A New Fast Acquisition Algorithm for GPS Receivers

Transcription

1 A Nw Fast Acuston Algorthm for GS cvrs Hung Sok So *, Chansk ark **, and Sang Jong L *** * pt. of Elctroncs Engnrng, Chungnam Natonal Unvrsty, ajon Kora (l : ; Fax : ; E-mal: hungsrk@cslab.cnu.ac.kr ** School of Elctrcal & Elctroncs Engnrng, Chungbuk Unvrsty, Chongju Kora (l : ; Fax : ; E-mal:chansp@cbucc.chungbuk.ac.kr *** vson of Elctrcal and Computr Engnrng, Chungnam Natonal Unvrsty, ajon Kora (l : ; Fax : ; E-mal: sjl@cslab.cnu.ac.kr Abstract: In many GS applcatons, such as hgh dynamcs vhcls or an applanc whch uss slp mod to sav powr consumpton, a fast acuston of sgnal s strongly rurd. In ths papr, a nw fast mthod to acur GS sgnal s proposd. h proposd mthods fnd th canddats of opplr shft usng Suard- algorthm, whch s basd upon a sgnal suarng mthod and dramatcally rducs th sarch spac of opplr shft. hs papr also proposs XMC (Xtndd Mult-Corrlator to ffcntly sarch C/A cod. It s dstngushd from th mult-corrlator n that th combnd rplca of svral cods s usd. h xpctd prformanc of XMC mthod s ual to that of th mult-corrlator whl computatonal burdn s rducd to 9%. Kywords: fast acuston, XMC, xtndd mult-corrlator, Suard-. Introducton Most GS rcvrs prform tm-consumng two-dmnsonal sarch to acur th sgnal from satllts bcaus thy hav no cod phas and opplr shft nformaton. It taks at last a fw sconds vn f th almanac s known. ut n many applcatons, such as hgh dynamcs vhcls or an applanc whch uss slp mod to sav powr consumpton, a fast acuston of sgnal s strongly rurd. Corrlators for fast acurng th GS sgnal ar typcally catgorzd nto thr typs: mult-corrlator, matchd fltr, and FF[7]. Howvr, ths mthods hav lmtd applcatons bcaus of computatonal burdns, powr consumptons and thr complxts. A nw algorthm to acur GS sgnal s proposd n ths papr. It fnds th canddats of opplr shft usng a nw mthod calld Suard-, whch s basd upon a sgnal suarng mthod. It dramatcally rducs th sarch spac of opplr shft bcaus th Suard- mthod gvs svral numbrs of canddats of opplr shft. Anothr nw mthod calld XMC (Xtndd Mult-Corrlator s proposd to ffcntly sarch C/A cod. XMC s an xtnson of th mult-corrlator mthod. It s dstngushd from othr mthod n that th combnd rplca of svral cods s usd nstad of sparat ons. h phas of cod can b stmatd wth small numbrs of corrlator s arms undr ths structur. hortcally, 9% numbrs of arms ar usd to gt an uvalnt prformanc of th mult-corrlator. hus th xpctd prformanc of XMC mthod s ual to that of th mult-corrlator whl th complxts and computatonal burdns ar rducd to 9%. It s xpctd that th proposd mthod b asly adaptd to many applcatons whr th fast acuston ar rurd.. Acuston Algorthms. h Sral and aralll Acuston GS sgnal acuston s a sarch procss. h C/A cod dmnson s assocatd wth th rplca cod. h opplr dmnson s assocatd wth th rplca carrr. h uncrtanty n both opplr and C/A cod phas suggsts that a -dmnsonal uncrtanty rgon must b sarchd n ordr to locat th rcvd sgnal. Fgur llustrats th -dmnsonal sarch rgon. Whn th GS rcvr has no almanac avalabl (calld by cold star, th cod uncrtanty rgon s 3 chps, and th opplr uncrtanty rgon s about Hz ~ Hz typcally. Fruncy Uncrtanty h numbr of total clls N opplr bn cll M clls Cod Uncrtanty Cod bn Fgur. Cod / opplr uncrtanty rgon In Fgur, ach opplr sarch ncrmnt s calld a opplr bn, and ach C/A cod phas sarch ncrmnt s calld a cod bn. h combnaton of on cod bn and on opplr bn s a cll. In a sral sarch, th sarchng procdur s xcutd on cll at a tm n sunc, whl n a paralll sarch (Mult-corrlator, groups of clls (M clls ar tstd smultanously. ypcally, th cod bn sz s / chp of CA cod []. h opplr bn sz s about /(3, whr s th I (pr-cton ntgraton tm []. A block dagram of a sngl dwll acuston systm s shown n Fgur. h nput sgnal s th combnaton of th satllt sgnal (s( and th nos (n(. hs nput sgnal s mxd wth th gnratd carrr and cod, and passd through an ntgratd-and-dump (IF wth a pr-cton ntgraton tm of. For a fxd dwll schm, a larg numbr, N, of suard-law-ctd sampls of th cohrnt ntgraton ar accumulatd, summd, and compard wth a prst thrshold.

2 s ( -9dg Carrr Gnrator I ( Q ( Cod Gnrator I( Q( IF I(k Q(k ( ㆍ Y (k IF ( ㆍ Cod and Fruncy Adjust N ( Y ( k N k Fgur. A sngl dwll C/A acuston systm tcton > η In Fgur, th nput sgnal (th rcvd SV sgnal and th nos can b wrttn as [4] s ( A cos( ω t ( whr A s th rcvd SV sgnal ampltud, C ( s th C/A cod modulaton, ω s th IF carrr fruncy, n( s th nos, and φ ( s th carrr phas whch ncluds th 5 bps b-phas data modulaton. h gnratd n-phas and uadratur mxng sgnals ar wrttn as I ( ˆ ω t ˆ φ ( ( sn( ˆ ω t ˆ φ Q whr ωˆ s an stmat of th rcvd fruncy and φˆ s an arbtrary phas. h dmodulatd n-phas and uadratur phas sgnals ar mxd wth th gnratd C/A cod (t-τ whch s for dspradng th sprad spctrum sgnal. h dspradd sgnals ar thn fltrd by IF. h fltrd sgnals ar wrttn as [4] Y ( I ( Q ( sn( ω / A / ω h tst statstc for sgnal acuston s gvn by [4] whr N N [ k (6 Z( k I ( k Q ( k ] (7 N s th numbr of post-cton sampls. h random varabl, Z(k, s th output of th suar-law ctor. A thrshold valu, η, s stablshd for dsrd cton and fals alarm probablts. If Z(k xcds η n any gvn cll(s, a vrfcaton procdur s ntatd; othrws, nos only s assumd, and th procdur s rpatd for th nxt cll [3]. h probablty of th fals alarm,, s th probablty that Z xcds th thrshold η whn only th nos s prsnt. W can wrt th probablty of th fals alarm as { > η} r Z n ( Z (8 h cton probablty s th probablty that Z xcds th thrshold η whn th sgnal and nos ar prsnt. h cton probablty can b wrttn as η { Z > η} s r n( Z (9 Lt s normalz th random varabl Z and th thrshold η by σ / N as η I ( s( I ( t n( I ( t n( I ( t n ( A ( τ cos( t ( cos( ˆt ˆ n ( ω φ ω φ ( th hgh fruncy trm ( ω( ˆ ω to zro n IF sn A ( ω / ( ω / ( τ cos ( ω / φ n ( * Z N Z ( σ * η N (3 η σ Snc, by th assumpton, th Y(k s ar ndpndnt random varabls, for larg N (N >, Z * s approxmatly Gaussan dstrbutd. hus, th probablty of th fals alarm and th cton probablty ar [6] ( / ( ω / sn Q( A ω ( τ sn φ (4 ( ω / n ( whr ω ω ˆ,, and n s th n-phas ω φ φ ˆ ( φ ( nos, n ( s th uadratur phas nos. n ( and n ( ar zro-man Gaussan statstcally ndpndnt random varabls wth avrag nos powr gvn by σ N /, N s th sngl sd nos powr spctral dnsty, and s th I (rcton Intgraton tm. h corrlaton functon (τ btwn th ncomng C/A cod and th gnratd C/A cod s gvn by τ ; τ < ( τ ; othrws Whn th rcvd SV sgnal and gnratd cods ar xactly synchronzd, th pr-cton ntgraton powr wthout noss s (5 η* ( β π N * η N Q N Q β N γ Q γ ( γ * ( Z N N * ( Z N( γ N ( γ * η* π N * ( ( whr γ A /( σ and Q x s th Gaussan probablty ntgral. ( A good approxmaton to th rurd N as a functon of and s [3].

3 ' N ( ln π,.5 4 ln.5 4 ( γ γ (3 h man acuston tm for sral sarch may b xprssd as [3] ( k N N ( Ac, (4 whr k p s dfnd as a multplr of th dwll prod, and N s th numbr of total clls. In th cas of a paralll sarch (n th mult-corrlator, svral clls (M ar tstd concurrntly for sgnal prsnc. h man acuston tm for paralll sarch may b wrttn as [3] k M ( ( N N ( Ac, M. XMC (Xtndd Multpl Corrlator (5 hr ar many tchnus for th fast acuston of GS sgnal. Among thm, mult-corrlator, matchd fltr and FF ar most popular. h mult-corrlator uss a largr numbr of corrlaton arms, and corrlaton valus btwn th rcvd cod and th rplca cod gnratd at ach arm ar obtand smultanously. In matchd fltr, mathmatcally uvalnt form of th mult-corrlator, corrlatons ar prformd btwn th rplca cod and a st of th rcvd cods that ar dlayd at ach arm. FF s a fruncy doman uvalnt form of th matchd fltr or th mult-corrlator. It rducs procssng tm sgnfcantly and can b usd n trackng procss. hs papr proposs a nw fast mthod to sarch C/A cod calld XMC (Xtndd Mult-Corrlator. In XMC, th combnd rplca of svral cods s usd nstad of sparat ons. A block dagram of XMC corrlaton arm s shown n Fgur 3. s ( Carrr Gnrator -9dg I ( Q ( Cod Gnrator I' ( IF ( Q' ( I' ( k Q' ( k ( ㆍ IF ( ㆍ Y '( k Cod and Fruncy Adjust Fgur 3. On corrlaton arm of XMC N N ( Y '( k ' k tcton > η' h man fatur of ths corrlaton tchnu s shown n th shadowd block of Fgur 3. ffrntly from othr corrlaton tchnus, th dmodulatd n-phas and uadratur phas sgnals ar mxd wth th combnd rplca of thr C/A cods for dspradng th sprad spctrum sgnal. Othr structurs ar sam as th sngl/multpl corrlator. h combnd rplca of thr C/A cods s wrttn as C '( (6 whr s th dsrd valu. hus, th IF output sgnals ar wrttn as I' ( s( I ( ( n( I ( ( Q'( s( Q ( ( n( Q ( ( W dfn nw varabls (7 (8 I ( ( n '( (9 Q ( ( n '( thn th IF output sgnals can b wrttn as sn I' ( A ( ω / [ ( τ ( τ ( τ ] cos( ω / φ ( ( ω / n '( sn Q' ( A ( ω / [ ( τ ( τ ( τ ] sn( ω / φ ( ( ω / n '( Whn th rcvd SV sgnal and gnratd cods ar xactly synchronzd (τ, th pr-cton ntgraton powr wthout noss s gvn by Y '( I' ( Q' ( sn( ω / A / ω [ ( ] ( Comparng Euaton ( wth Euaton (6, w can fnd that th pr-cton ntgraton powr n XMC s strongr than that n convntonal (sngl/multpl corrlator. If s a half chp (about.5 msc, thn ths valu s uadrupl as larg as th valu n Euaton (6. h n-phas nos n '( and th uadratur phas nos n '( ar zro-man Gaussan statstcally ndpndnt random varabls. hrfor, th avrag powr of ach nos can b shown as ( 3 ( ( ( ( 3 4 ( ( N / σ ' σ (3 h probablty of th fals alarm, th cton probablty and th man acuston tm ar sam as Euaton (8~(5. In XMC, svral cod phass can b tstd n just on corrlator arm. hrfor, th numbr of total cod bns s dcrasd n XMC. W found that th numbr of total cod bns s about 7.5 % of that of convntonal (sngl/multpl corrlator through xprmnts rsults. In ths cas, thortcally, 9% numbrs of arms ar usd to gt an uvalnt prformanc of th mult-corrlator whn th rurd probablty of th fals alarm s -4 and th rurd cton probablty s.95. hs valu can b vrfd usng Euaton (~(5, (~(3..3 Suard- Sarchng Mthod In practc, all knds of GS corrlators must ct th SV sgnals n th carrr-phas (or opplr dmnson by rplcatng th carrr fruncy plus opplr. Many canddats of opplr must b sarchd whn th GS rcvr has no almanac avalabl. Othrws, f GS

4 corrlators can rduc th numbr of opplr bn, ths corrlators can acur th GS sgnal fastr than any othr corrlator. hs papr proposs a nw mthod for rducng th numbr of opplr bn. hs nw mthod s calld by Suard- sarchng mthod, and s basd upon a sgnal suarng mthod for L codlss trackng []. A block dagram of Suard- sarchng mthod s shown n Fgur 4. s ( '' s ''( n' '( I ''( -9dg I' '( IF I' '( k ( ㆍ Y ''( k N '' ( Y ''( k N '' k tcton > η'' Y I" ( Q" ( 4 A sn( ω" / 4 " / ω ( " (8 Comparng Euaton ( wth Euaton (8, w can fnd that th pr-cton ntgraton powr n Suard- sarchng mthod s wakr than that n convntonal (sngl/multpl corrlator. If s 5 nsc and A s unty, thn ths valu s about 4% of Euaton (6. h n-phas nos n and th uadratur phas nos n " ( ar zro-man Gaussan statstcally ndpndnt random varabls. hrfor, th avrag powr of ach nos can b shown as Q ''( Q' '( k IF ( ㆍ " N / s ''( n''( Q' '( σ, (9 Carrr Gnrator Fruncy Adjust Fgur 4. Suard- sarchng mthod h man fatur of Suard- sarchng mthod s shown n th shadowd block of Fgur 4. hs mthod s to suar th L sgnal, that s, to multply t by dlayd tslf, to rmov th b-phas C/A cod modulaton and rsult n a dmodulatd. hrfor, ths corrlator can t ct th SV numbr bcaus th C/A cod s rmovd, but can fnd twc of opplr fruncy. tals ar followng. h suard of nput sgnal s wrttn as s n ( s( ( s( t " t " ( A cos( ωt A t " cos( ω( t " t ( " t " (4 whr s th dsrd valu, but must b lss than th rcprocal of IF carrr fruncy. h gnratd n-phas and uadratur mxng sgnals ar wrttn as I ˆ ω t ˆ φ (5 sn( ˆ ω t ˆ φ Q Comparng Euaton (5 wth Euaton (, w can fnd th stmat of rcvd fruncy s twc of that of Euaton (. It mans that th corrlator ct twc of opplr fruncy rathr than th opplr fruncy tslf. hus, th IF output sgnals ar wrttn as I s I ( A t " cos( t ( cos( ( t " ( t " cos( ˆt ˆ ω φ ω φ ω φ A ωt t " ˆ ωt ˆ φ A t " cos( ω( t " t " cos( ˆ ωt ˆ φ n( t " ˆ ωt ˆ φ ( A t " ωt ω( t " t " cos( ˆ ωt ˆ φ n A sn( ω" / cos( ω" / φ" ( " n ( ω " / (6 Q s Q (7 A sn( ω" / sn( ω" / φ" ( " n ( ω " / whr ω and. hrfor, " ( ω ˆ ω φ φ φ ˆ " ( ( t φ th pr-cton ntgraton powr wthout noss s gvn by h probablty of th fals alarm, th cton probablty and th man acuston tm ar sam as Euaton (8~(5. For wak sgnal powr and strong nos powr, Suard- sarchng mthod nds th longr I tm. Whn G s usd n F/IF chpst and s 75 nsc, I tm should b mor than about msc for acurng opplr fruncy. If G usd n F/IF chpst, th Suard- corrlator has channls, 8 vsbl satllts ar prsntd, and th opplr uncrtanty rgon s about Hz ~ Hz, thn t taks about 3. sc for fndng opplr canddats. hrfor, th numbr of opplr bn s rducd to 8, and th GS rcvr usng ths Suard- sarchng mthod can acur th GS sgnal dramatcally fastr than any othr rcvr. 3. Conclusons hs papr proposd a nw algorthm to acur GS sgnal, Suard- sarchng mthod and XMC. Suard- sarchng mthod dramatcally rducs th numbr of opplr bns. XMC s dstngushd from othr mult-corrlator n that th combnd rplca of thr cods s usd nstad of sparat ons, and 9% numbrs of arms ar usd to gt an uvalnt prformanc of th mult-corrlator. abl. Acuston prformancs FF [sc] (Mn / Max Sral Sarch Corrlator 3 / Mult-Corrlator 3 / 44 XMC 3 / 4 Sral Sarch Corrlator wth Suard- sarchng mthod XMC wth Suard- sarchng mthod 33 / / 35 abl shows th acuston prformanc (FF, m o Frst Fx n cold start mod. hs prformanc s calculatd whn ach corrlator has channls, 8 vsbl satllts ar prsntd, th opplr uncrtanty rgon s about Hz ~ Hz, sral sarch corrlator has 3 corrlator arms, and th mult-corrlator and XMC hav corrlator arms. In abl, w can s that XMC wth Suard- sarchng mthod has a much mprovd acuston prformanc. It s xpctd that proposd mthods b usful for GS rcvrs n many applcatons, such as hgh dynamcs vhcls or an applanc whch uss slp mod to sav powr consumpton,

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