Quantifying Improvements from the Integration of GPS and a Tactical Grade INS in High Accuracy Navigation Applications

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1 Quantifying Improvmnts from th Intgration of GPS and a Tactical Grad INS in High Accuracy Navigation Applications M.G. Ptovllo, M.E. Cannon and G. Lachapll Dpartmnt of Gomatics Enginring Univrsity of Calgary BIOGRAPHIES Mark Ptovllo is currntly finishing his PhD in Gomatics Enginring at th Univrsity of Calgary. H otaind his BSc from th sam dpartmnt in 1998 and has n working in th ara of satllit and inrtial navigation sinc that tim. Som of his past rsarch includs intgration of GPS and GLONASS, charactrization of oscillator staility using standalon GPS, and ral-tim satllit-asd hading dtrmination. Dr. M. Elizath Cannon is a Profssor of Gomatics Enginring at th Univrsity of Calgary. Sh has n involvd in GPS rsarch and dvlopmnt sinc 1984, and has workd xtnsivly on th intgration of GPS and inrtial navigation systms for prcis aircraft positioning. Dr. Cannon is a Past Prsidnt of th ION. Dr. Gérard Lachapll is a Profssor and Had of th Dpartmnt of Gomatics Enginring whr h is rsponsil for taching and rsarch rlatd to location, positioning, and navigation. H has n involvd with GPS dvlopmnts and applications sinc H has hld a Canada Rsarch Chair/iCORE Chair in wirlss location sinc ABSTRACT Intgration of GPS with inrtial snsors can nfit many aspcts of navigation from improvd accuracy to incrasd rliaility. Th xtnt of such nfits howvr, is typically a function of th quality of th inrtial systm usd. In this rgard, littl work has n don to quantify th usfulnss of tactical grad inrtial masurmnt units (IMUs) in high-accuracy (cntimtr lvl) intgratd systms. Instad, prvious studis hav typically focusd ithr on high quality IMUs or hav considrd applications with mtr lvl accuracy. Howvr, as low-cost gyro and acclromtr accuracis continu to improv to th tactical grad lvl, th nd to invstigat and quantify th nfits of such snsors in intgratd systms coms vr mor important. In this papr, a Honywll HG1700 IMU is intgratd with a NovAtl OEM4 dual-frquncy GPS rcivr for high-accuracy navigation. Th accuracy of th intgratd systm during complt and partial GPS data outags is invstigatd. Us of th GPS/INS position solution during data gaps is thn usd to quantify th rduction of th amiguity sarch spac, rlativ to th GPS only cas. Th impact of diffrnt filtring stratgis on amiguity rsolution aftr GPS data gaps is also invstigatd. Spcifically, th advantag of cntralizd and dcntralizd filtrs on amiguity rsolution is invstigatd in trms of tim ndd to fix and fix accuracy. Finally, rliaility thory is usd to assss th thortical roustnss of th intgratd systm. INTRODUCTION Th intgration of Gloal Positioning Systm (GPS) rcivrs with Inrtial Navigation Systms (INS) has n wll invstigatd in th past. Th advantags of intgratd systms, rlativ to GPS-only, ar rportd to a full six dgr of frdom navigation solution, improvd accuracy, smoothr trajctoris, and rducd suscptiility to jamming and intrfrnc (Grnspan, 1996). Othr studis such as Skaloud (1998) and Schrzingr (2000, 2001) hav lookd at th nfit of using th inrtial solution for improving amiguity rsolution prformanc. Th xtnt to which th aov advantags hold is wll known to dpndnt on th quality of th Inrtial Masurmnt Unit (IMU) usd in th intgration. With this in mind, it is not surprising that past invstigations hav typically lookd only at using high quality inrtial systms for high accuracy (cntimtr-lvl) applications. Unfortunatly, th cost of high quality inrtial units can prohiitiv for many applications and/or agncis. Prsntd at ION NTM-03, Anahim, CA, January 22-24,

2 Howvr, with th dcrasing cost of tactical grad inrtial snsors, thir us in intgratd navigation systms is dsiral. Th qustion ariss howvr, as to whthr ths lowr cost units will still of nfit for applications dmanding th highst accuracis? From a diffrnt standpoint, could th cost of a tactical grad IMU justifid y improvmnts in th intgratd solution, rlativ to th GPS-only cas? This papr aims to quantify th nfits of using a tactical grad IMU in high-accuracy navigation systms, rlativ to using GPS alon. In particular, th following prformanc paramtrs ar invstigatd: Position accuracy during complt and partial GPS data outags. Rsults of this invstigation will dtrmin th oprational conditions undr which th systm can usd to maintain a givn lvl of prformanc. Th tim ndd to dtrmin th intgr amiguitis aftr complt and partial GPS data outags. Th vracity of th amiguity fix will also considrd. Th thortical rliaility of th systm, in trms of its aility to dtrmin and rmov masurmnt rrors. Spcifically, th impact of undtctd rrors on th final position and vlocity stimats will quantifid. Th aility of th systm to dtct a on-cycl cycl slip will also shown. A Honywll HG-1700 IMU (1 dg/h) is usd with a dual frquncy NovAtl OEM4 GPS rcivr to assss th aov paramtrs. A varity of data intgration stratgis ar invstigatd, as appropriat for th paramtr of intrst. In particular, loos intgration, loos intgration with INS sding and tight intgration stratgis ar considrd. Th us of singl and dual-frquncy data ar also usd for som of th aov invstigations. Th papr gins with a rif discussion of th rlvant mthodology. This includs a rviw of th intgration stratgis usd hrin, th amiguity rsolution procss and its rlationship with th position accuracis, and an ovrviw of rliaility thory. Th fild tsts usd for quantifying improvmnts ar thn dscrid along with th analysis mthodology itslf. Finally, rsults ar prsntd for ach of th aov prformanc paramtrs. METHODOLOGY This sction is intndd as a rviw of th matrial rlvant to this papr. In particular, it rviws th GPS/INS intgration approachs implmntd hrin, th GPS and INS stup, th rol of position accuracy in th amiguity rsolution procss and systm rliaility thory. For dtails on ths topics, th radr is rfrrd to th citd rfrncs. GPS/INS Intgration Stratgis At th cor of any intgratd navigation systm is a mans y which th information is fusd togthr to produc a, prfraly optimal, output. For GPS and INS intgration, thr ar asically four lvls of intgration, which ar rokn down according to how much information is shard. Ths four lvls, listd in incrasing complxity, ar (Jkli, 2001; Schrzingr, 2000): 1. Uncoupld intgration 2. Loos intgration 3. Tight intgration 4. Dp intgration Th uncoupld approach is crud and will simply not of much us in a high-accuracy systm. Th dp intgration, although wll suitd to th prolm at hand, rquirs accss to GPS rcivr hardwar, or at last th tracking loop information, oth of which wr unavailal. For ths rasons, ths intgration stratgis wr not usd. Th loos and tight intgration stratgis ar th most commonly usd in litratur. For convninc, th trms loosly coupld and tightly coupld ar also usd hrin to rprsnt th sam stratgis. In oth cass, th GPS rcivr and IMU ar ssntially working indpndntly with th diffrnc twn thm ing th typ of information that is shard. In th loos intgration, sparat GPS and INS filtrs ar implmntd and th position and/or vlocity of th GPS filtr ar usd as osrvations in th INS filtr. In tight intgration, only on filtr is usd to stimat all rlvant GPS and INS stats. Figur 1 and Figur 2 graphically show th two intgration stratgis. In Figur 2, th gray oxs and lins corrspond to th loos intgration stratgy and ar includd for comparison purposs only (i.. no GPS filtr is usd in th tight intgration approach). All things ing qual, th two approachs yild idntical rsults assuming th propr covarianc information is shard twn filtrs in th loos intgration. Unfortunatly, this solution quality is rarly ralizd caus in th loos intgration stratgy, procss nois must addd to oth th GPS and INS filtrs. This incrasd nois, rlativ to th nois addd to th INS filtr alon (with tight intgration), will introduc som small discrpancis. Comparison of th two approachs shows ths discrpancis to on th ordr of on millimtr and will thrfor not considrd significant. This ing said, th advantag of th loos intgration stratgy is that th dimnsion of th stat vctors is rducd rlativ to th tight intgration cas. This allows for computationally mor fficint programs du to a rducd numr of floating point oprations ndd in th Kalman filtring algorithm. A scond Prsntd at ION NTM-03, Anahim, CA, January 22-24,

3 potntial advantag is that th output from a GPS rcivr or xisting softwar program can dirctly usd to updat th INS filtr, instad of having to comput a solution intrnally in th navigation softwar, thus providing furthr computational savings and rducing dvlopmnt tim. Th disadvantag of th loos intgration stratgy is that th GPS filtr ssntially oprats indpndntly of th rst of th systm. Whil this poss no considral prolm undr idal conditions, if a full filtr rst du to loss of lock (for xampl) is rquird, th GPS-only filtr is sujct to th sam shortcomings as a GPS-only systm. To hlp circumvnt this prolm, Figur 1 shows a dottd lin from th INS filtr to th GPS filtr. Whn a full GPS rst is rquird th inrtial position and vlocity can usd to initializ, or sd, th GPS filtr. In so doing, th GPS filtr can nfit from th additional information providd y th INS. For clarity, th us of sding will always statd xplicitly, as in sding th GPS filtr or loos intgration with INS sding. This is don to avoid confusion with th mor asic loos intgration or loosly coupld trms in which sding is not usd. IMU Amiguity Rsolution Mch Equations INS Kalman Filtr Pos/Vl GPS Kalman Filtr Raw Data GPS Rcivr Intgratd Solution Pos/Vl Sd Figur 1 - GPS/INS Information Flow Diagram Using Loos Intgration Stratgy Th advantag of th tight intgration stratgy is that all information is containd within a singl filtr. This provids ssntially thr nfits. First, it provids a statistically rigorous sharing of information (to th xtnt that th input statistics ar corrct). Scond, caus procss nois is only addd to on filtr, th filtring of th GPS osrvations is incrasd. Th final advantag is that programming a singl Kalman filtr can simplify softwar dvlopmnt, an important practical considration. Th disadvantag of th tight intgration is that th INS stat vctor must augmntd y th float amiguity stats whn thy nd to stimatd. This maks th filtring algorithms slowr du to th incrasd numr of floating point oprations. IMU Amiguity Rsolution Mch Equations GPS/INS Kalman Filtr GPS Kalman Filtr Raw Data GPS Rcivr Figur 2 - GPS/INS Information Flow Diagram Using Tight Intgration Stratgy With th intgration stratgis idntifid, th charactristics of th individual filtrs ar discussd in th nxt sction. GPS, INS and GPS/INS Filtr Stup Intgratd Solution Th GPS-only filtr usd in th loosly coupld approachs can thortically stimat any information osrval using GPS data. Typically, this will includ position, vlocity and possily acclration rrors, ut may includ attitud paramtrs if multipl rcivrs ar availal. For th application considrd hr, th filtr is assumd to stimat only position and vlocity rrors with th lattr ing modld as random walk procsss. Of cours, amiguity stats ar also stimatd as ndd. Th inrtial quations ar mchanizd in th Earth Cntrd Earth Fixd (ECEF) fram. This fram was chosn for its rlativ as of implmntation, rlativ to th Local Lvl implmntation. Th systm rrors stats Prsntd at ION NTM-03, Anahim, CA, January 22-24,

4 ar stimatd in a Kalman filtr using on of th prviously discussd intgration stratgis. Th INS paramtrs stimatd in th navigation filtr includ: Position rrors (3) Vlocity rrors (3) Attitud misalignmnts (3) Gyro iass (3) Acclromtr iass (3) Th dyn amic modls for th aov paramtrs can writtn as a sris of first ordr diffrntial quations as follows: δ p δv ε d = δv = F ε = Ω i = α = βd ε + w + w N δp + R 2Ω ( d + w ) ( + w ) Dots dnot tim drivativs and th suprscripts and dnot paramtrs in th ECEF and ody fram, rspctivly. Th symols ar intrprtd as follows: (1) δ p is th 3-vctor of position rrors δ v is th 3-vctor of vlocity rrors F is th skw-symmtric matrix of spcific forc ε is th 3-vctor of attitud rrors (misalignmnts) N is th tnsor of gravitational gradints Ω i is th skw-symmtric matrix of th rotation rat of th Earth rlativ to inrtial spac R is th rotation matrix from th ody fram to th ECEF fram is th 3-vctor of acclromtr iass d is th 3-vctor of gyro iass α, β ar paramtrs for modling th ias trms as first ordr Gauss Markov procsss is a nois trm w i As implid y quation (1), th vlocity and attitud rrors ar modld as random walk stats, whos procss nois is drivd from th masurmnt nois of th acclromtrs and gyros rspctivly. It should also notd that th ias stats could modld as any appropriat nois procss. For th tightly coupld intgration, th GPS position and vlocity rror stats coincid with th INS position and vlocity rrors. In this way, th tightly coupld filtr is idntical to that of th INS filtr discussd aov, augmntd y th ncssary GPS amiguity stats. i 2 δv + R 1 Amiguity Rsolution and Position Accuracy Th amiguity rsolution procss is what allows for th highst possil accuracy to otaind in a rasonal tim priod. By xploiting th intgr natur of th carrir phas amiguitis, th numr of unknowns can rducd, thus incrasing th numr of dgrs of frdom for th ntir systm. Som amiguity rsolution algorithms ar asd in th position domain. Ths includ th Last Squars Amiguity Sarch Tchniqu (LSAST) (Hatch, 1990) and th Amiguity Function Mthod (AFM) (Counslman and Gourvitch, 1981). For ths mthods, th rlationship twn th position stimat and th stimatd amiguitis is ovious. Howvr, amiguity rsolution mthods in th amiguity domain, such as Fast Amiguity Sarch Filtr (FASF) (Chn, 1994) and Last squars AMBiguity Dcorrlation Adjustmnt (LAMBDA) (Tunissn and Tirius, 1994) to nam a coupl, ar still rliant on th knowldg of th rcivr s position. It follows thrfor that if th position stimat can improvd, th amiguity rsolution procss can xpditd. To show th dsird rlationship, th following quation rprsnting th updatd amiguity covarianc matrix aftr a rst of th amiguity stats is takn from Schrzingr (2002): + a a a T T 1 [ D AP A D + P + R ] P P = P P (2) δp A suprscript - dnots a quantity for updat and a suprscript + dnots a quantity aftr updat. Th rmaining trms ar as follows: P a is th covarianc matrix of th amiguity stats D is th doul diffrnc oprator A is th singl diffrnc dsign matrix of th osrvations is th covarianc matrix of th position rrors P δp R φ is th covarianc matrix of th phas osrvations It should notd that this quation assums th filtr is only updatd with carrir phas masurmnts. If mor osrvations ar addd, such as cod or Dopplr masurmnts, th quation will chang slightly with th ffct ing a furthr rducd amiguity covarianc matrix. Rgardlss, th usfulnss of quation (2) is that it shows th covarianc matrix of th amiguitis dcrass with a smallr apriori covarianc matrix of th position rrors, thus rducing th amiguity sarch spac. In this contxt, th ojctiv is to us th INS-drivd position covarianc matrix to rduc th amiguity sarch spac (in th loos intgration with INS sding and tight a φ a Prsntd at ION NTM-03, Anahim, CA, January 22-24,

5 intgration approachs). It also follows that as th inrtial position covarianc incrass ovr tim during a data outag, th nfit to th amiguity rsolution procss will dcras accordingly, with th limit ing th GPSonly cas. Rliaility Thory Rliaility rfrs to th aility of a systm to dtct and rmov lundrs in th masurmnts givn to said systm, so as to liminat thir ffct on th stimatd paramtrs (Baarda, 1968). Unfortunatly, rliaility is oftn ovrlookd in systm dvlopmnt dspit th dirct impact such an analysis has on mting th ovrall systm prformanc ojctivs. Th rliaility of satllit-asd systms has n invstigatd thoroughly in Lu (1991) and Ryan (2002). To dat vry littl work has n dirctd at th rliaility of intgratd systms. It is partially for this rason that such an invstigation is ing undrtakn. In ordr to dtct a lundr in a Kalman filtr, a tst must prformd on th innovation squnc (misclosurs). Assuming that a lundr occurs on only on masurmnt at a tim, it can shown that a lundr on th i th masurmnt, i, will produc a ias of th sam magnitud in that masurmnt s misclosur. To dtct this lundr, th following tst statistic is mployd (Tunissn, 1989): with th rsult of quation (3), th following stps ar takn for th rliaility analysis: 1. Slct th confidnc lvl and powr of th tst according to som critria. This is usually dtrmind y th rquird systm prformanc. 2. Dtrmin th corrsponding non-cntrality paramtr, δ, from th valus slctd in stp 1. This corrsponds to th thrshold valu of th tst statistic in quation (3). 3. Comput th magnitud of th smallst lundr that can dtctd as: δ i = (6) ( P ) 1 v ii This magnitud of lundr rprsnts th Minimum (or Marginal) Dtctal Blundr (MDB). Th lmnt-ylmnt product of this valu with th i th column of th Kalman gain matrix, yilds th ffct of this lundr on ach of th stimatd paramtrs. Th rsulting vctor is trmd th xtrnal rliaility or protction lvl (PL) vctor. It rprsnts th ffct of an undtctd lundr of magnitud i on th stimatd paramtrs. Looking at only th appropriat lmnts of th xtrnal rliaility vctor (i.. thos that corrspond to crtain stats), th impact on th position, vlocity or any othr stats can dtrmind. c t = whr: 1 ( P ) T 1 i Pv v = i v ii (3 1 ( Pv ) ii v is th innovation squnc P is th covarianc matrix of th innovation squnc c i v () ii is a null row vctor with unity at th i th position th is th i diagonal lmnt of a matrix ) Undr th null hypothsis (H 0) that a lundr dos not xist, th tst statistic, t, can shown (iid) to normally distriutd with zro man: H 0 : t ~ N(0, 1) (4) Howvr, undr th altrnat hypothsis (H a) that a lundr is prsnt, th tst statistic is distriutd as: H a : t 1 ( ( P ), 1) ~ N (5) i v ii Graphically, this is shown in Figur 3. Also shown ar th aras corrsponding to th proaility of committing a Typ I (α) or Typ II (β) rror. With this in mind, along Figur 3 - Distriution of Innovation Tst Statistic With and Without Blundr Prsnt ANALYSIS PROCEDURE This sction dscris th quipmnt usd, th fild tsts that wr prformd and th procssing mthods usd for analyzing th data. Equipmnt Th GPS as station rcivr was a NovAtl OEM4, dual frquncy rcivr. This is a high quality GPS Prsntd at ION NTM-03, Anahim, CA, January 22-24,

6 rcivr, capal of gnrating low nois cod, Dopplr and carrir phas masurmnts. Th rmot station (i.. vhicl) quipmnt consistd of th NovAtl Black Diamond Systm (BDS). Th BDS intgrats a Honywll HG-1700 IMU and a NovAtl OEM4 GPS rcivr into a singl unit. Th IMU data is rcivd and tim taggd y th GPS rcivr for ing output through on of th rcivr s srial ports. This should liminat any potntial timing rrors twn th GPS and IMU data. Both th rmot and rovr rcivrs usd NovAtl 600 antnnas. Som of th mor rlvant prformanc spcifications for th Honywll HG-1700 IMU ar shown in Tal 1. Also shown ar som typical valus for a navigation-grad IMU typically usd for high-accuracy intgratd systms. A quick comparison shows that th HG-1700 is of considraly poorr quality and thrfor rprsnts a good candidat for assssing th nfits of tactical-grad snsors for high-accuracy applications. Tal 1 - Spcifications for Honywll HG-1700 IMU and a Typical Navigation-Grad IMU (Modifid from Shi, 2000; Skaloud, 1999) Paramtr Gyro Bias (dg/h) Angular Random W alk (dg/ h) HG-1700 IMU 1.0 Navigation Grad IMU Accl Bias (mm/s ) V locity Random W alk (mm/s/ h) Fild Tsts A fild tst was conductd and th data collctd wr analyzd as dscrid in th following sction. Th tst was hld just wst of Calgary, Alrta, Canada nar th Springank airport. This ara was slctd caus it provids good GPS satllit visiility. In th ara ar accssil pillars with known coordinats, on of which was usd as a as station. Th as station rcivr was powrd y a gas gnrator, as was th corrsponding logging computr. Th rmot vhicl usd was th Univrsity of Calgary s Satllit-Basd Navigation and Wirlss Location Rsarch Group s tst van; a Dodg Grand Caravan. Th IMU was rigidly mountd to th floor pins of on of th captain chairs and th GPS antnna was mountd on th roof of th van. Th lvr arm twn th IMU and th GPS antnna was accuratly masurd to th millimtr-lvl. Two data collction runs wr prformd. Each run gan with a static initialization priod of aout 12 minuts followd y aout 20 minuts of driving. Vhicl spds varid from stationary to 120 km/h. Vhicl dynamics wr somwhat limitd, with most of th data ing collctd at constant vlocity. Th distanc from th tst vhicl to th as station rangd from a fw mtrs during th initialization to up to 5 and 8 km during runs on and two rspctivly. Although this rprsnts a fairly idal cas, th INS filtr should al to handl mor aggrssiv (ground) vhicl dynamics with littl difficultly. Furthrmor, th analysis procdur usd (s low) considrs a wid rang of vhicl dynamics. Procssing Stratgy Procssing of th data was don using th Univrsity of Calgary s Satllit And Inrtial Navigation Tchnology (SAINT ) softwar. SAINT is asd on th Univrsity of Calgary s nw Navigation Dvlopmnt Lirary (NDL ), a suit of C++ classs writtn to facilitat navigation algorithm and softwar dvlopmnt y allviating th usr of many significant programming dtails. GPS procssing is don using L1 or widlan carrir phas data, as wll as L1 C/A cod and Dopplr masurmnts. All osrvations ar procssd using th doul diffrnc tchniqu. Rsolution of th GPS intgr amiguitis is prformd using th LAMBDA mthod. Th first procssing stp involvd th dtrmination of truth information. Spcifically, gnration of a rfrnc trajctory and amiguity valus wr dsird. This was accomplishd y procssing all of th data togthr using th tight intgration stratgy. In oth runs, th L1 and widlan carrir phas amiguitis wr fixd during th static alignmnt. For th first run, ths amiguity valus wr maintaind throughout th run. For th scond tst, all ut two of th amiguitis wr lost aftr passing undr a highway sign. Th amiguitis wr rcovrd a short tim latr and wr kpt until th nd of th data st. An analysis of th rsiduals and th static position at th nd of th run confirmd that th amiguitis wr indd rsolvd corrctly. To crtain, th tims during which th amiguitis wr ing rsolvd, and a short tim thraftr, wr avoidd in th following analysis. Givn th aov, th rfrnc trajctory is considrd to accurat to ttr than thr cntimtrs, and th amiguitis ar considrd prfct. To confirm, a comparison of th truth solution with th solution otaind from th Univrsity of Calgary s FLYKIN+ softwar was prformd. Th position diffrncs in this cas wr also at th 1-2 cm lvl. Th scond procssing stp was to simulat GPS data outags (also rfrrd to as gaps). This was don y Prsntd at ION NTM-03, Anahim, CA, January 22-24,

7 artificially raising th satllit cutoff lvation from th tn-dgr dfault. For complt data outags, th lvation mask was raisd to 90. For partial data gaps, th lvation mask was slctd on a run-y-run asis. Spcifically, th lvation mask was st to 44.5 and 58.0 for th first and scond runs rspctivly. In ach cas, th numr of visil satllits rmaining was ithr two or thr. Thr wr six data outags simulatd in ach run, for a total of twlv. Th data gaps wr slctd to ncompass a wid rang of vhicl dynamics, from constant vlocity to rlativly larg along-track and latral acclrations. In this way, th nfit of th INS undr mor ralistic oprational conditions can valuatd. Figur 4 and Figur 5 show th trajctoris of th first and scond runs, along with th location of th diffrnt data outags. Figur 5 - Trajctory and Data Outags Rlativ to Bas Station For Run #2 Th rliaility analysis dos not tchnically rquir any data. In this way, th rliaility analysis could conductd offlin through a covarianc analysis. Howvr, for simplicity, th rliaility rsults hrin wr drivd from th actual filtr information otaind from data procssing. Th lvl of significanc (α) and th powr of th tst (1-β) wr chosn to 0.1% and 10% rspctivly. This rsults in a non-cntrality paramtr of RESULTS Figur 4 - Trajctory and Data Outags Rlativ to Bas Station For Run #1 Finally, rsults otaind during th simulatd data outags ar compard with th rfrnc solution. Position accuracy during th data outags is assssd through th diffrnc twn th two solutions. Sinc th rfrnc solution is accurat to th cntimtr lvl, th position diffrnc is du almost ntirly to rrors in th INS in th asnc of GPS updats. Whn th GPS data is rintroducd at th nd of th data outag, th ncssary GPS amiguitis must r-stimatd. Onc ths ar rsolvd to thir intgr valus, thy ar compard with th rfrnc amiguity valus to nsur thir vracity. Also of intrst in this rgard is th tim rquird for th amiguitis to rsolvd to thir (hopfully corrct) intgr valu. Th aov procssing stratgy is rpatd for ach of th diffrnt intgration stratgis discussd aov using L1 and widlan carrir phas data. Th duration of th simulatd data gaps was varid from 2 to 40 sconds to hlp dtrmin th lngth of tim ovr which th INS would provid significant improvmnts to th GPS-only solution. Rsults ar sparatd into th thr catgoris prviously discussd, and ar prsntd in th following sctions. Position Accuracy To assss th positioning capaility of intgratd systm during data outags, th North, East and Up position rrors wr computd as a function of th tim sinc th last GPS updat for ach simulatd outag. Th Root Man Squar (RMS) rror across all simulatd data gaps was computd and is assumd to a good stimat of th inrtial systm s aility to ridg data outags. Figur 6 shows th RMS position rror of th intgratd solution otaind from L1 data, during complt GPS outags. Th rsults for th widlan ar only slightly wors and ar not shown hr. As sn, th position accuracy dgrads to aout 1.2 m aftr 30 sconds. Howvr, if on considrs that a diffrntial cod solution will provid a similar accuracy (i.. 1 to 1.5 m), th nfit of th inrtial systm coms apparnt. Mor spcifically, th inrtial systm can provid RMS position accuracis as good as, or ttr than, diffrntial GPS for data outags of up to 30 sconds. This improvd position accuracy has two main advantags. First, it initializs th navigation filtr to a considraly ttr valu than if th inrtial systm was asnt. This in turn should provid fastr filtr convrgnc. Scond, th improvd position Prsntd at ION NTM-03, Anahim, CA, January 22-24,

8 stimat will allow for improvd amiguity rsolution prformanc, as pr quation (2). This will rvisitd in th nxt sction. It should also notd that th stimatd position accuracy of th systm closly matchs th rsults shown in Figur 6. Figur 7 shows th intgratd systm s RMS position rror during partial GPS outags, using L1 carrir phas data. Th graph is shown on th sam scal as Figur 6 to facilitat comparison. As can sn, th RMS position rror is considraly ttr than with complt data outags. Figur 6 - RMS Position Error Across All Complt Data Outags Using L1 Carrir Phas Data Figur 7 - RMS Position Error Across All Partial Data Outags Using L1 Carrir Phas Data Amiguity Rsolution Th aility of th intgratd systm to rcovr from complt and partial GPS outags and rturn to a corrctly fixd intgr amiguity solution is xtrmly important. Sinc it is th xploitation of th intgr natur of th amiguitis that allows for high accuracy position stimats in a timly mannr, it follows that th amiguity rsolution procss is vital to achiving th intgratd systm s ojctivs. In this contxt, thr ar two paramtrs that ar of intrst. First, how long dos it tak th amiguity rsolution procss to rsolv th amiguitis to intgrs? Scond, ar th intgr amiguitis that wr slctd corrct? Whil th tim to fix is important for th highst accuracy in a timly mannr, it is asolutly crucial that th amiguitis rsolvd corrctly. A wrong fix of on cycl on a singl satllit is capal of producing position rrors that far xcd th navigation systm s stimatd accuracy for that position, thus prsnting a srious prolm to usrs of th systm. Figur 8 shows th avrag tim ndd to rsolv th L1 carrir phas amiguitis aftr complt data outags for th first run. It is notd that in this cas, all amiguitis wr rsolvd corrctly and so th focus of th analysis will th tim ndd to fix. Th trm avrag is usd caus th valus rprsnt th avrag tim to fix across all data gap durations. As sn, th inrtial systm provids considral improvmnts in th tim ndd to rsolv th amiguitis. Howvr, thr is also a notical improvmnt whn using th tight intgration ovr th loos intgration with GPS sding. This improvmnt is du to th rducd lvl of procss nois in th tight intgration approach, and th highr corrlation twn th amiguity and INS stats within th filtr. Whil th rsults of Figur 8 ar promising, thy ar slightly mislading. To s why, considr Figur 9, which shows th tim it taks to fix th amiguitis for ach simulatd data gap. Th rsults of Figur 8 ar otaind from this graph y avraging th rsults for a particular data gap across all gap durations. This graph shows that for gap durations of up to 30 sconds, th inrtial systm can provid vn largr improvmnts than indicatd y Figur 8. This is particularly notical for data gaps 1 through 3. Aftr aout 30 sconds, th inrtial systm s position accuracy is at th lvl of th GPS diffrntial cod solution. Consquntly, at that point, th nfit of th inrtial systm is almost ngligil. For th scond run, th tim to fix th L1 amiguitis aftr a complt data outag is shown in Figur 10. In this cas, th GPS-only solution appars to rsolv fastr without th inrtial systm in svral cass. Howvr, if on considrs that vry tim th GPS tim to fix is lss than th corrsponding valu using th inrtial systm (ithr using th loos intgration with INS sding, or th tight intgration), th rsults com clar. In total, thr wr nin incorrct amiguity fixs using GPS only and non using ithr of th intgratd approachs. Also of not is that svral tims th amiguitis could not rsolvd for th nd of th data st. Whil this is not Prsntd at ION NTM-03, Anahim, CA, January 22-24,

9 an idal situation, it is crtainly ttr than fixing incorrctly. Tal 2 summarizs th numr of tims th amiguitis wr fixd incorrctly or th amiguitis could not rsolvd. It should notd that all of ths prolms happnd on data gaps 4 and 5. Ths rprsnt th longst aslins ovr which th amiguitis had to rsolvd, suggsting that th diffrntial rrors wr playing a rol in th rsults otaind. To confirm this hypothsis, an invstigation of th rsiduals showd a trnd with aslin lngth, with longr aslins producing largr carrir phas rsiduals. of th inrtial systm can significant, as shown in Figur 11. In particular, th thr longr amiguity rsolution tims for th GPS-only cas corrspond to cass whn th data outag was simulatd approximatly 7 km from th as station. Whil this dos not rprsnt a trmndously long aslin, th ffcts of th diffrntial rrors (most likly th ionosphr) may xhiiting an ffct on th GPS only filtr. Howvr, th inrtial systm can assist in circumvnting this prolm. Again, in all cass th amiguitis wr rsolvd corrctly. Figur 8 - Avrag Tim To Fix L1 Amiguitis Aftr Complt Data Outags (Run #1) Figur 10 - Tim To Fix L1 Amiguitis Aftr Each Complt Data Outag (Run #2) Tal 2 - Numr of Tims Each Intgration Stratgy Fixd Wrong or Could Not Fix Error / Intgration Stratgy Prolm GPS-Only Sding Tight Wrong Fix Could Not Fix Figur 9 - Tim To Fix L1 Amiguitis Aftr Each Complt Data Outag (Run #1) Whn using widlan amiguitis, th us of th inrtial systm is not as significant, du th rlativ as with which th widlan amiguitis can rsolvd. For xampl, th first run shows that th GPS-only filtr can rsolv th amiguitis within on scond aftr vry data outag. In contrast, oth intgratd approachs show instantanous amiguity rsolution. This rprsnts only a modst improvmnt. For th scond run howvr, rsults indicat that undr som circumstancs, th nfit Amiguity rso lution aftr pa rtial data outags show rsults that paralll thos just discussd. Howvr, it should notd that in this contxt, loosly coupld intgration wi th INS sding has no ral maning sinc th INS sding was intndd for us only aftr complt data outags. With this in mind, th tims ndd to fix th L1 amiguitis aftr ach partial data gap is shown in Figur 12 and Figur 13 for th first and scond runs rspctivly. Again, considral improvmnts ar sn whn using th inrtial systm. Whn trying to rsolv widlan amiguitis, th GPS only filtr was al to dtrmin th corrct amiguity instantanously for vry data outag simulatd in th first run. Rsults for th scond run ar shown in Figur 14. As with th complt data outags, th advantag of th inrtial systm is only vidncd ovr th longst Prsntd at ION NTM-03, Anahim, CA, January 22-24,

10 aslins. Othrwis, th roustnss of th widlan amiguity is sufficint vn for th GPS only cas. From th aov analysis, it can concludd that th introduction of an inrtial systm can yild significant improvmnts in th amiguity rsolution procss aftr data outags. In particular, oth th loos and tight intgrations showd th aility to dramatically rduc th tim ndd to rsolv th amiguitis, rlativ to th GPS only cas. Also, and prhaps mor importantly, using th inrtial information allows for mor roust amiguity rsolution, whil th GPS-only approach may produc incorrct fixs. Figur 11 - Tim To Fix Widlan Amiguitis Aftr Each Complt Data Outag (Run #2) Figur 14 - Tim To Fix Widlan Amiguitis Aftr Each Partial Data Outag (Run #2) Comparing th loos intgration with INS sding and th tight intgration stratgis shows that th tightly coupld approach dos offr som advantags. Whil ths advantags ar not ncssarily significant in all applications, thy may nd to takn into considration undr som circumstancs. Figur 12 - Tim To Fix L1 Amiguitis Aftr Each Partial Data Outag (Run #1) Figur 13 - Tim To Fix L1 Amiguitis Aftr Each Partial Data Outag (Run #2) Systm Rliaility For as of analysis, th RMS MDB and protction lvls wr computd on a satllit-y-satllit asis for ach of th cod, Dopplr and carrir phas masurmnts. Data outags wr not simulatd for this purpos. Using this approach, th diffrnc in th cod rliaility paramtrs with and without th inrtial systm was oftn not significant. This is du to th rlativly low wight givn to th C/A cod masurmnts, rlativ to th carrir phas. Ths rsults will thrfor not shown hr. For Dopplr masurmnts, th most rlvant rliaility paramtrs ar shown in Tal 3. Thr is a markd diffrnc in th magnitud of th MDB that can dtctd with and without th inrtial systm. Howvr, mor importantly, th tight intgration can rduc th protction lvls y on to two ordrs of magnitud. This rprsnts a trmndous advantag ovr GPS-only. Similar rsults ar otaind for th L1 carrir phas osrvations, as shown in Tal 4. In this cas, th Prsntd at ION NTM-03, Anahim, CA, January 22-24,

11 (position) protction limits for th tight intgration ar ttr than thos of GPS only y a factor of aout thr to six. Whil not as imprssiv as with th Dopplr masurmnts, this still rprsnts a significant improvmnt ovr th GPS-only cas. Also, th MDB for th tight intgration, whn convrtd to units of cycls, is on th ordr of on cycl. This implis that th systm is capal of dtcting a cycl slip of on cycl 90% (1-β) of th tim, with 99.9% (1-α) confidnc. In contrast, GPSonly has carrir phas MDBs that ar gratr than on cycl. In this cas, to rach th on-cycl lvl, th β paramtr would hav to incrasd. Statd diffrntly, for th GPS only filtr to rach th sam prformanc as th tightly coupld filtr, th corrsponding powr of th tst would hav to dcras. Finally, it is notd that only th standalon GPS and tight intgration rliaility paramtrs ar shown. Although it is possil to considr th rliaility of th loos intgration approach, this is yond th scop of this papr. This ing said, it is notd that th loos intgration provids slightly poorr rliaility than dos th tight intgration in trms of protction lvls. In fact, in most cass th diffrncs ar quit small, namly 1-2 mm/s for vlocity and lss than 1 cm for position. Howvr, thr ar som satllits for which thr is a significant advantag to using th tight intgration with th carrir phas masurmnts. For ths satllits, th protction lvls can svral cntimtrs ttr with th tight vrsus th loos intgration. CONCLUSION This papr invstigatd th nfits of using a tactical grad INS to augmnt GPS for high-accuracy applications. Simulation of GPS data outags showd that th standalon prformanc of th inrtial systm is capal of providing dcimtr-lvl accuracy for complt outags lasting up to 20 sconds. During partial data outags, systm prformanc was shown to improv y factor of aout two. Using diffrnt GPS/INS intgration stratgis, th aility of th intgratd systm to rsolv th intgr amiguitis aftr a data gap was also invstigatd. Rsults showd that using a loos intgration with INS sding of th GPS filtr or a tight intgration significantly rducd th tim to fix amiguitis aftr a data outag, primarily with L1 amiguitis. In som cass, L1 amiguity rsolution tims wr rducd y 100%, that is, instantanous amiguity rsolution was possil. Widlan amiguitis wr al to rsolvd instantanously a larg portion of th tim, howvr, th improvmnts ovr GPS alon wr not as significant as with L1. Howvr, prhaps mor important than th amiguity rsolution tim, th rliaility of th amiguity fixs was shown to considraly highr with th intgratd systm. Rsults from on tst show that nin wrong fixs with GPS only wr liminatd whn using th information from th inrtial systm. Tal 3 - RMS MDB and Vlocity Protction Lvls For Dopplr Masurmnts (Run #2) PRN MDB (cm/s) Horizontal PL (cm/s) Vrtical PL (cm/s) GPS Only Tight Int. GPS Only Tight Int. GPS Only Tight Int Tal 4 - RMS MDB and Position Protction Lvls For L1 Carrir Phas M asurmnts (Run #2) PRN MDB (cm) Horizontal PL (cm) Vrtical PL (cm) GPS Only Tight Int. GPS Only Tight Int. GPS Only Tight Int Prsntd at ION NTM-03, Anahim, CA, January 22-24,

12 Finally, a rliaility analysis of th GPS-only and tightly intgratd systms was prformd. Whil th lattr significantl y rducd th MDB for th Dopplr and carrir phas masurmnts, th ral advantag of th tight intgration was in th protction lvls. Spcifically, th RMS vloc ity protction lvls wr rduc d y up to two ordrs of magnitud whn considring an undtctd Dopplr lundr. Similarly, th tight intgration rducd th ffct of an undtctd carrir phas lundr y a factor of thr to six. REFERENCES Baarda, W., (1968), A Tsting Procdur for Us In Godtic Ntworks, Nthrlands Godtic Commission, Pulications on Godsy, Nw Sris, Vol 2(5), Dlft. Chn, D., (1994), Dvlopmnt of a Fast Amiguity Sarch Filtr (FASF) Mthod for GPS Carrir Phas Amiguity Rsolution, PhD Thsis, UCGE Rport #20071, Dpartmnt of Gomatics Enginring, Th Univrsity of Calgary. Counslman, C.C. and S.A. Gourvitch, (1981), Miniatur Intrfromtr Trminals for Earth Survying: Amiguity and Multipath with Gloal Positioning Systm, IEEE Transactions on Goscinc and Rmot Snsing, Vol GE-19, No. 4, Octor. Grnspan, R.L., (1996), GPS and Inrtial Navigation, Gloal Positioning Systm: Thory and Applications, Volum II, Amrican Institut of Aronautics and Astronautics, Washington, DC, pp Schrzing r B.M., (2001), Roust Inrtially-Aidd RTK Position Masurmnt, Procdings of th Intrnational Symposium on Kinmatic Systms in Godsy, Gomatics and Navigation, Dpartmnt of Gomatics Enginring, Th Univrsity of Calgary, pp Schrzingr B.M., (2002), Roust Positioning with Singl Frquncy Inrtially Aidd RTK, Procdings of NTM 2002, Th Institut of Navigation, Alxandria, VA., pp Skaloud, J., (1998), Rducing Th GPS Amiguity Sarch Spac By Including Inrtial Data, Procdings of GPS 1998, Th Institut of Navigation, Alxandria, VA., pp Skaloud, J., (1999), Optimizing Gorfrncing of Airorn Survy Systms y INS/DGPS, PhD Thsis, UCGE Rport #20126, Dpartmnt of Gomatics Enginring, Th Univrsity of Calgary. Tunissn, P.J.G. and M.A. Salzmann, (1989), A Rcursiv Slippag Tst For Us In Stat-Spac Filtring, Manuscripta Godatica, No. 14, pp Tunissn, P.J.G. and C.C.J.M. Tirius, (1994), Intgr Last-Squars Estimation of Th GPS Phas Amiguitis, Procdings of th Intrnational Symposium on Kinmatic Systms in Godsy, Gomatics and Navigation, Dpartmnt of Gomatics Enginring, Th Univrsity of Calgary, pp Hatch, R., (1990), Instantanous Amiguity Rsolution, Procdings of th Intrnational Symposium on Kinmatic Systms in Godsy, Gomatics and Navigation, Dpartmnt of Gomatics Enginring, Th Univrsity of Calgary, pp Jkli, C., (2001), Inrtial Navigation Systms with Godtic Applications, Waltr D Gruytr. Lu, G., (1994), Quality Control for Diffrntial Kinmatic GPS Positioning, MSc Thsis, UCGE Rport #20042, Dpartmnt of Gomatics Enginring, Th Univrsity of Calgary. Ryan, S.J., (2002), Augmntation of DGPS for Marin Navigation, PhD Thsis, UCGE Rport #20164, Dpartmnt of Gomatics Enginring, Th Univrsity of Calgary. Schrzingr B.M., (2000), Prcis Roust Positioning with Inrtial/GPS RTK, Procdings of GPS 2000, Th Institut of Navigation, Alxandria, VA., pp Prsntd at ION NTM-03, Anahim, CA, January 22-24,