Enhancing the Performance of Ultra-Tight Integration of GPS/PL/INS: A Federated Filter Approach

Transcription

1 Journal of Global Positioning Systms (2006) Vol. 5, No. 1-2: Enhancing th Prformanc of Ultra-ight Intgration of GPS/PL/INS: A Fdratd Filtr Approach D. Li, J. Wang, S. Babu School of Survying and Spatial Information Systms, Univrsity of Nw South Wals Abstract. h intgration of GPS, PL and INS snsors can b implmntd at thr diffrnt lvls. Compard with loos and tight intgration, ultra-tight intgration offrs numrous advantags including incrasd robustnss undr high dynamics, and improvd antijamming prformanc. In currnt ultra-tight intgration scnarios, a cntralisd Kalman filtr is commonly mployd to fus ithr In-phas (I) and Quadratur (Q) data from th tracking loop or th psudorang masurmnt and Position, Vlocity, Attitud (P, V, A) masurmnts from th Inrtial Navigation Systm (INS). hough rlativly simpl, this cntralisd filtr structur has som disadvantags. Firstly, to rduc th computational load, th filtr only maks coars stimats of Inrtial Masurmnt Unit (IMU) random rrors, which significantly dgrads th systm prformanc. Scondly, for mor accurat stimats, th filtr bcoms much mor complicatd, rsulting in a larg incras in th computation tim. All of ths hindr th prformanc of ultra-tight intgration considrably. his papr proposs a fdratd filtr structur for th ultra-tight intgration of GPS, PL and INS snsors. h nw filtr structur distributs th computing tasks to diffrnt Kalman filtrs, lading to rducd filtr complxitis and improvd systm prformanc. IMU random rrors ar stimatd sparatly by th pr-filtr at a high data rat, whilst th main filtr has a simplifid structur, i.. no stimation of th IMU random rrors, and oprats at a rlativly slow rat. his papr will discuss th dynamic modlling mthod basd on th Walsh transform for implmnting th pr-filtr and th simplification of th main filtr. Simulation tsts wr prformd to compar th prformanc of th fdratd filtr with that of th usual cntralisd Kalman filtr in th stimation of th IMU random rrors. h rsults show that with th simplification of th Kalman filtr structur, th fdratd filtr dsign can achiv th almost qually prcis stimats as th cntralisd Kalman filtr dos but with lss computational burdn. Hnc th fdratd dsign is mor suitabl for implmnting th ultra-tight intgration for ral-tim applications. Finally, th simulatd high dynamic flight tst rsults of ultra-tight intgration basd on th fdratd Kalman filtr ar prsntd. Kywords. GPS, tracking loop, dynamic modl, IMU, INS, Kalman filtr Introduction h Global Positioning Systm (GPS), Inrtial Navigation Systm (INS) and Psudolit (PL) tchnologis all play vry important rols in navigation systms. As an indpndnt navigation systm, GPS provids a varity of usful navigation data,.g. psudorang, psudorang-rat, tc. hough th prcision is indpndnt of tim, th prformanc will bcom unrliabl whn th quipmnt xprincs high dynamics, or whn th rcivr is xposd to jamming or intrfrnc from communication quipmnt, tc. In comparison to GPS, though INS is autonomous and provids good short-trm accuracy, but its usag as a stand-alon navigation systm is limitd du to th timdpndnt growth of th inrtial snsor biass (ittrton & Wston, 1997). PLs ar ground-basd transmittrs that can transmit GPS-lik signals. hy hav som advantags in that thir positions can b dtrmind prcisly, and th Signal-to-Nois atios (SN) ar rlativly high. h intgration of GPS, INS and PL is incrasingly important, bcaus thir combind prformanc, in principl, ovrcoms th shortcomings of th individual snsor systms. Initially, th GPS and INS wr intgratd in loos mod, whr th navigation solutions from th individual systms ar combind togthr by an optimal intgrating filtr. In this systm-lvl intgration, GPS and INS systms wr tratd indpndntly. hough asy to implmnt, th navigation solution can b improvd. As a

2 Li t al.: Enhancing th Prformanc of Ultra-ight Intgration of GPS/PL/INS: A Fdratd Filtr Approach 97 rsult, th intgration volvd into th so-calld tightlycoupld mod, whr th raw masurmnts from GPS,.g. psudorang, psudorang-rat, ar combind with INS masurmnts or positions (Snnott, 1997). h systm prformanc is rmarkablly improvd. In svr nvironmnts, such as undr high dynamics, and/or intntional or unintntional F intrfrnc, th prformanc of th loos and tightly-intgratd systm will b dgradd bcaus th GPS solutions bcom incrasingly unrliabl. For a mor robust navigation solution, th intgration lvl movs into both th individual systms, spcially into th GPS rcivr itslf. hat is, th ultra-tight intgration navigation filtr combins ithr th I and Q masurmnts from th GPS tracking loop or th psudorang masurmnts with th INS navigation paramtrs to produc th optimal Dopplr stimat. his rmovs th dynamic strss of th cod and phas tracking loops, thus kping thm in stabl tracking mod during high dynamics (Alban, 2003; Bsr, 2002; Poh, 2002). his tracking loop lvl intgration is mor complicatd than th othr two as it rquirs good knowldg of GPS rcivr s tracking loop architctur. Diffring from th convntional GPS rcivr usd in th othr two configurations, in which th tracking loop is closd and th local rfrnc signal is th only fdback of th loop filtr, th ultra-tightly intgratd systm s fdback signal is drivd from both th loop filtr and th intgratd navigation filtr. his improvs th accuracy of GPS masurmnts by maintaining a narrow tracking loop bandwidth without dgrading its dynamic tracking capability. In an ultra-tightly intgratd systm, usually th updating frquncy of th GPS tracking loop is 1kHz. Howvr, du to larg-sizd matrix computations and hardwar limitations, th intgratd Kalman filtr output rat is btwn 1-10Hz. Accurat stimats nd a complicatd filtr structur, which typically mans mor computing tim. For ral-tim applications, not only th prcision of stimats, but also th computing tim should b takn into account. Hnc thr must b a compromis in th systm dsign. his papr proposs a fdratd Kalman filtr structur to implmnt th ultra-tight intgration. h computation by th intgratd filtr is distributd into diffrnt parts, so that th main filtr intgrats th GPS masurmnts and INS data whil th othr filtr, i.. pr-filtring filtr, is spcifically dsignd to compnsat for th IMU rrors. hs two Kalman filtrs work in paralll, so that th computing tim is kpt to a minimum. Whn using a Kalman filtr to stimat and compnsat for th IMU rrors, a pivotal tchniqu is to dtrmin th dynamic modl of th IMU snsors, which is usd to driv th stat transition matrix for implmnting th Kalman filtr. his papr will discuss th dynamic modlling of an IMU mploying a novl modlling mthod basd on th Walsh and its transform. h prcision of th dynamic modl of th IMU dirctly influncs th accuracy of th INS data, and vntually th quality of th aiding Dopplr. In this papr, a dynamic modlling mthod will b discussd and simulation xprimnts will b carrid out to dmonstrat th proposd dynamic modlling mthod. Svral tst scnarios hav bn usd to invstigat th ultra-tight rcivr basd on th fdratd Kalman filtr structur, compard to a standalon rcivr. h rsults show that th ultra-tight intgration producs a mor robust and accurat solution undr high dynamics and low SN nvironmnts. 2 Kalman Filtr Structur for h Ultra-ight Intgration h purpos of th ultra-tight intgration is to kp th GPS rcivr stabl for high dynamic applications, with th intgration of inrtial masurmnts. As th dynamics ar rmovd from th tracking loop, th loop bandwidth will b rducd to th minimum, dpnding on th accuracy of th aiding masurmnts drivd from th inrtial snsors and th stability of th rcivr clock. As a rsult, in this cas, vn in high dynamics and low SN applications th tracking loop could rmain in a narrow PLL, which mans prcis masurmnts and thrfor an accurat and robust position solution. In gnral, in ithr th ultra-tight intgration or th stand-alon GPS rcivr opration, th loop filtr masurs th rrors btwn th incoming and rfrnc signals and fds thm into th Numric Control Oscillator (NCO) to align th phas of th local rfrnc signal so that it s frquncy and phas ar idntical to thos of th incoming signal. Usually this procss will tak 1 milliscond, i.. on C/A cod priod. h updat rat of th loop is 1kHz. In th ultra-tight intgration, th aiding Dopplr from th intgratd filtr should b providd at th sam rat. h intgratd filtr which outputs th aiding Dopplr is implmntd by Kalman filtr tchniqus. Bcaus thr ar intnsiv computations th computing tim of th Kalman filtr is longr than 1 milliscond; rsulting in a data updat rat of 1-10Hz. o synchronis th tracking loop and th aiding Dopplr, th output rat of th Kalman filtr must b incrasd by simplifying its structur (but which would othrwis rsult in a dgradation of th quality of th aiding Dopplr and othr stimats). On mthod to solv this problm is to intrpolat th lowr aiding Dopplr rat to th rquird rat, i.. 1kHz, with a multi-rat signal procssing algorithm (Babu and Wang, 2004). For improvd stimats, th Kalman filtr should b carfully dsignd. Howvr, th long computation tim for accurat rsults will rduc th output rat and rsult in dgradation of th prformanc of th intrpolation.

3 98 Journal of Global Positioning Systms o solv this paradox thr must b a compromis btwn th computing tim and th stimating accuracy of th Kalman filtr. h fdratd Kalman filtr structur is invstigatd to implmnt th ultra-tight intgration, whrby th computation of th intgratd filtr is dividd into diffrnt filtrs. Figur 1 dpicts th systm structur of ultra-tight intgration basd on a fdratd Kalman filtr. h main filtr intgrats th GPS masurmnts and th INS data, whil th othr on, i.. th pr-filtring Kalman filtr, will oprat in paralll with th main filtr to stimat and compnsat for th IMU rrors. his structur succds in distributing th computational burdn into diffrnt filtrs, all oprating at th sam tim. h Kalman filtr is usd to gnrat optimal stimats of a dynamic systm. h ky to implmnting th prfiltring Kalman filtr is to dtrmin its stat transition matrix, which could b dirctly dducd from th dynamic modl of th stimatd systm. For dscribing th charactristics of th dynamic systm, w can us th dynamic modl or th stat transition matrix. Fig. 1 Configuration of th fdratd Kalman filtr for th ultra tight intgration o implmnt th pr-filtring Kalman filtr rquirs a knowldg of th IMU dynamic modl. Usually thr ar tim-domain and frquncy-domain basd mthods to stablish this dynamic modl. Howvr ths two mthods ar infficint bcaus thy ar computationally intnsiv, complx and it is asy to introduc rrors in th multi-modlling stps (Li, 2004). In this papr th IMU dynamic modl is drivd by a nw dynamic modlling mthod basd on th Walsh and its transform. h advantags of this modlling mthod ar that th intgration can b rplacd by matrix multiplication, and th paramtrs of th dynamic modl can b dirctly drivd from th matrix opration. hus th rrors can b rducd to obtain a mor accurat modl of th dynamic systm. 3 Implmntation of h Fdratd Kalman Filtr 3.1 Implmntation of h Pr-filtring Kalman Filtr h ffctiv way to liminat th rrors of th IMU is th complmntary Kalman filtr tchniqu. Basd on th Kalman filtr thory, prcis stimats can only b drivd from th accurat dynamic modl. Usually th charactristic of th dynamic systm is dscribd by mans of a transfr, which is th rprsntation of th diffrntial quation in th s- domain. h IMU dynamic modl can b rprsntd by 1 st or 2 nd ordr transfr s (Li and Sun, 2004). h outputs of th IMU should b stimatd in ral-tim, which usually has a high output rat. In this cas, th 1 st ordr IMU modls ar usd to simplify th structur of th pr-filtring Kalman filtr and, as a rsult, this incrass th output rat. h transfr of IMU can b givn as: K Φ( s ) = (1) s + 1 whr K is th systm gain and is th tim constant of systm. hs two paramtrs hav an impact on th systm dynamic prformanc. h dtrmination of th IMU dynamic modl bcoms a problm of paramtr idntification in quation (1). Using th Walsh dynamic modlling mthod, firstly th calibratd data ar collctd from th IMU. Scondly, W m, p and ω ar gnratd. hn th Walsh transform of input/output data ar carrid out. And finally th cofficints K and ar xtractd by matrix oprations. Onc K and hav bn dtrmind and th nois w has bn introducd, th transfr quation (1) can b transformd into a stat-spac dscription: 1 x& = x + w (2) y = x + v whr is th tim constant, and w is th systm nois. Discrtising th continuous stat-spac quation (2) (Zhng, 2000): X( k + 1) = GX( K) + HW Y( k) = X( k) + V s G = 1 s t H = dt 0 whr s is th sampling priod, is th tim constant of systm, G is th systm stat transition matrix, H is th systm nois transition matrix, th procss and masurmnt modl of th Kalman filtr can b drivd using th dynamic modl of th IMU: (3)

4 Li t al.: Enhancing th Prformanc of Ultra-ight Intgration of GPS/PL/INS: A Fdratd Filtr Approach 99 Φ (k + 1) = GΦ Y IMU (k) = Φ IMU (k) + Hw(k) (k) + v(k) IMU IMU (4) whr Φ IMU = [ ϕgyro1, ϕgyro2, ϕgyro2, ϕacc1, ϕacc2, ϕacc3], is th stat vctor of th Kalman filtr. Hr ϕ gyro1, ϕ gyro2, ϕ gyro2, ϕacc1, ϕacc2, ϕ ar th acc3 stimatd outputs of th IMU, and w(k), v(k) ar zroman whit nois. Y IMU = [ y gyro 1, y gyro 2, y gyro 3, y acc 1, y acc 2, y acc 3 ] and y gyro1, ygyro2, ygyro3, yacc 1, yacc2, y ar th original acc3 outputs of th IMU usd as th masurmnts for th prfiltring Kalman filtr. Whn th original outputs of th IMU ar usd as th masurmnts of th pr-filtring Kalman filtr, th stimatd outputs ar th optimal stimation of th raw outputs of th IMU, i.. a pr-filtring Kalman filtr can produc th optimal stimats of th IMU outputs. Hnc, ths calibratd IMU outputs drivd from th prfiltring Kalman filtr can b usd in th inrtial navigation algorithm to gnrat th navigation solutions for position, vlocity and attitud. 3.2 h Simplifid Structur of th Main Kalman Filtr h main advantag of th fdratd Kalman filtr is that it can distribut th computational tasks of a cntralisd Kalman filtr into two parallll Kalman filtrs, i.. th pr-filtring and th main Kalman filtr. h structur of main Kalman filtr can b simplifid at th sam tim without dgrading th quality of th stimats. h IMU rrors, i.. th gyro and acclromtr random drifts, ar stimatd and compnsatd for in th pr-filtr. hr ar svral diffrnt options for implmnting th ultra-tight intgration Kalman filtr. In on of thm, th GPS-masurd psudorang is usd as th masurmnt for th Kalman filtr. Basd on th optimal stimats of rcivr vlocity, th aiding Dopplr can b obtaind to fd back th tracking loop (Alban, 2003). In this papr, this structur is adoptd to implmnt th ultra-tight intgration. Usually th stat vctor in this typ of ultratight Kalman filtr structur compriss 16 variabls: x( t) = [ δϕ δλ δh δv δv n δvz α β γ (5) b b b b b b δf δf δf δω δω δω δt ] ibx iby ibz ibx whr δϕ, δλ, δh ar th position rrors, i.. latitud, longitud and hight rrors. δ v, δvn, δv ar th vlocity z rrors, i.. ast, north and up vlocity rrors in th local lvl coordinat systm, rspctivly. α, β, γ ar th attitud rrors, i.. pitch, roll and hading angl rrors in th body coordinat systm. b b b δ f, δf, δf ar th 3 iby ibx ibz iby b ibz acclromtr random drifts, b b b δω ibx, δωiby, δω ar th 3 ibz gyro random drifts, and δt is th GPS rcivr clock bias. b h masurmnt usd in th Kalman filtr is th diffrnc btwn th INS-drivd psudorang and th GPS-masurd psudorang; thrfor it is a of rcivr position rrors and GPS rcivr clock bias rrors: δρ = 1 δϕ + 2δλ + 3δh + δtb + V (6) whr 1, 2, ar th lmnts of th unit vctor btwn 3 satllit and rcivr. V is th masurmnt nois. δρ is th psudorang diffrnc, which is drivd from ρins ρ GPS, hr ρ INS is th INS-drivd psudorang masurmnt which contains th rcivr position rrors, and ρ is th GPS-masurd psudorang which GPS contains th rcivr clock bias rrors. Onc w obtain th optimal stimats of rcivr vlocity, th aiding Dopplr can b calculatd: r (1 vvla) fdopplr = f (7) tx c whr f is th GPS L1 frquncy, V tx vl is th rlativ vlocity btwn satllit and rcivr, a r is th lin-ofsight unit vctor btwn satllit and rcivr, and c is th spd of light. For a dtaild discussion of how to driv th aiding Dopplr from th stimatd vlocity radrs ar rfrrd to Babu and Wang (2004) and Kaplan (1996). In th fdratd Kalman filtr structur, as th prfiltring Kalman filtr compnsats for th IMU rrors, thr is no nd for th main Kalman filtr to stimat th IMU random rrors, thrfor th numbr of stat variabls can b rducd to 10 (rmoving th 6 IMU drift stat variabls), and th structur of th Kalman filtr (i.. th stat transition matrix) can b simplifid. If th numbr of stat variabls is 16 or 10, th numbr of lmnts in th stat transition matrix will b 16 2 =256 or 10 2 =100 rspctivly. Hnc bcaus th valu of vry lmnt should b calculatd by th softwar, rducing th numbr of stat variabls can significantly rduc th computational burdn of th Kalman filtr. Furthrmor, rducing th stat variabls can simplify th structur of th Kalman filtr by nglcting th corrlations btwn th IMU rrors and th othr variabls. Bcaus th attitud and vlocity rrors ar corrlatd with th IMU random drift rrors, for xampl, th attitud pitch angl and th ast vlocity rror quations ar givn as: & α δv v tg n = + ( ωi sinϕ + ϕ) β ( ωi cosϕ + ) v γ δω b ibx

5 100 Journal of Global Positioning Systms v v 2 vn vu (2ωi cosϕ + sc ϕ) vδϕ δvu δvn b v& n = f zα f xγ + δfiby 2( ωi sinϕ + tgδ ) δv (8) δ whr = + h, and h is th arth radius and hight rspctivly, and ω i is th angl rat of arth rotation. f x, f z ar th acclromtr masurmnts in th body coordinat systm. In th fdratd Kalman filtr structur, th pr-filtring Kalman filtr stimats and compnsats for th IMU random drifts, thus th main Kalman filtr dosn t nd to stimat thm. As dscribd abov, th corrlations of th IMU random drift rrors with th othr stat variabls can b nglctd. h attitud and vlocity rror quation could b simplifid: δv v v & α = n + ( ωi sinϕ + tgϕ) β ( ωi cosϕ ) γ + v v 2 vn vu (2ω i cosϕ + sc ϕ) vδϕ δvu δvn v& n = f zα f xγ 2( ωi sinϕ + tgδ ) δv (9) δ Hnc th stat transition matrix can b simplifid. Hr w still us th psudorang diffrncs as th masurmnts for th Kalman filtr. Hnc th masurmnt modl is th sam as that in th cntralisd Kalman filtr, which is dscribd by quation (6). 4 Exprimntal sults 4.1 IMU Dynamic Modlling sults Givn th 2nd ordr dynamic systm: b1s + b2 G ( s) = = 1 (10) 2 2 s + a s + a s s th Walsh modlling rsults ar shown in abl 1. Using ths modlling rsults th dynamic modls ar constructd, as shown in Figur 2. h dashd lins rprsnt th outputs of ths modls and th solid lins rprsnt th outputs of th modl in quation (10) which wr applid to th sam unit stp input signal. abl 1. Modling rsults of mthod using diffrnt numbrs of Walsh Modl a Paramtrs 1 a2 b1 b Walsh Walsh Walsh 256 Walsh h rsults show that th accuracy of th stimatd modl paramtrs dpnds on th numbr of Walsh s usd for th modlling. For th simulation tst, 128 Walsh s produc good modlling rsults. 4.2 Pr-filtring Kalman Filtr sting sults First, th flight trajctory with known dynamics, with charactristics shown in abl 2, was gnratd. Fig. 2 Modling rsults of diffrnt numbr of Walsh A comparison btwn IMU outputs with/without using th pr-filtring Kalman filtr was mad in ordr to study how th pr-filtring improvs th IMU outputs. In th simulation tst, th dynamics of th trajctory ar known, i.. th position, attitud and vlocity, and th original IMU outputs could b dducd from this information. Aftr adding nois to th original IMU outputs, th simulatd raw IMU outputs corrsponding to th flight trajctory could b obtaind. Simulation tim lasts for 60 sc. h output rat of th IMU is 100Hz. Figur 3 dpicts th IMU outputs that hav larg rrors from th known trajctory. abl 2. Paramtrs of flight trajctory Initial position (latitud, longitud, high) (dgr) Initial vlocity (ast, north, up) (m/s) Initial acclration (m/s2) Initial attitud (roll, pitch, hading) (dgr) Simulation tim(s) 60 Simulation tim stp (s) 0.01 Flight status Constant acclration = 0.5g Aftr optimally stimating th IMU outputs by th prfiltring Kalman filtr, most of th IMU random drift rrors wr rmovd, and th filtrd IMU outputs ar

6 Li t al.: Enhancing th Prformanc of Ultra-ight Intgration of GPS/PL/INS: A Fdratd Filtr Approach 101 shown in Figur 4, indicating an improvmnt in IMU outputs. 4.3 Main Kalman Filtr sting sults o tst th prformanc of th fdratd Kalman filtr, th comparison of th stimats from ths two configurations, i.. th fdratd and cntralisd Kalman filtr, is carrid out. gratly rducd bcaus of th simplifid stat transition matrix. Hnc, th updat rat of th stimats can b incrasd, which is hlpful whn implmnting th Kalman filtr for ral-tim applications. 4.4 Ultra-ight GPS/INS civr Exprimntal sults As shown in th prvious sction, th fdratd Kalman filtr structur vlocity stimats with th sam accuracy as th cntralisd Kalman filtr. Fig. 3 Original outputs of IMU In th cntralisd Kalman filtr structur, th IMU random drifts rrors ar stimatd togthr with othr stat variabls. h optimal navigation solutions of position, attitud and vlocity, rprsntd as th latitud, longitud, arth-lvl vlocity and roll, pitch, hading (compnsatd by th stimatd rrors drivd from th Kalman filtr) ar shown in Figur 5. In th fdratd Kalman filtr, as th IMU random drift rrors ar alrady stimatd during th pr-filtring, th main Kalman filtr dosn t nd to stimat th IMU rrors again. o compar with th rsults of th cntralisd Kalman filtr, th compnsatd position, attitud and vlocity ar givn in Figur 6. From Figur 6 it can b obsrvd that th fdratd Kalman filtr dlivrs th sam prcision of stimats as th cntralisd Kalman filtr approach, howvr th computing tim is Fig. 4 Filtrd outputs of IMU

7 102 Journal of Global Positioning Systms xcd th thrshold, th cod tracking loop will los lock. Bcaus th carrir tracking loop rlis on th stability of th cod tracking loop, it will also los lock at th sam tim. Figur 8 shows that th varity of cod loop powr of th ultra-tight rcivr is smallr than that of a stand-alon rcivr, maning it has mor stabl tracking capability. h Q masurmnts rprsnt th tracking loop rrors. Figur 9 dmonstrats that th ultra-tight rcivr has smallr tracking rrors than th stand-alon rcivr undr th sam dynamic conditions, i.. mor accurat masurmnts could b obtaind from th tracking loop. Fig. 5 Navigation solutions basd on th cntralisd Kalman filtr structur hrfor th accuracis of th aiding Dopplr for both configurations is of th sam lvl, which mans that th ultra-tight GPS/INS rcivr basd on th fdratd Kalman rcivr has th sam quality of output as th cntralisd Kalman filtr, but bnfits from fastr compution. Figur 7 illustrats th prformanc of th ultra-tightly intgratd GPS/INS rcivr and th stand-alon GPS rcivr. h tracking loop bandwidth is st at 12Hz. Normally, by comparing th powr of th carrir tracking loop with th tracking thrshold it can b dtrmind if th tracking loop is in FLL or PLL mod, which illustrats th stability and accuracy of th tracking loop. As mntiond abov, th FLL mans lowr masurmnts accuracy. For bttr tracking ffct, th tracking mod should quickly switch from FLL to PLL. From Figur 7 it can b shown that whn th dynamics of th simulatd trajctory is high, th stand-alon GPS rcivr tracking loop had larg tracking rrors and rmaind in th FLL mod. Onc th dynamics bcom largr or th bandwidth is rducd, it will los lock. Howvr, th ultra-tightly intgratd rcivr could rmain in th PLL tracking mod with th sam dynamics, thrfor it can b concludd that th ultratight intgratd rcivr is mor robust for th high dynamic applications. Usually th varity of th cod loop powr rprsnts th stability of th cod tracking loop. If it is larg nough to Fig. 6 Navigation solutions basd on th fdratd Kalman filtr structur

8 Li t al.: Enhancing th Prformanc of Ultra-ight Intgration of GPS/PL/INS: A Fdratd Filtr Approach 103 Fig. 7 Comparison of tracking loop status btwn th ultra tight intgration and stand-alon rcivr Fig. 9 racking loop Q masurmnts 5 Concluding marks In this papr a fdratd Kalman filtr structur for th ultra-tight intgration of GPS/INS/PL has bn invstigatd, in which th IMU random rrors ar stimatd and compnsatd for by a pr-filtring Kalman filtr. In this way th computational burdn can b sparatd into diffrnt parts and procssd in paralll. h pivotal tchniqu to implmnt this structur, th dynamic modlling mthod of th IMU basd on th Walsh and its transform, is invstigatd and th simulation xprimnts hav dmonstratd its accuracy and fasibility. h Kalman filtr was implmntd on th IMU dynamic modl. st rsults hav shown that th IMU rrors can b ffctivly rmovd by pr-filtring so that th accuracy of th aiding Dopplr drivd from th intgratd Kalman filtr is th sam as that of th cntralisd Kalman filtr, but rquirs lss computation tim. his fdratd Kalman filtr structur is thrfor spcially attractiv, spcially for ral-tim applications. Fig. 8 Cod tracking loop status Acknowldgmnts his rsarch is supportd by an AC (Australian sarch Council) Discovry sarch Projct on obust Positioning Basd on Ultra-tight Intgration of GPS, Psudolits and Inrtial Snsors. h authors would lik to thank Prof. Chris izos for his valuabl commnts on th arly vrsion of this papr. frncs Li D., Sun Y. (2004) sarch of h Dynamic Modlling of FOG Basd on Walsh Function. Ship Enginring, Dc, 2004 Alban S., Akos D., ock S. & Gbr-Egziobhr D. (2003) Prformanc Analysis and Architcturs for INS-Aidd GPS tracking loops. Institut of Navigation NM, Anahim, CA, January, Kaplan E.D. (1996) Undrstanding GPS: Principls and Applications. Artch Hous, MA sui J.B.Y. (2000) Fundamntals of Global Positioning civrs A Softwar Approach. John Wily & Sons, Inc Bsr J., Alxandr S., Cran., ounds S., Wyman J., Badr B. (2002) runavm: A Low-Cost Guidanc/Navigation Unit Intgrating a SAASM-basd GPS and MEMS IMU in a Dply Coupld Mchanization. 15th Int. ch. Mting of th Satllit Division of th U.S. Inst. of Navigation, Portland, O, Sptmbr, Babu., Wang J. (2004) Comparativ study of intrpolation tchniqus for ultra-tight intgration of GPS/INS/PL snsors. GNSS 2004, Sydny, Australia, 6-8 Dc. Babu., Wang J. (2004) Improving th Quality of IMU- Drivd Dopplr Estimats for Ultra-ight GPS/INS Intgration. GNSS 2004, ottrdam, h Nthrlands, May. Farrll J.A. & Barth M. (1999) h Global Positioning Systm and Inrtial Navigation. McGraw-Hill.

9 104 Journal of Global Positioning Systms Hntschl. & Fttwis G. (2000) Sampl at Convrsion for Softwar adio. IEEE Communications Magazin, August, Mitra S.K. (1999) Digital Signal Procssing A Computr Basd Approach. ata McGraw-Hill Edition, India, ISBN Vaidyanathan P.P. (1990) Multirat Digital Filtr, Filtr Banks, Polyphas Ntworks, and Applications: A utorial. Proc. IEEE, 78, Wang J., Dai L., suiji., izos C., Grjnr-Brzzinska D., oth C. (2001) GPS/INS/Psudolit Intgration: Concpts, Simulation and sting. 14th Int. ch. Mting of th Satllit Division of th U.S. Inst. of Navigation, Salt Lak City, Ohio, Sptmbr, Ward P. (1998) Prformanc Comparisons Btwn FLL, PLL and a Novl FLL-Assistd PLL Carrir racking Loop Undr F Intrfrnc Conditions. 11th Int. ch. Mting of th Satllit Division of th U.S. Inst. of Navigation, Nashvill, nnss, Sptmbr,