCESSNG Volum 8, 014 ntgraton to mprov th SNR. Th cohrnt ntgraton tm s an ntgr multpl of 1ms, whch s th prod of C/A cod. Fgur 1 shows th schm of sgnal pr-procssng, whr sampld GPS sgnal s multpld by two orthogonal carrr rplcas and thn d-sprad and ntgratd to mprov th SNR. Th pr-procssd rsult can b xprssd as follows r[ ] = Ad[ ] R( ) Snc( ft)xp[ j π ft + θ] + n '[ ] () whr T s th numbr of cohrnt ntgratd sampls. R( ) s corrlaton functon of C/A cod, s th cod phas dffrnc n (3), th duraton of navgaton data bt d[] s 0ms. Th ffct causd by data bt transtons should b rmovd whn mor than on data bt duraton s nvolvd n tracng procss. n [, 8, 9], dffrnt mthods of ral-tm navgaton data bts stmaton ar rportd. Th navgaton data bts can also b obtand from a narby rfrnc staton. Thrfor, d[] s consdrd as nown n th follog parts. n th follog part of ths papr, an opn loop and slf-adaptv ntgraton mthod basng on FFT algorthm wll b dvlopd to gv a rlabl and stabl stmaton on f. Fg. 1 Schm of pr-procssng btwn rcvd sgnal and local C/A cod rplca, n'[ ] s a complx Gaussan nos charactrzd by zro man and σ T varanc [7]. Whn cod phas dffrnc s gratr than 1 chp, th valu of C/A cod corrlaton functon approachs zro. R( ) shows th ffct of cod phas stmaton rror on carrr frquncy stmaton. Snc( x) dnots th ntgraton loss causd by frquncy rror. Th pr-procss rsult can also b smply wrttn as r[ ] = A' d[ ]xp( θ)xp( j π ft) + n '[ ] (3) whr A' = AR( ) Snc( ft), n '[ T] ~ N(0, σ T). Durng th procssng prod, frquncy rror f and cod phas rror τ can b tratd as constants, so th modfd sgnal magntud A ' s also a constant. As w can s, r [ ] has a sngl frquncy spctrum wth samplng prod T. n tradtonal GPS rcvrs, a phas dscrmnator s always usd to gt a vald masurmnt on r [ ]. Tang optmal arctangnt dscrmnator as an xampl, as sgnal powr gos war, ts nos prformanc dtrorat nonlnarly[3]. What s mor, tradtonal phas dscrmnators do not tll th rlablty of ts outputs bcaus thy only provd nos-mxd obsrvaton rsults. On th contrary, Fourr Transform provds anothr way to achv frquncy obsrvaton and ts rlablty. Fourr transform calculats powr on all sampld frquncs, ncludng frquncy wth sgnal and frquncs wthout sgnal. So for vry obsrvaton, rlablty masurmnt can b asly mad by comparng th sgnal powr to nos powr. Thus, furthr procssng dcson can b mad basd on th rlablty.. OPEN LOOP TRACKNG ARCHTECTURE Fourr transform s wdly usd n sgnal acquston [10], and untl now thr ar som wors [6, 11] usng t n GPS sgnal tracng. n comparson wth clos-loop tracng archtcturs such as PLL or EKF-basd tracng loop, FFT-basd archtctur nds larg storag rsourc, arthmtc rsourc and long calculaton prod. Howvr, FFT-basd archtctur has som aspcts whch ar rally attractv to carrr tracng. Frst, Fourr transform gvs an ovrvw of sgnal spctrum and GPS sgnal, aftr d-spradng, s a sngl frquncy sgnal, whch mans thr should b only on pa n th Fourr transform rsult. So th obsrvaton rlablty s nhrntly ncludd n th Fourr transform rsult. Scond, n ach calculaton prod Fourr transform only nd currnt data sampls, and hstory rsults hav no ffct on th currnt rsult. So ts shoc rspons rat s much hghr than loops. Thrd, FFT-basd tracng archtctur do not nd addtonal loc-loss dtctor. Du to such advantags, a FFT-basd opn loop tracng archtctur s proposd n ths papr. Fg. Bloc dagram of FFT-basd opn loop tracng archtctur Fg. shows th bloc dagram of FFT-basd Opn loop tracng archtctur. Th pr-procssd sampls r [ ] ar stord n a buffr and truncatd nto groups. Lngth of ths groups s qual to th FFT lngth. A 3-pont or 64-pont FFT s usd hr. FFT lngth dcds frquncy rsoluton whn th samplng frquncy ps constant. n th pr-procssng SSN:

3 NTERNATONAL JOURNAL OF CRCUTS, SYSTEMS AND SGNAL PROCESSNG Volum 8, 014 modul th cohrnt ntgraton tm s T, and f FFT lngth s L, frquncy rsoluton can b xprssd by 1 f = (4) LT Spctral laag causd by dscrt Fourr transform rsults ( ) n attnuaton on SNR, so a dow functon h L s usd to ( ) rduc th spctral laag. Th Fourr transform of h L s dnotd as H ( ω ). Thr ar mportant factors to b consdrd whn choosng a propr dow functon: man lob wdth and sd lob supprsson rato (SLSR). Bcaus r [ ] s a narrowband sgnal, so SLSR s much mor mportant than man lob wdth. On ffctv mthod to supprss th sd lob s usng th Hannng dow. Th frst sd lob attnuaton of Hannng dow s -3dB whl th rctangl dow has only 13dB attnuaton on th frst sd lob. Th FFT rsult s jπ l Y = r () lh ()xp l l = 0 L (5) whr h () l s Hannng dow π l h ( l) = cos (6) L By tang (3) n to (5), w gt sn ( π Lfε ) Y = AH ' xp jπ fε ( ) (7) sn π f ( ) Whn f = ft ε L 0, Y ( ) mts ts mum valu. Frquncy rror can thn b drvd as f = + ε (8) LT whr ε shows th dscrt proprty of FFT, that FFT cannot ma an accuracy stmaton and thr s always a frquncy quantzaton rror. Th valu of quantzaton rror dos not xcd half of frquncy rsoluton 1 ε (9) LT As shown n Fg., thr s an accumulaton bypass dnotd by (). Th accumulaton opraton s dfnd as M 1 1 Sxx = Y (, ) (10) M = 0 whr M s accumulaton prod whch s dcdd dynamcally by th succdng analyzr, and Y (, ) dnots th FFT rsult on th th samplng frquncy n calculaton prod. t s obvous that th accumulaton bypass provds powr spctrum stmaton on r [ ]. Du to accumulaton opraton, th SNR of powr spctrum stmaton can b rducd by a factor of M [1, 13]. Accumulaton bypass s controlld by th analyzr, both on ntgraton opraton and clarng opraton. Th man functon of analyzr shown n Fg. s valuatng th rlablty of FFT rsult and accumulaton rsult from th bypass basd on SNR. Hr SNR s dfnd by ε Y S ( ) xx SNR =, (11) Y S ( ) ndpa xx ndpa whr Y s th pa valu of FFT rsult Y ( ), and Y s th scond pa valu of Y ( ) ; ndpa Sxx s th pa valu of accumulaton rsult S ( ) xx and Sxx ( ) s th scond pa valu of S ( ) ndpa xx. A thrshold TH SNR s usd hr to fltr bad stmatons. Nw stmaton s not avalabl untl SNR s gratr than TH SNR. Anothr functon of th analyzr s to gnrat control sgnals to FFT modul and accumulaton bypass. Ths control sgnals ar classfd nto 3 stats, as dscrbd n th follog. 1. Fast calculaton. n ths stat, 3-pont FFT s usd, and th accumulaton bypass clars ts hstory rsult at th bgnnng of th currnt prod. Ths s th basc stat of th opn loop tracng archtctur. Whn SNR s gratr than th thrshold, whch mans a nw stmaton was avalabl n th prvous prod, th hstorc accumulaton rsult s clard and a nw accumulaton prod bgns.. Accumulaton. n ths stat, 3-pont FFT s usd, and th accumulaton bypass s worng. Ths stat happns n th cas that SNR n th prvous prod was smallr than th thrshold. n ths stat no rlabl stmaton s obtand so NCO ps ts oscllaton frquncy. 3. Fn calculaton. n ths stat, 64-pont FFT s usd, and th accumulaton bypass stops worng. Ths stat s dsgnd to ncras th rlablty of th frquncy stmaton whch s analyzd n th nxt part. Whn tracng s stabl, whch s dfnd by mor than 5 contnuous Fast calculaton prods, FFT lngth sprads to 64 ponts. Currnt stat dos not chang from Fn calculaton nto Fast calculaton untl SNR s not gratr than thrshold. Worng stat swtchs automatcally among ths 3 stats. Thrfor, ths opn loop tracng archtctur s slf-adaptv to th dynamc nvronmnt. n th follog part, prformanc of th abov proposd archtctur s analyzd thortcally. V. PERFORMANCE ANALYSS Frquncy rror stmaton s drvd from (8), whr dnots th ndx of mum pa valu. By tang (8) nto (7), th xprsson of pa valu s obtand by Y A' LH Snc( πlε) (1) { } whr th approxmaton sn( πε ) πε s adoptd, and th nos s not tan nto consdraton. n (), n'[ ] = n' [ ] + jn' Q[ ], whr n'[ ] and n'[] Q ar both ndpndnt Gaussan Wht Nos wth dstrbuton of σ { n', n' Q} ~ N 0, (13) T so th FFT rsults of n'[ ] s SSN:

4 NTERNATONAL JOURNAL OF CRCUTS, SYSTEMS AND SGNAL PROCESSNG Volum 8, 014 π N ' = n '() l + jn ' Q () l h ()xp l j l l = 0 L (14) Snc n'() l and n' Q () l (l=0, 1,, L-1) ar ndpndnt Gaussan random varabls, th lnar combnatons of thm ar also Gaussan random varabls. Dvd (14) nto ral part and magnary part N' R = { n'()cos l ωl, + n' Q ()sn l ωl, } h () l (15) l = 0 { ω ω } N' = n'()sn l n' ()cos l h () l (16) m l, Q l, l = 0 whr ωl, = πl L. Both R[ N'( )] and m[ N'( )] ar zro-man Gaussan random varabls, and thr varancs ar [14] Lσ H Var{ N ' R } = Var{ N ' m } = (17) T Th powr spctrum of nos obys xponntal dstrbuton wth rat paramtr 1 LTσ H. Th possblty dnsty functon (PDF) of nos powr spctrum s T T f( x) = xp x (18) Lσ H Lσ H Whn nos s gnord, th rsult of (1) s dtrmnstc. Whn tang nos nto consdraton, FFT rsult on th man pa [ ] P = P Y + Var N ' LH σ (19) [ A' LH Snc( πlε) ] + T Th powr on th man pa obys non-cntral Ch-squard dstrbuton wth dgr of frdom v=. So ts PDF s [15] 1 x + λ gx ( ) = xp 0 ( λx) (0) whr λ s dfnd by ( πlε) A' T LSnc λ = (1) σ and ( ) 0 x s zro ordr modfd Bssl functon of th frst nd. Th cumulatv dstrbuton functons (CDF) of f(x) and g(x) ar dnotd by F(x) and G(x) rspctvly. W hav F( x) = ( ) = 1 xp Tx x f t dt t 0 = Lσ H () x ( ) () G x = g t dt (3) t = 0 Fg. 3 shows an xampl of probablty dstrbuton. Th rcvd satllt sgnal powr n (1) s assumd to b normalzd, and th carrr-to-nos rato (CNR) s 15dB-Hz. t also assums dal cod tracng, so that attnuaton R( ) Fg. 3 Probablty dstrbuton of powr spctrum (CNR=15dB-Hz) frquncy bcoms a complx Gaussan random varabl, whos man s Y [ ] and varanc s Var[ N '( )]. Lt PY [ ( )] dnots th powr of sgnal wthout nos, w hav causd by cod phas rror can b gnord. Th lft part of Fg. 3 shows CDF, whl PDF s shown n th rght part. t can b sn that th probablty s almost th sam whn th nos powr lvl s no mor than 5dB, and th nos powr lvl has a hgh llhood (>0.7) to stay blow 15dB. On th contrary, thr s a hgh probablty (>0.9) that th sgnal powr ls btwn 15dB and 0dB. SSN:

5 NTERNATONAL JOURNAL OF CRCUTS, SYSTEMS AND SGNAL PROCESSNG Volum 8, 014 Equaton (3) shows that th GPS sgnal s a sngl frquncy sgnal aftr d-spradng. So aftr Fourr transform, sgnal only xsts on th corrspondng frquncy, whl th rst powr spctrum can b consdrd as nos spctrum. Dnot frquncy ndx wth sgnal by s, th FFT rsults oby th follog dstrbuton Gx ( ); = s Pr { Y < x} = (4) F( x); s n th Fast calculaton stat and Fn calculaton stat, vald frquncy stmaton s obtand whn th currnt SNR s gratr than th thrshold, wth pa valu P. Dnot th vnt Th man pa appars on th frquncy wth pa valu P and all othr powr valus ar smallr than P / TH SNR by E thn th probablty of E s P g( P ) F ; = s s TH SNR Pr{ E} = (5) P P f ( P ) G F ; s TH SNR s, TH SNR A corrct stmaton s obtand only whn E happns and = s. Th rror rat can thn b drvd by { E } Pr P Pr { } 1 s = s E = (6) Pr L { E } n th Accumulaton stat, th avrag of powr spctra n accumulaton prod s tan as th stmatd powr spctrum. Th accumulaton procss wll not stop untl SNR s gratr than th thrshold. Th avrag acton lads to rducton of nos varanc. Thr ar M sgmnts rfrrng to (10), so th varanc s rducd by M [1]. Th rlatonshp btwn M and rror stmaton probablty s shown n Fg. 5, whr a thrshold of 1.3 s usd and CNR s 13dB-Hz. As w can s n Fg. 5, th mnmal rror stmaton probablty s gratr than 0.75 whn no accumulaton tan plac (M=1). Howvr whn th accumulaton stat lasts for 3 prod (M=3), th rror probablty dcrass to around 0.05 whn P s btwn 15dB and 0dB. Aftr accumulaton, th rlablty of stmaton s mprovd sgnfcantly. Fg. 5 Probablty of rror stmaton undr dffrnt accumulaton lngths n Fn calculaton stat, 3-pont FFT s rplacd by 64-pont FFT. Th changs ar shown n Fg. 6, whr CNR s 15dB-Hz and th thrshold s 1.3. Th lft part shows th dffrnc n PDFs. Th typcal ara of sgnal powr wth hgh probablty rss from 13~18dB to 17~1dB. Th dffrnc n stmaton rlablty s shown n th rght part. Whn usng 64-pont FFT, th mnmal probablty of rror stmaton dcrass from 0.5 to 0.. Dffrnt thrsholds ar compard n Fg. 4. Th CNR s 15dB-Hz. Whn P locats n th ara btwn 10dB and 15dB, th rat of rror stmaton s rlatvly low. Rfrrng to th PDF shown n Fg. 3, sgnal powr has a bg probablty to locat n ths ara. Fg. 4 also shows that probablty of rror stmaton dcrass f th thrshold ncrass. f th thrshold s st to b 1.7, th probablty of rror stmaton s lss than 0.. Howvr, ncrasng th thrshold mans th nos powr stays at a lowr lvl, whch quals to th dcras of th probablty of Fg. 4 Probablty of rror stmaton vs. P E. A vald stmaton can t b obtand f dosn t happns. Such a tradoff should b consdrd whn choosng th valu of th thrshold E V. SMULATON RESULTS n ths scton, prformanc of th proposd opn loop tracng archtctur basd on FFT algorthm undr wal sgnal nvronmnts s valdatd by smulatons. To focus on th carrr tracng prformanc, dal cod tracng s assumd. Th Dopplr frquncy s modld as changng lnarly ovr tm, wth a fx but nos affctd Dopplr rat. Th ntal frquncy rror s -50Hz, whch s guarantd by th prcson of th acquston modul. Th fxd Dopplr rat s st to b -0.5Hz/sc, and th nos addd to th Dopplr rat s Gaussan wht nos wth zro man and unt varanc. SSN:

6 NTERNATONAL JOURNAL OF CRCUTS, SYSTEMS AND SGNAL PROCESSNG Volum 8, 014 Samplng frquncy of th rcvd satllt sgnal s MHz, and th cohrnt ntgraton tm s 0.005sc. Thrfor th numbr of cohrnt ntgraton sampls s loop s 3. To valdat th tracng ablty undr wa sgnal nvronmnts, th smulaton s stup up as follows. At th bgnnng of th smulaton, th CNR s 33dB-Hz. t dcrass Fg. 6 Dffrncs btwn fast calculaton stat and fn calculaton stat Cass wth dffrnt CNRs ar tstd and rrors of frquncy stmaton ar shown n Fg. 7. n Fg.s 7(a), 7(b) and 7(c), th CNRs ar 13dB-Hz, 14dB-Hz and 15dB-Hz rspctvly. n Fg. 7(a), t tas a long tm to achv stabl tracng stat. n Fg. 7(b), a bg stmaton rror happns around 47sc, and th tracng stat qucly rcovrs n th nxt updat prod. n Fg. 7(c), whn th CNR s 15dB-Hz, thr s no bg stmaton rror among th tst prod, and at most part of th prod th stmaton rror s wthn +/-5Hz. n all th 3 tst cass th proposd archtctur ps tracng to th Dopplr frquncy, and no loc-loss happns durng 70 sconds. t can b concludd that th opn loop tracng archtctur basd on FFT algorthm s stabl and rlabl undr wa sgnal nvronmnts. by 4dB-Hz vry 100 sconds untl 13dB-Hz. Th CNR rmans 13dB-Hz for 00 sconds and thn rss wth a spd of 4dB-Hz pr 100 sconds. A smpl CNR stmator s usd as loc ndcator. Th rsults ar shown n Fg.8. For th proposd opn loop archtctur, th stmatd CNR fluctuats havly whn th truth valu drops to 13dB-Hz. Howvr, t stll ps tracng to th carrr. Whn th CNR rss up agan, th varaton trnds of th stmatd CNR s sam to th truth valu. For th compard EKF basd archtctur, loss of loc happns whn CNR drops to 13dB-Hz. Th stmatd CNR dcrass to 0 as shown n Fg.8, whch mans no sgnal powr s dtctd. And whn th CNR rss up agan, th stmatd CNR was not rcovrd. Fg. 7 Prformanc undr dffrnt CNRs Th proposd archtctur s also compard wth classcal clos loop archtctur basd on xtndd Kalman fltrng. Th dtals of an EKF basd carrr tracng loop can b found n [, 8]. Th cohrnt ntgraton prod of th EKF basd loop s st to b 5ms, th sam as t usd n th proposd opn loop archtctur. And th non-cohrnt lngth of th EKF basd Fg. 8 Comparson wth th classcal clos loop archtctur SSN:

7 NTERNATONAL JOURNAL OF CRCUTS, SYSTEMS AND SGNAL PROCESSNG Volum 8, 014 Th slf-adaptv proprty of ths opn loop archtctur s tstd by statstcs of tm spnt n th 3 dffrnt tracng stat, fast calculaton, accumulaton and fn calculaton. t s shown n Fg. 9. Whn th CNR s 15dB-Hz, th proposd archtctur s worng n Fn calculaton stat most of th tm. As nos powr rsng, th archtctur nds mor tm for accumulaton. Whn th CNR dcrass to 13dB-Hz, rar tm s spnt n Fn calculaton stat, and th worng stat swtchs btwn Accumulaton and Fast calculaton to obtan a stabl condton. Fg. 9 Tm statstcs n dffrnt stats [7] A. Van Drndonc, P. Fnton, and T. Ford, "Thory and prformanc of narrow corrlator spacng n a GPS rcvr," Navgaton, vol. 39, pp , 199. [8] N. Zdan and J. Garrson, "Bt synchronzaton and Dopplr frquncy rmoval at vry low carrr to nos rato usng a combnaton of th Vtrb algorthm wth an xtndd Kalman fltr," 001, pp [9] A. Solovv, F. Van Graas, and S. Gunawardna, "Dcodng navgaton data mssags from wa GPS sgnals," Arospac and Elctronc Systms, EEE Transactons on, vol. 45, pp , 009. [10] D. Aopan, "Fast FFT basd GPS satllt acquston mthods," 005, pp [11] S. Satyanarayana., D. Boro., and G. Lachapll, "A Non-Cohrnt Bloc Procssng Archtctur for Standalon GNSS Wa Sgnal Tracng," n ON GNSS 011, Portland, OR, 011. [1] K. Barbé, R. Pntlon, and J. Schouns, "Wlch mthod rvstd: nonparamtrc powr spctrum stmaton va crcular ovrlap," Sgnal Procssng, EEE Transactons on, vol. 58, pp , 010. [13] J. G. Proas and D. G. Manolas, "Dgtal sgnal procssng: prncpls, algorthms, and applcatons," 199. [14] Q. Lu and Z. L, "Th statstc proprty and applcatons of Gaussan wht nos squnc spctrum," Acoustcs and Elctroncs Engnrng, vol. 1, 003. [15] J. Marcum, "A statstcal thory of targt dtcton by pulsd radar," nformaton Thory, RE Transactons on, vol. 6, pp , V. CONCLUSONS An FFT basd opn loop carrr tracng archtctur for GNSS sgnals undr wa sgnal condtons s proposd. Th proposd archtctur wors rlabl for that t can nspct th rlablty of stmaton valu by computng th nstantanous SNR. Morovr, th archtctur s slf adaptv to th nvronmnt bcaus t can adjust th avrag lngth of powr spctrum durng th accumulaton stat automatcally. By adjustng th avrag lngth, th rlablty of th frquncy rror stmaton mprovs sgnfcantly. Du to th tm ndpndnt proprty of th Fourr transform, onc a sgnfcant stmaton rror happns, th archtctur can qucly rstor to th stabl tracng stat. Smulaton shows that th archtctur can mantan a stabl carrr tracng wth CNR as low as 13dB-Hz. W thrfor argu that for wa sgnal applcatons of GNSS, opn loop archtctur may b a good choc n comparson wth th tradtonal clos loop archtctur. REFERENCES [1] J. Splr Jr, "GPS sgnal structur and prformanc charactrstcs," Navgaton, vol. 5, pp , [] M. L. Psa and H. Jung, "Extndd Kalman fltr mthods for tracng wa GPS sgnals," 001, pp [3] C. O Drscoll, M. G. Ptovllo, and G. Lachapll, "Choosng th cohrnt ntgraton tm for Kalman fltr-basd carrr-phas tracng of GNSS sgnals," GPS solutons, pp. 1-1, 011. [4] A. Razav, D. Gbr-Egzabhr, and D. M. Aos, "Carrr loop archtcturs for tracng wa GPS sgnals," Arospac and Elctronc Systms, EEE Transactons on, vol. 44, pp , 008. [5] D. J. Jwo and S. H. Wang, "Adaptv fuzzy strong tracng xtndd Kalman fltrng for GPS navgaton," Snsors Journal, EEE, vol. 7, pp , 007. [6] F. van Graas, A. Solovv, M. Ujt d Haag, and S. Gunawardna, "Closd-Loop Squntal Sgnal Procssng and Opn-Loop Batch Procssng Approachs for GNSS Rcvr Dsgn," Slctd Topcs n Sgnal Procssng, EEE Journal of, vol. 3, pp , 009. SSN: