Prformanc Analysis and Architctur Dsign of Vctor-Basd Ultra- ightly Coupld GPS/INS Intgration on satllit Faults XING-LI SUN 1 WAN-ONG CHEN YAN HAN 1 1 School of Information and Communication Enginring, North Univrsity of China, Xuyuan Road,No.3, Jiancaoping District, aiyuan, CHINA ianin Ky Lab for Advancd Signal Procssing, Civil Aviation Univrsity of China, North Road, No.898, Dongli District, ianin, CHINA sunxingli14@nuc.du.cn Abstract: GPS vctor rciv mak th tasks of signal tracking and navigation stat stimation ar intgratd into an algorithm which can complmnt traditional scalar rcivr tracking indpndnt and paralll tracking disadvantag. hrough intgration with INS, th GPS signal in amming or wak nvironmnt basd on vctor tracking ultra-tightly coupld GNSS/INS intgration systm has significant advantags. But vctor tracking channls ar closly linkd, ach channl signal tracking procsss influnc ach othr, if on or svral channls ar fault, which will induc th positioning rror of th intgration systm and mayb mak th normal channl tracking prformanc dcras or vn instant lock. In this papr, w ust prformanc th ultra-tightly coupld GPS/INS cntralizd architctur bas on vctor tracking, whn a singl channl or multipl channls fault occurs, mak th intgratd systm positioning ffct wr analyzd thortically,and through simulation and xprimnt vrify th ffcts of quantitativ, at th last, w dsign a fault-tolrant architctur and us robust H-infinity filtr algorithm for Ultra-tightly coupld GPS/INS Intgration. Ky-Words: vctor tracking, ultra-tightly coupld GPS/INS intgration, thortical prformanc, GPS fault, fault-tolrant architctur, H-infinity filtr 1 Introduction h Global Positioning Systm (GPS) rlis on th radio-frquncy (RF) signals for positioning has bn stablishd as a dominant tchnology to provid location and navigation capabilitis with a high rliability and accuracy. And GPS rcivr has bcom a ubiquitous navigation instrumnt to civilian and military applications. Howvr, dspit its succss th GPS systm suffrs from a basic shortcoming. GPS howvr is still subct to svr prformanc dgradation in signal-dgradd, significant dynamics, dns foliag and urban canyon nvironmnts. Bcaus of th GPS signals rcivd nar th surfac of th Earth ar xtrmly wak. RF intrfrnc, whthr intntional or unintntional, can also asily disrupt GPS availability. As littl as 1.5 pico-watts of incidnt RF intrfrnc ar capabl of disabling a civilian C/A cod rcivr [1]. h rliability and functionality of th GPS systm suffr du to th rlativ waknss of th GPS signals. h Inrtial Navigation Systm (INS) is slfcontaind dad rckoning (DR) navigation systms provid dynamic information through dirct masurmnts from an Inrtial Masurmnt Unit (IMU). According to its masurmnt principl INS systms provid an autonomous solution for position, vlocity and attitud with high data rat and bandwidth[]. From this point of viw an inrtial snsor is th optimal choic for most of th applications in navigation and positioning. Its typical rror bhaviour, howvr, causs only a short trm stability of a high accuracy lvl. h INS suffrs from tim-dpndnt rror growth which causs a drift in th solution, thus compromising th long trm accuracy of th systm. h rat at which navigation rrors grow ovr tim is govrnd prdominantly by th accuracy of th initial alignmnt, rrors in inrtial snsors and th dynamics of th tractory followd. Du to th INS and GPS hav strong complmntary advantags, and hav bn a rsarch focus in th intgratd navigation aras. h GPS/INS intgratd systm taks advantag of th complmntary attributs of both systms to yild a systm that outprforms ithr singl systm oprating alon. h combination of GPS and INS not only offrs th accuracy and continuity in th solution, but also nhancs th rliability of th systm. GPS, whn combind with INS, can rstrict INS rror growth ovr tim, and allows for onlin stimation of th snsor rrors, whil th INS can E-ISSN: 4-678 176 Volum 16, 17
nhanc th rliability and intgrity of th systm. It can bridg th position and vlocity stimats whn thr is no GPS signal rcption or can assist GPS rcivr opration whn GPS signal is dgradd. Ultimatly, th navigation solution drivd from an GPS/INS systm is bttr than ithr standalon solution[3]. h xact mannr and lvl at which th systms ar fusd togthr varis widly from implmntation to implmntation. h improvmnt in prformanc brought about by th combination of th two systms is largly dtrmind by th xact mannr in which thy ar fusd. Som invstigators hav dscribd that thr stratgis ar usd for GPS and INS intgration, namly loosly intgration, tightly intgration, and ultra-tightly (or dp) intgration. With th dpning of coupling of GPS and INS, th prformanc of th intrgradd systm will b gratly improvd. hr is no uniform dfinition of ultra-tightly coupld (UC) in th intrnational rsarch institutions [4,5], and th UC is mntiond in this articl which is a vctor-basd tracking UC GPS/INS systm. h primary advantags of vctor-tracking ar nois is rducd in all channls making thm lss likly to ntr th non-linar tracking rgions; it can oprat with momntary blockag of on or mor satllits; and it can b bttr optimizd than scalartracking approachs. Vctor-tracking is also abl to improv tracking in wak-signal or amming nvironmnts, spcially whn intgratd with inrtial snsors [6]. h vctor tracking significant advantag is mainly rflctd in th numbr of satllit tracking mor than four and good satllit gomtric distribution [7] [8]. h satllit signals ar invitabl xistnc rrors in th gnration, transmission, procssing, and whn GPS satllit chang may b fault. With th rcivr dal with satllits numbr incras at th sam tim, this is bound to incras th probability of th satllit channl fault happn. h xisting litratur on vctor tracking GPS/INS UC systm is mostly confind to th anti-amming and high dynamic adaptability, lss rsarch for fault analysis. In this papr, w carry out thortical rsarch on vctor tracking GPS/INS UC cntralizd architctur, And th fault mchanism ar discussd, whn a singl channl or multipl channls masurmnts hav fault, w analysis th intgratd systm positioning prformanc from thortic, which can provid a thortical basis for futur rsarch GPS/INS UC systm fault tolrant architctur, fault tolrant filtring algorithm and choos th appropriat satllit constllation. Algorithm and implmntation of vctor-basd GPS/INS UC cntralizd architctur his papr focuss on th rsarch of GPS/SINS UC basd vctor tracking, so th diffrnc btwn th traditional scalar and vctor tracking is introducd firstly..1 Scalar and Vctor tracking Rcivr.1.1 raditional Scalar tracking rcivr Fig.1 shows a block diagram of th traditional scalar rcivr architctur. racking loops in ach channl ar usd to stimat th psudorang and psudorang-rat for ach satllit in viw of th rcivr. h stimatd psudorangs and psudorang-rats ar fd forward to th navigation procssor. h navigation procssor uss th stimatd psudorangs and psudorang-rats to stimat th rcivr s position, vlocity, and clock stats[9]. In Fig.1, th flow of information is strictly lft to right. No information from th navigation procssor is fd back to th tracking loops. Additionally, th tracking loops in ach channl oprat indpndntly of ach othr; thrfor no information is xchangd btwn thm. Each channl of th rcivr tracks its rspctiv signal indpndnt of th othr channls. hrfor, th traditional rcivr architctur dos not xploit th inhrnt coupling btwn th rcivr s dynamics and th dynamics sn by th tracking loops. Corrlator 1 Cod/Carrir Corrlator N Cod/Carrir Radio Front Cod/Carrir dtctor Channl 1 Cod/Carrir dtctor Antnna Loop Filtr Channl 1 Loop Filtr Channl N Fig.1 raditional Scalar Rcivr architctur h bnfits of scalar rcivr ar th rlativ as of implmntation and a lvl of robustnss that is gaind by not having on tracking channl corrupt anothr tracking channl. Howvr, on th downsid, th fact that th signals ar inhrntly rlatd via th rcivr s position and vlocity is compltly ignord. Furthrmor, th possibility for Navigation Procssor PV E-ISSN: 4-678 177 Volum 16, 17
on tracking channl to aid anothr channls is impossibl. For mor information on scalar-tracking rcivr, plas rfr to th rfrncs [1,11]..1. Vctor tracking rcivr Fig. shows a block diagram of a vctor tracking rcivr architctur. For th rcivr shown in Fig., th tasks of signal tracking and navigation stat stimation ar no longr sparat procsss. h singl Extndd Kalman Filtr (EKF) simultanously tracks th rcivd signals and stimats th rcivr s position, vlocity, tc. A Vctor Dlay Lock Loop (VDLL) only tracks th PRN cod phass through th cntral filtr. h task of carrir tracking is still handld by scalar tracking loops in ach channl in th VDLL. A Vctor Dlay/Frquncy Lock Loop (VDFLL) uss th cntral filtr to track th PRN cod phass and th carrir frquncis. h focus of th rsarch in this papr is on th VDFLL. Radio Front Corrlator 1 Cod/Carrir Corrlator N Cod/Carrir Cod/Carrir dtctor Channl 1 Cod/Carrir dtctor Channl N Antnna Navigation Filtr PV Fig. vctor tracking rcivr architctur h rason vctor tracking is possibl rlis on th basic natur of th GPS ntwork. h principl bhind GPS is that th rcivr s position and vlocity can b dtrmind basd on th phas and frquncy of th rcivd signals. Vctor tracking algorithms tak this basic ida and rvrs it. h phas and frquncy of th rcivd signals ar prdictd from th rcivr s stimatd position and vlocity. Rsiduals ar formd in ach channl by taking th diffrnc btwn th prdictd and rcivd signals. h rsiduals ar thn usd to updat th stimats of th rcivr s position and vlocity. h vctor tracking approach xploits th coupling btwn th rcivr s dynamics and th dynamics sn by th tracking loops. Instad of vry channl of th rcivr tracking th dynamics of th individual signals, th usr dynamics that ar causing th chang in th signals ar trackd. h primary advantags of vctor-tracking ar; nois is rducd in all channls making thm lss likly to ntr th non-linar tracking rgions; it can oprat with momntary blockag of on or mor satllits; and it can b bttr optimizd than scalartracking approachs. Vctor-tracking is also abl to improv tracking in wak-signal or amming nvironmnts, spcially whn intgratd with inrtial snsors. h primary drawback is that all satllits ar intimatly rlatd, and any rror in on channl can potntially advrsly affct othr channls.. Cntralizd GPS/INS UC with Vctor racking Vctor tracking rcivr procsss th signal tracking and positioning by th filtr togthr, and multipl channl signal tracking and motion modl fusion filtring [4][5]. A Vctor Dlay/Frquncy Lock Loop (VD/FLL) uss th filtr to track th psudo random nois (PRN) cod phass and th carrir frquncis. h filtr stimat all channls psudorang and psudorang-rat according to rcivr s navigation paramtrs and satllit phmris data, and th stimation information is snt to th local signal gnrator carrir and cod. In th cycl of ach intgrator and rst, th discriminator output of psudorang and psudorang-rat rsidual information is usd to updat th filtr stat[1,13]. Antnna Corrlator 1 Cod/Carrir Corrlator N Cod/Carrir IMU Discrim inator Channl 1 Discrim inator Channl N Mchanization Equation Intgratd GNSS/INS filtr PVA Fig.3 Vctor-basd GPS/INS UC architctur Extnsion of vctor-tracking to UC with an INS is possibl by augmnting th architctur with an inrtial masurmnt unit (IMU) and rplacing th navigation filtr with an intgratd GPS/INS filtr [3].h intgratd filtr output rsults such as positioning and vlocity ar quivalnt to provid th rfrnc movmnt tractory for th GPS rcivr. h ssntial is that using th INS E-ISSN: 4-678 178 Volum 16, 17
subsystm and its intgral algorithm rplac th stat forcasting procss basd on vctor rcivr stat quation. Compard with vctor rcivr has th following advantags: th INS subsystm can grasp th rcivr movmnt ral tim according to th snsing valu, and th vctor rcivr vn vry rasonabl motion modl which cannot dscrib all th diffrnt movmnt modl for th rcivr, th architctur shown in Fig.3. h systm stats ar thr position rror componnts, th thr vlocity rror componnts, thr "platform" misalignmnt angls, thr gyro drifts, thr acclromtr zro bias of INS as wll as clock bias and clock drift of GPS rcivr, and th position and vlocity rror stats ar all in th ECEF fram[14]. 31 31 31 31 31 11 11 171 X() t P V d b t f (1) P V V F N r iv Rb d i Rb b Xt () d Ad Wd b Bb W () b t t f wb f f w d FtXt () () GW W dnotd as: X () t F () t X () t G W (3) h systm nois sction is b GW ( g RKf b Wd Wb) (4) h dynamic matrix of th quation of stat is a 17 ordr spars matrix. h concrt structur is: 33 I3 3 3 3 3 3 3 3 N i F R 3 3 b 3 3 3 3 i 3 3 R b Ft () (5) 33 3 3 3 3 A 3 3 3 3 3 3 3 3 3 3 B C 17 17 whr b GW g R Kf W W w w (6) b d b b d i is anti-symmtric matrix of th arth angular vlocity w. F is anti-symmtric matrix of th spcific forc f. 3x 3xy 3xz 1 r r r km 3xy 3y 3yz N 1 3 r r r r 3xz 3yz 3z 1 (7) r r r w w km is th product of gravitational constant and P x y z is carrir position th arth mass; coordinat on gographic coordinat systm. th Rb matrix is rfrrd to as th dirction cosin matrix from th body fram to th navigation fram. hrough laboratory and fild tsting instrumnt, can obtain gyro constant drift and acclromtr constant bias trm, and corrct th corrsponding masurmnts (spcific forc and angular vlocity). Howvr, th rsidual rror still xists, which can b considrd as a stochastic procss, which is rprsntd by a stochastic modl. Hr using d and b two vctor rspctivly, th gyro drift and acclromtr bias of th random componnt. And that is oftn xprssd as colord nois, first-ordr Markov procss. whr A diag( i ) and B diag( i ) ar diagonal matrix, th lmnt is qual to th invrs corrlation tim of th corrsponding stochastic procss. h filtr stat is updatd by th discriminator output of all channls. h output of th cod discriminator is convrtd into psudorang rsiduals, th carrir frquncy discriminator output is convrtd to psudorang-rat rsiduals, th masurmnt quation ar: Z() t H() t X v() t (8) whr ax,1 ay,1 az,1 1 3 1 9 1 1 3 ax,1 ay,1 a,1 1 9 1 z Ht () axn, ayn, azn, 1 3 1 9 1 13 axn, ayn, azn, 19 1 Zt () [ ] 1 1 N N NN E-ISSN: 4-678 179 Volum 16, 17
In this formula th variabls ax, N, ay, N, a z, N ar th componnts of th lin-of-sight unit vctor from th usr to th N-th satllit. h discrtization of th systm stat quation and masurmnt quation ar: X( k) Φ( k k 1) X( k 1) W( k 1) (9) Z( k) H( k) X( k) V( k) h valu of th filtr is discrtizd according to th filtring quation; w do not rpat thm hr. 3 h ffct of positioning rror whn masurmnts hav faults h mchanism of fault gnrating is introducd in this sction firstly, and thn analysis th masurmnt fault on th impact of positioning rror from th thortical. 3.1 Fault mchanism Individual inrtial snsor faults ar du to hardwar failur and can manifst as no outputs at all, null radings, rpatd radings, or simply much largr rrors than spcifid. Onc a snsor fault has bn dtctd, no furthr data from that snsor should b accptd. Unlss thr ar rdundant inrtial snsors, this mans discarding th whol inrtial navigation solution. Larg rrors xhibitd by all th inrtial snsors can b an indication of a muchhighr vibration nvironmnt than th systm is dsignd for or of a mounting failur. h whol IMU or INS may also xhibit a powr failur, softwar failur, or communications failur, in which cas a rst should b attmptd. So this papr mainly considrs th GPS faul[15]t. GPS fault mods may b dividd into four catgoris: satllit faults; unusual atmosphric propagation; local channl failurs, which compris faults affcting individual channls of a singl st of usr quipmnt; and gnral usr quipmnt faults. A summary may b found in [1].In this papr, w only focus on local channl failurs to rsarch. Othr causs of local channl failurs ar multipath, tracking loops in th procss of losing lock, and rcivr hardwar and softwar faults affcting individual channls. Satllit faults and wid-ara atmosphric problms may b dtctd as local channl failurs whr no monitoring ntwork is usd or to provid a backup to a ntwork. FDI and FDE lvl protction against singl-channl failurs can usually b obtaind providd sufficint satllits ar trackd. h faulty signal is simply discardd and a navigation solution computd using th rmaining signals. h fault was mntiond in this papr rfrs to th masurmnt of discriminator output hav bias. Most of th litraturs gnrally considrd th VD/FLL tracking ar unbiasd, but in th fact th VD/FLL algorithm will b introducd to th bias [11], vn in GPS/INS UC algorithm, th INS stimatd only to th acclration and cannot b stimatd highr ordr acclration drivativ, which will rsult VD/FLL discriminator output bias bcaus th carrir complx dynamic appars. Varity of factors will lad to th masurmnt bias such as th diffus rflction multipath ffcts, atmosphric dlay modl imprcis and so on in th ral condition, which impact on th positioning masurmnt accuracy. 3. h thortical analysis on positioning rror whn masurmnts hav faults In ordr to simplify th thory analysis of positioning rror, w mad two assumptions on th masurmnt rror modl: (1) h masurmnt rrors of psudorang rsiduals ar th sam normal distribution and th man ar all and variancs ar whn th channl has no fault. () Diffrnt channls masurmnt rrors ar unrlatd, so th covarianc of masurmnt rrors vctor V( k ) is a diagonal matrix. Assuming at tim k, only channl has fault in all tracking channls bcaus complx dynamics or multipath, considr th following channl modl with fault: Z ( k) Z r( k) Z f ( k) (1) Whr Z r ( k) H ( k) X ( k) V ( k) is th normal masurmnt, and th covarianc of th ks, masurmnt nois V ( k ) is Z ( ) ( ), f k f k is th fault masurmnt information, and ( k) is a random vctor, which rprsnts th fault valu, ks, f is a picwis function, ks, 1, [ ks, ] f (11), [,( k 1)] [( s1), ) h filtr updatd stat at tim k and its covarianc ar Xˆ ( k) Xˆ ( k) Xˆ ( k) (1) r f P( k) I K( k) H( k) P( k k1) I K( k) H( k) (13) KkRkKk ( ) ( ) ( ) whr Xˆ r ( k ) is th normal masurmnt filtring stat, and X ˆ f ( k ) indicats th filtring stat rror causd by fault masurmnt, thir valus wr: ˆ 1 X ( ) ( )[ ( 1) ˆ r k P k P k k X ( k k 1)] (14) 1 Pk ( )[ H ( kr ) ( kz ) ( k)] r E-ISSN: 4-678 18 Volum 16, 17
ˆ 1 X f ( k) P( k) H ( k) R ( k) Z f ( k) (15) Undr normal conditions, th kalman filtring quation corrct th stat valu by (14) quation. Aftr corrction positioning rrors oby normal distribution with zro man valu and th varianc is Pk ( ).whn channls hav fault, positioning will lad to bias, th bias ar dtrmind by (15), th magnitud of bias ar rlat with th masurmnt valu and satllits gomtry distribution. h positioning rrors ar no longr zro man, whn channls hav fault. 4 h Architctur and Algorithm Dsign of Ultra-ightly Coupld GPS/INS Intgration Basd on Vctor h satllit signals ar invitabl xistnc rrors in th gnration, transmission, procssing. hus th dmand on fault tolranc of ultra-tightly coupld GPS/INS intgration navigation systm is growing highr and highr, which includs th ability of fault dtction, isolation and systm rconfiguration. W must adopt appropriat algorithm to improv th prformanc and mak bst us of th advantags and bypass th disadvantags. In this papr, w propos a fault-tolrant vctor tracking filtr algorithm and robust algorithm for Ultra-tightly coupld GPS/INS Intgration using fdratd Kalman filtr, was show th Fig 4. Radio Fond IMU Channl 1 Channl Channl N Cod Carri r ax, ay, az,,, I1, Q1 x y z I, Q I, Q n n Strapdown algorithm Prfiltr 1 Chi-squar tst 1 Prfiltr Chi-squar tst Prfiltr N Chi-squar tst N Error corrction V, Vn, Vu, f 1 1, f n, f n Intgratd filtr H Position vlocity Attitud Fig.4 th Fault Dtction Architctur and Robust filtr of Ultra-ightly Coupld GPS/INS Intgration Basd on Vctor In th architctur, through th us of a mastr filtr and a plurality of paralll tracking filtr (also calld pr-filtr)to raliz th navigation function, which in ach of th pr-filtr in ach priod of filtr slction rsidual tst mthod, aftr 1s with innovation squnc dtcting mthod to tst, th rsidual dtction mthod asy to dtct abrupt faults, and innovation squnc dtcting mthod of slowly varying fault dtction has good dtction ffct, gratly rducing rcivr channl fault ffct VDLL fitr VFLL f on intgratd navigation systm of fusion rsults, guarant systm in fault can maintain a high accuracy. Whil th main filtr using H- infinity(h ) robust filtring. GPS rcivr for ach channl with a pr-filtr to achiv tracking, paralll tracking function, th filtr can achiv th ssnc of th optimal tracking loop. All channls of th tracking filtr output and SINS output to a intgratd filtr, and finally raliz th information fusion and navigation and positioning algorithm, gt th final navigation output. Aftr th final solution of intgratd filtr to aid th rcivr tracking loop, th architctur with high accuracy, high stability and strong fault tolranc and robustnss. On th on hand, th GPS signal is usd to updat th SINS, on th othr hand, SINS and satllit phmris is also usd to calculat vctor with rspct to th GPS psudorang and psudorang rat rror. Bcaus SINS has a high positioning accuracy and spd masurmnt accuracy in a crtain rang, using ths information to track th GPS signal can gratly improv th positioning accuracy, dynamic prformanc and rliability of GPS. h prcision of GPS information in turn can b improvd by improving th prcision of SINS, which maks th systm mor accurat than singl systm. h GPS rcivr loop can ffctivly improv th quivalnt bandwidth of th loop, improv th anti-intrfrnc ability of th rcivr, rduc th rror causd by th dynamic strss, and improv th tracking prformanc of th rcivr. 4.1 Fault Dtction bas on KF innovations h Kalman filtr is a powrful tool for dtcting faults. h masurmnt innovations, ( k),of a Kalman filtr, provid an indication of whthr th masurmnts and stat stimats ar consistnt. Innovation filtring may b usd to dtct larg discrpancis immdiatly[1]. For a tru Kalman filtr, th masurmnt innovation vctor is: ( k) Z( k) Zˆ ( k k1) (16) h covarianc of th innovations, A( k), compriss th sum of th masurmnt nois covarianc and th rror covarianc of th stat stimats transformd into masurmnt spac. hus: A( k) H( k) P( k k1) H ( k) R( k) (17) which is th dnominator of th Kalman gain.h normalizd innovations ar dfind as: ( k) yk (18) A( k) E-ISSN: 4-678 181 Volum 16, 17
4. H-infinity filtr Kalman filtring assums that th mssag gnrating procss has a known dynamics and that th xognous inputs hav known statistical proprtis. Unfortunatly, ths assumptions limit th utility of minimum varianc stimators in situations whr th mssag modl and/or th nois dscriptions ar unknown[13]. W dfin th following cost function: N 1 z k z k k S 1 k J1 N 1 (19) x x ( w v ) 1 1 1 k P Q k k k Rk whr P, Q k, Rk and S k ar symmtric, positiv dfinit matrics chosn by th nginr basd on th spcific problm, and is our usr-spcifid prformanc bound. H-infinity filtr algorithm procss is on th follow: Sk LkSkLk 1 1 1 Kk Pk[ I SkPk Hk Rk HkPk] Hk Rk () xk 1 Fkxk FkKk( yk Hkxk) 1 1 P FP[ I SPH R H P] F Q k1 k k k k k k k k k k h following condition must hold at ach tim stp K in ordr for th abov stimator to b a solution to th problm: 1 1 P S H R H (1) k k k k k 5 Simulation Analyss W mainly focus on th simulation and vrification work in sction 3 and 4. 5.1 Position ffct whn satllit channl fault In th sction 3, th prformanc of th navigation is analysd, and th analytic xprssion is obtaind. his sction will us simulation tools to furthr analys and vrify th prvious conclusions. In this papr, w only analyss th singlchannl fault, multi-channl fault analysis is similar. h channl fault causs th positioning rror hav bn analysd and drivd analytic formula in sction h ffct of positioning rror whn masurmnts hav faults. In this sction w will quantitativ vrification of th positioning rror by thortical simulation. h simulation conditions of this papr: th usr position in ECEF fram ar (- 171918, 438595, 47694), mdium accuracy IMU, intgratd filtr updat tim is 1ms, using th tmpratur compnsatd crystal oscillator (CXO) typ clock, numbr of satllits ar 1 and 5 constllation rspctivly, h Dilution of Prcision (DOP) valus for th diffrnt satllits constllation ar shown in abl 1, whrin th 5 constllation is slctd from th 1 constllation channl 1,3,5,7 and 9. abl 1 DOP valus for diffrnt satllit configuration Satllits Numbr PDOP HDOP VDOP 1 1.6149 1.1986 1.83 5 3.675.3736.456 In ordr to maintain VD/FLL tracking, th fault ar d, d/ and d/3 which wr translatd into psudo rangs rsiduals, whrin th masurmnt nois of ach channl is calculatd by formula in rfrnc [8] accord to CN.whr th symbol d is th corrlator spacing of th arly and prompt PRN rplicas, xprssd in fraction of a chip. A corrlator spacing of on half chip is usd for all th simulation rsults. 5.1.1 h impact on positioning rror of singlchannl fault on th sam constllation W prformd simulation to analysis that only channl numbr 5 has fault, whn all channls C/N chang. 3D Position Bias Error/m 1 1 8 6 4 Fault=d Fault=d/ Fault=d/3 Fault-fr 31 35 4 45 5 CN/dB-Hz Fig.5 h channl 5 bias induc positioning bias whn tracking 1 satllits on diffrnt C/N 3D Position Bias Error/m 1 1 8 6 4 Fault=d Fault=d/ Fault=d/3 Fault-fr 31 35 4 45 5 CN/dB-Hz E-ISSN: 4-678 18 Volum 16, 17
Fig.6 h channl 5 bias induc positioning bias whn tracking 5 satllits on diffrnt C/N Fig.5 and Fig.6 ar 1 constllations and 5 constllations simulation rsults rspctivly. h rsults show that th positioning bias bcoms largr as th signal nrgy bcoms largr undr th sam constllations distribution; th positioning bias ar largr on 5 constllations than 1 constllations undr th sam C/N, th positioning bias ar rlatd with DOP factor, th DOP factor ar largr, th largr positioning bias. hrfor, it is particularly important for fault dtction, whn signal ar strong and positioning satllits numbr ar lss. 5.1. h impact on positioning rror whn diffrnt singl-channl faults on th sam constllations h signal C/N ar 4dB-Hz all th tim, w prformd simulation to analysis whn th diffrnt singl-channl hav fault on 1 constllations, was shown in Fig.7, th rsults show that diffrnt channls hav diffrnt positioning bias, and th positioning bias is rlatd to fault valu and th unit vctor btwn usr and th satllit. Fig.7 Diffrnt channls obsrvation bias induc positioning bias whn tracking 1 satllits abl Diffrnt channls obsrvation bias d induc positioning whn tracking 5 and 1 satllits Num 3D Position Bias Error/m 4 3.5 3.5 1.5 1.5 1 3 4 5 6 7 8 9 1 Channl numbr Channl Fault=d Fault=d/ Fault=d/3 1 3 4 5 1.65.91.95.68.19 5 4.3 4.6 3.71 3.35 4.1 abl is positioning bias whn tracking 5 and 1 satllits on th sam singl -channl fault, th rsults show that: in th sam channl fault th 5 constllation positioning bias ar largr than th 1 constllation, th positioning bias hav rlation with DOP factor, th DOP factor is largr, th gratr th positioning bias. 5.1.3 Simulation rsults of multi-channl fault rsulting in positioning bias W simulation that multi-channls hav fault at th sam tim on 1 constllation distribution.fault numbr N dnot th fault channl numbr 1,...N,rspctivly. h xprimntal rsults show that, along with th fault channl incras th position bias bcoms larg. And th signal nrgy is strongr, th gratr th positioning bias was shown in Fig.8. 3D Position Bias Error/m 15 1 5 Fault numbr=1 Fault numbr= Fault numbr=3 Fault numbr=4 Fault-fr 3 35 4 45 5 CN/dB-Hz Fig.8 h multichannl bias induc positioning bias whn tracking 1 satllits on diffrnt C/N 5.1.4 h positioning accuracy simulation on rmov fault channl or not With th chang of th signal nrgy, w simulation th positioning accuracy, and channl 5 still has fault. Fig.9 shows th rsult of diffrnt constllations distribution, whthr rmoval of th fault channl or not, thr is almost no ffct on th positioning accuracy, but th gomtric distribution hav a gratr impact on th positioning accuracy. 3D Position 1- /m 1 1 8 6 4 5 Satllits Fault=d 5 Satllits Fault rmoval 1 Satllits Fault=d 1 Satllits Fault rmoval 3 35 4 45 5 CN/dB-Hz Fig.9 Fault rmoval and prsnc of channl 5 induc positioning rror whn tracking 1 and 5 satllits on diffrnt C/N E-ISSN: 4-678 183 Volum 16, 17
5. Simulation on th architctur Vctor- Basd UC GPS/INS Intgration 5..1 Simulation systm dsign and data gnration IMU data and GPS intrmdiat frquncy (IF) data wr gnratd by simulation tst. Sinc th computational rquirmnts of th softwar rcivr ar so stringnt, only 15-s data ar considrd hr h vhicl turn north linar motion and th tractory covrd static priods, acclrations, dclrations, rks and uniform vlocity with th following sttings. h vhicl original position is on N:5., E:5., Alt:5m. Vhicl is stationary during tim priod from s to 35s.During tim priod of from 35s to 45s, from 55s to 75s, from 77s to 9s and from 1s to 11s, Vhicl is uniform rks motion, and th uniform rks(m/s³) ar 1,-,,1 sparatly. During tim priod of from 45s to 55s, from 7s to 77s and from 9s to 1s, Vhicl is uniform acclration motion, and th uniform acclration (m/s ) is 1,- and 1 sparatly. h vhicl is uniform vlocity motion during tim priod from 11s to 15s. h motions of a vhicl ar gnratd by abov tractory. h gnration of simulatd signals of inrtial snsors is an invrs procss of INS navigation mchanization. Givn that all th INSs 15s only without alignmnt rrors and th only inrtial snsor rror sourc of ach INS is th gyro bias,.g. in run bias of.1dg/h, prcision IMU in this papr. W considr tracking of th GPS L1 carrir frquncy in this work. h IF data ar obtaind by YUMA almanac rduction which obtain from th wbsit of U.S Navigation Cntr. h GPS simulator tim is July 3, 6,1::8. h sampling frquncy is 1MHz, and th IF is 3.563MHz.h GPS satllit sky plot during vhicl tst is shown Fig.1. Fig.11 shows corrsponding lin of sight (LOS) Dopplr btwn PRN1 and rcivr. 8 6 4 7 - -4-6 -8-5 5 Fig.1 GPS satllit sky plot during vhicl tst Dopplr of PRN 1 (Hz) 6 3 4 9 1 5 1 33 1 4 18 Fig.11 LOS Dopplr btwn PRN1 and rcivr 5.. Simulation rsult analyss In ordr to facilitat th comparison and analysis, this sction wr in th colord nois is xistnt conditions with H-infinity filtring and xtndd Kalman filtring rsults wr compard, bcaus th dirction of X and Y dirction positioning and vlocity rror curv is similar, so this articl only givs in X dirction and Z dirction combination filtr wr usd H-infinity and EKF filtring rror curv, as shown in Fig.1- Fig.15. 15 3 45 8 6 75 9 4 17-5 5 5 75 1 15 im(sc) 7 8 15 3 13 6 1 9 E-ISSN: 4-678 184 Volum 16, 17
Fig.1 X-axis Position rrors comparison EKF to H algorithms during colord nois Fig.13 X-axis vlocity rrors comparison EKF to H algorithms during colord nois Fig.14 Z-axis Position rrors comparison EKF to H algorithms during colord nois Fig.15 Z-axis vlocity rrors comparison EKF to H algorithms during colord nois EKF with positioning and vlocity masuring th divrgnc tim growth, cannot work normally, and H-infinity filtr is rliabl, but th position and vlocity accuracy is slightly wors. his is illustratd with th EKF filtring compard and H- infinity filtr has vry strong robustnss, vn if th input signal with constant drift and random, filtrs convrgnc. Du to th currnt GPS if analogy simulation cannot gt th data of th fault channl, so this papr has no simulation for fault tolranc, th nxt will carry out rsarch and vrification for fault tolranc. 6 Conclusions In this papr, w first xplain th structur of basd vctor tracking GPS/INS UC systm, and illustrat th fault mchanism, thn analys th UC systm positioning rror in dtail whn masurmnts hav fault and finally through th simulation xprimnts quantitativ analysis, at th last w dsign a fault dtction architctur and robust filtr of UC GPS/INS intgration. h rsults show that: (1) whn th masurmnts hav fault, th positioning rsults will appar bias, and masurmnts bias ar gratr, th gratr th positioning bias; () whn diffrnt satllit channl appars th sam fault, th diffrnt ffcts on th positioning bias in th sam constllation, dpnding on th lin of sight rlvant btwn th satllit and th usr; (3) th sam channl fault is diffrnt in th diffrnt constllations, and hav rlatd with th satllit gomtry distribution, th gomtry distribution ar bttr th smallr th rror; (4) th strongr th signal nrgy, th channl fault hav gratr impact on positioning bias. (5) h application of H- infinity filtring tchnology is ffctiv on th GPS/INS navigation systm with colord nois. (6) Using H-infinity filtring tchniqu of GPS/INS UC systm filtring, th stat quation of th systm don't nd of gyro and acclration rror modlling and stimation, thrby rducing th dimnsionality of th stat variabls of th systm, rduc th amount of computation, can improv th filtring spd, is conduciv to th ral tim implmntation of intgratd navigation systm. In practical applications, a lot of factors can lad to masurmnts fault, but w cannot distinguish th rason. In ordr to rduc th fault satllit channl ffct on ovrall systm prformanc, nxt w will furthr vrification th fault tolrant and H-infinity robust filtr algorithm. E-ISSN: 4-678 185 Volum 16, 17
Funding his work is supportd by th National Natural Scinc Foundation of China (Grant numbr 6141468). Rfrnc [1]P.Ward,J.W.Btz,andC.J.Hgarty, Undrstanding GPS: Principls and Applications, Artch Hous Publishrs, 6. []Stfan Kisl, Markus Langr, Grt F, rommr. Ral im Implmntation of a Non-Cohrnt Dply Coupld GPS/INS Systm. Procdings of th 14 Intrnational chnical Mting of h Institut of Navigation, San Digo CA, 14.pp.1-1. [3]Matthw Lashly, David M.Bvly, John Y.Hung. Analysis of Dply Intgratd and tightly coupld architcturs, IEEE/ION Position Location and Navigation Symposium. California,15.pp.38-396. [4]D. Bnson. Intrfrnc bnfits of a vctor dlay lock loop (VDLL) GPS rcivr, Procdings of Annual Mting of th Institut of Navigation,13,pp.749-756. [5]Nazia Kanwal, Vctor tracking loop dsign for dgradd signal Environmnt.,ampr Univrsity of tchnology,11. [6] Knndy, S. and Rossi, J. Prformanc of a dply coupld commrcial grad GPS/INS systm from KVH and NovAtl Inc. In Procdings of IEEE/ION Position Location and Navigation Symposium Confrnc,Montry, CA, 8,pp.17-4. [7]Matthw Lashly, David M and John Y. Prformanc Analysis of Vctor racking Algorithms for Wak GPS Signal in High Dynamic. IEEE Journal Of Slctd In Signal Procssion, 1,3().pp.661-673. [8]Matthw Lashly. Modlling and Prformanc Analysis of GPS Vctor racking Algorithms, Auburn Univrsity,9. [9]Dong Xurong,Zhang Shouxin,Hua Zhongchun. GPS/INS intgratd navigation positioning and application. National Univrsity of Dfns chnology Prss. 1998. [1] Bhatti, U. I., and W. Y. Oching, Failur Mods and Modls for Intgratd GPS/INS Systms, Journal of Navigation, Vol.6,No.,7, pp.37 348. [11]Xiao Zhibing,ang Xiaomi,Pang Jing,Wang Xufi. h study of cod tracking bias in vctor dlay lock loop. Scintia Sinica Phys,Mch & Astron, Vol.4,No.1,13,.pp.568-574. [1] Cimposu EM, Ciubotaru BD, Stfanoiu D. Fault Dtction and Diagnosis Using Paramtr Estimation with Rcursiv Last Squars, Control Systms and Computr Scinc (CSCS), 13 19th Intrnational Confrnc on: 18 3. [13] Dan Simon. Optimal Stat Estimation: Kalman, H Infinity, and Nonlinar Approachs, John Wily & Sons,6. [14]M.G. Ptovllo, C. O Driscoll,G. Lachapll. Wak Signal Carrir racking Using Extndd Cohrnt Intgration with an Ultra-ight GNSS/IMU Rcivr, Europan Navigation Confrnc,8.pp.1-11. [15]Himan Zarza, Salh Yousfi and Abdrrahim Bnsliman, RIALS: RSU/INS-aidd localization systm for GPS-challngd road sgmnts,wirlss Communications and Mobil Computing,Vol. 16, NO. 1, 16,pp 19 135. E-ISSN: 4-678 186 Volum 16, 17