Attitude Determination GPS/INS Integration System Design Using Triple Difference Technique

Transcription

1 Joural of Elctrcal Egrg & Tchology Vol. 7, No., pp. 1~, Atttud Dtrmato GPS/INS Itgrato Systm Dsg Usg Trpl Dffrc Tchqu Sag Ho Oh*, Dog-Hwa Hwag, Chask Park** ad Sag Jog L*** Abstract GPS atttud outputs or carrr phas obsrvabls ca b ffctvly utlzd to compsat th atttud rror of th strapdow rtal avgato systm. Howvr, wh th tgr ambguty s ot corrctly rsolvd ad/or a cycl slp occurs, a rroous GPS output ca b obtad. If th rroous GPS output s appld to th atttud dtrmato GPS/INS (ADGPS/INS) tgratd avgato systm, th prformac of th systm ca b dgradd. Ths papr proposs a ADGPS/INS tgrato systm usg th trpl dffrc carrr phas obsrvabls. Th proposd tgrato systm cotas a cycl slp dtcto algorthm, whch th rtal formato s combd. Computr smulatos ad flght tst wr prformd to vrfy ffctvss of th proposd avgato systm. Rsults show that th proposd systm gvs a accurat ad rlabl avgato soluto v wh th tgr ambguty s ot corrctly rsolvd ad th cycl slp occurs. Kywords: Atttud dtrmato, GPS, INS, Trpl dffrc 1. Itroducto Th atttud dtrmato GPS (ADGPS) rcvr ca provd atttud output usg carrr phas obsrvabls from multpl atas [1, ]. Th GPS atttud output has boudd rror charactrstc as th posto ad vlocty output from th GPS rcvr []. I ordr to mprov th prformac of a avgato systm, th GPS atttud output or carrr phas obsrvabl ca b combd wth th strapdow rtal avgato systm (SDINS) outputs. Svral ltraturs ca b foud o th tgrato of th INS wth th ADGPS rcvr. Evas t al. [3] show a cofgurato of th tgratd avgato systm for a umad aral vhcl (UAV) usg a rtal masurmt ut (IU) ad a ADGPS rcvr as a subsystm of th autoplot systm th DragoFly projct. Wolf t al. [] dscrb a tgratd GPS/INS systm that cossts of a low cost IU ad a ADGPS rcvr, TANS Vctor from Trmbl Navgato Ltd. Gldrloos t al. [] dscussd a GPS atttud systm tgratd wth rtal ssors for spac applcatos. Gbr-Egzabhr t al. [] hav troducd a xpsv atttud hadg rfrc systm (AHRS), whch low cost automotv grad rtal ssors ar tgratd wth a ADGPS rcvr wth ultra-short basl ata schm. I gral, th carrr phas obsrvabl modl s Corrspodg Author: Dpartmt of Elctrocs Egrg, Chugam Natoal Uvrsty, Kora (dhhwag@cu.ac.kr) * Hayag Navcom Co., Ltd., Kora (laborosh@hayagav.co.kr) ** Dpartmt of Elctrocs Egrg, Chugbuk Natoal Uvrsty, Kora (chasp@chugbuk.ac.kr) *** Dpartmt of Elctrocs Egrg, Chugam Natoal Uvrsty, Kora (sjl@cu.ac.kr) Rcvd: Jauary 13, 11; Accptd: Aprl 9, 1 composd of tru rag, tgr ambguty ad rror trms such as troposphrc dlay, oosphrc dlay, rcvr clock rror, mult-path rror ad rcvr os [7, 8]. Th sgl dffrc btw rcvrs or th doubl dffrc btw rcvrs ad satllts ca lmat som rror trms th carrr phas obsrvabl. Howvr, th tgr ambguty caot b rmovd by ths mthods ad should b rsolvd bfor th tgratd avgato systm utlzs carrr phas obsrvabls [1, 9]. Wh th GPS atttud outputs ad/or carrr phas obsrvabls cota corrct tgr ambguty rsoluto ad/or th cycl slp occurs, th ADGPS/INS tgratd avgato systm, may ot gv a dsrabl output. I ordr to guarat a rlabl ad accurat avgato soluto, a w tgrato algorthm s rqurd to ovrcom th tgr ambguty rror ad th cycl slp. Th tm dffrcd carrr phas masurmts hav b usd for adg th GPS/INS tgrato systm ordr to avod th hard ambguty rsoluto problm. Wdl [1] ad Soo [11] proposd a tghtly coupld GPS/INS tgrato systm wth th tm dffrcd carrr phas masurmt ordr to mprov posto accuracy. Grass ad L [1] showd that hgh-accuracy dffrtal postog rsults ca b obtad by usg tratv doubl dffrc procssg wth trpl dffrc mthod. Aothr applcato of carrr phas masurmts s th GPS atttud dtrmato. For th sam raso as th GPS/INS tgrato, svral paprs hav proposd th GPS atttud dtrmato mthod usg th tm dffrc of th doubl dffrcd carrr phas masurmts [13-1]. As s wll-kow, th trpl dffrc ca b subjct to sgfcat os corrupto. If thr s a cycl slp th GPS rcvr du to low sgal to os rato or loss of lock of th carrr trackg loop, th

2 1 Atttud Dtrmato GPS/INS Itgrato Systm Dsg Usg Trpl Dffrc Tchqu rcvr dos ot gv a accurat atttud output [17, 18]. Thrfor, ths waksss should b ovrcom ordr to us th advatag o th tgr ambguty of th tm dffrc of th doubl dffrcd carrr phas masurmt. Ths papr proposs a ADGPS/INS tgrato systm usg th trpl dffrc tchqu. To lmat th tgr ambguty th GPS carrr phas masurmt, th trpl dffrc carrr phas obsrvabl s usd ad a w form of masurmt quato s drvd for th tgrato Kalma fltr. For th cycl slp, a rtaltgratd dtcto algorthm s cludd th proposd tgrato systm. Wh a cycl slp s dtctd, th avgato systm dos ot us th carrr phas obsrvabl th Kalma fltr.. Structur of th Proposd Navgato Systm Fg. 1 llustrats ovrall structur of th proposd avgato systm. Th tgrato algorthm cossts of SDINS part, trpl dffrc carrr phas (TDCP) grato part, Kalma fltrg part, ad cycl slp dtcto part. Th SDINS part computs posto, vlocty, ad atttud from masurd acclratos ad agular rats of th IU. Th TDCP grato part calculats th TDCP obsrvabls from th carrr phas masurmts. Th Kalma fltrg part stmats SDINS rrors usg th posto output, vlocty output, atttud output, ad TDCP obsrvabls from SDINS ad GPS rcvr. 1 stats rror modl s usd for th Kalma fltr; posto rror, vlocty rror, atttud rror, gyroscop rror, ad acclromtr rror. Th gyroscop ad acclromtr rrors ar modld as radom bas [19]. Th cycl slp s dtctd by comparg th masurd carrr phas obsrvabls wth th stmatd from th output of th SDINS []. Wh th cycl slp s dtctd, th Kalma fltr dos ot us TDCP obsrvabls ordr to lmat fluc of th cycl slp. 3. Itgrato Algorthm 3.1 Carrr phas obsrvabl Sc th carrr phas obsrvabls hav hghr rsoluto ad lowr masurmt os tha th cod phas obsrvabls, thy hav b usd for th hgh prcso survyg ad th atttud dtrmato of vhcls wth multpl GPS atas. Th rlatv postog tchqu has b usd for dtrmato of vctor btw two rcvrs or atas usg th carrr phas obsrvabls. I ths cas, th dffrc tchqu s usd for rjctg fluc of th commo rrors cotad th udffrcd carrr phas obsrvabls [7, 8]. Th udffrcd carrr phas obsrvabl ca b modld as λφ ( k) = r ( k) + λn + cb + δ + w ( k) (1) A A A A A A whr ad A dots th satllt ad GPS rcvr (or ata), rspctvly; λ rprsts wavlgth of th L1 carrr ad r A s tru rag btw th rcvr (or ata) A ad th satllt. N A ad cb A dot tgr ambguty ad rcvr clock bas, rspctvly; δ A s th carrr phas rror that cluds th phmrs rror, oosphrc advac ad troposphrc dlay ad w A s th masurmt os that cluds th multpath rror ad rcvr os. Th doubl dffrc tchqu has b usd for atttud dtrmato bcaus t ca rmov rcvr clock bas ad othr commo rrors xcpt for th tgr ambguty ad masurmt os []. Th doubl dffrc carrr phas (DDCP) obsrvabl btw two atas s gv by { ( k) ( k) ( k) ( k) } j j λφs λ Φ S Φ Φ S Φ = r ( k) + λn + w ( k) S S S () whr ad j dot satllts; dots th mastr ata ad S th slav ata. r S s doubl dffrcd tru rag; N S ad w S ar th doubl dffrcd tgr ambguty ad masurmt os, rspctvly. Larzg () at th mastr ata posto gvs l ( k) = h ( k) r ( k) + λn + w ( k) (3) S S S Fg. 1. Ovrall structur of th proposd tgrato systm whr l dots larzd DDCP obsrvabl; h S s dffrc btw th l-of-sght (LOS) vctors from th mastr ata to satllt ad satllt j ; r s th basl vctor from th mastr ata to th slav

3 Sag Ho Oh, Dog-Hwa Hwag, Chask Park ad Sag Jog L 17 ata th arth ctrd arth fxd (ECEF) fram. Lt us df x( k) x( k) x( k 1) for a varabl x. Th larzd TDCP obsrvabl () ca b obtad by dffrcg (3) btw th k th poch ad th ( k 1) th poch. l ( k) l ( k) l ( k 1) S S S = h ( k) r ( k) h ( k 1) r ( k 1) + w ( k) w ( k 1) S S = h ( k) r ( k) h ( k 1) r ( k 1) + w ( k) S If o cycl slps hav occurrd th carrr phas obsrvabls, th tgr ambguty s rmovd from th DDCP obsrvabls (3). I th proposd tgrato schm, th TDCP obsrvabls ar usd for masurmts of th Kalma fltr. Th masurmt quato for th Kalma fltr s drvd th followg subscto. 3. Kalma fltr for tgrato Th rror modl for th Kalma fltr [19, 1] s dscrbd by xɺ ( t) = F( t) x( t) + w( t), w( t) ~ N(, Q( t) ) xɺ av F11 F1 xav wav = + xɺ x w ssor 9 ssor ssor whr x av ad x ssor ar th avgato ad ssor rror stat vctor, rspctvly. Th avgato rror stat vctor cossts of posto, vlocty, ad atttud rror whch s drvd th ps agl rror modl. Th ssor rror stat vctor cossts of acclromtr ad gyro rror whch ar modld as radom bass. Th masurmt quato s dscrbd by () () pochs s h ( k) = h ( k) h ( k 1) (8) Substtutg (8) to (), th larzd TDCP obsrvabl modl ca b rwrtt as follows l ( k) = h ( k) r ( k) h ( k 1) r ( k 1) + w ( k) S S = h ( k) r ( k) h ( k) h ( k) r ( k 1) + ws ( k) = h ( k) r ( k) r ( k 1) + h ( k) r ( k 1) + w ( k) I ordr to vstgat fluc of th scod trm h ( k) r ( k 1), th larzd trpl dffrc modl (9), a smulato was prformd. I th smulato, th atlab ad Satllt Navgato Toolbox from GPSoft wr usd to grat moto of th GPS satllts []. Fg. llustrats arragmt of atas for th ADGPS rcvr. oto of th GPS satllts was smulatd from 1, to 3, scod of GPS tm wh th ADGPS rcvr stays at orth lattud, ast logtud, ad m alttud. I ths cas, all atas ca obsrv at last satllts wh th mask agl s st to b 1. Usg th Cauchy-Schwarz qualty [3], th r product of h ( k) ad r ( k 1) ca b wrtt as (1). S (9) h ( k) r ( k 1) h ( k) r ( k 1) (1) Not that th orm (lgth) of th basl vctor r ( k 1) dos ot chag ad s 1 m Fg.. z( t) = H( t) x( t) + v( t), v( t) ~ N(, R( t) ) z1 H1 v1 z= = x+ z H v () whr H 1 s th masurmt sub matrx rlatd to th posto ad vlocty rror ad H th TDCP obsrvabls. I ordr to drv th masurmt quato for th tgrato Kalma fltr, th followgs ar assumd. Assumpto 1. Thr s o varato th LOS vctor btw two coscutv pochs. Fg.. Arragmt of GPS atas h ( k) h ( k 1) (7) Rmark 1 Dffrc of th LOS vctor btw two coscutv Fg. 3 shows varato of th orm of h ( k) durg th smulato trval. Th lgd (, j ) dots PRN umbr of th satllt. I Fg. 3, t ca b obsrvd that all th orms of

4 18 Atttud Dtrmato GPS/INS Itgrato Systm Dsg Usg Trpl Dffrc Tchqu rror (mm) (,) (,7) (,1) (,18) (,19) (,1) whr δψ s th SDINS atttud rror vctor dfd by th ps agl rror modl []. Rmark 3 It s wll kow that th SDINS atttud rror oscllats Schulr frqucy wth 8 muts prod []. It ca b assumd that th SDINS atttud rror dos ot chag btw two coscutv pochs as th assumpto 3. Th TDCP obsrvabl ca b rwrtt from () usg th assumpto 1 as follows GPS tm of wk (s) Fg. 3. Varato of orm of th LOS vctor h ( k) for satllts ar lss tha From th qualty (1) ad th smulato rsult, maxmum varato of th TDCP obsrvabl causd by th h ( k) s lss tha m. agtud of th GPS carrr phas masurmt os s kow to b approxmatly m at th L1 frqucy []. agtud of th TDCP obsrvabl masurmt os s approxmatly.1-3 m sc magtud of th TDCP obsrvabl masurmt os s tms that of th udffrcd. As a rsult of ths, fluc of th scod trm h ( k) r ( k 1) ca b glctd th larzd trpl dffrc modl (9) sc t s suffctly small valu compard wth th masurmt os of th TDCP obsrvabl. From th abov obsrvato, th assumpto 1 ca b accptabl ral applcatos. Assumpto. Thr s o varato th btw two coscutv pochs. ( ) ( 1) C matrx C k C k (11) whr C s th coordat trasformato matrx from th avgato fram to th ECEF fram ( fram). Rmark If a vhcl movs a vry hgh spd, for xampl, 1, km/h (=77.8 m/s), chag of th lattud or logtud s lss tha 1 rad 1 s. Etrs of th coordat trasformato matrx C ar xprssd sums ad multplcatos of th trgoomtrc fuctos, whch dpdt varabls ar lattud ad logtud of th vhcl. Varato of ach try valu s small ough to gor. From ths obsrvato, th assumpto ca b accptabl ral stuato. Assumpto 3. Thr s o varato th SDINS atttud rror btw two coscutv pochs. δψ ( k) δψ ( k 1) (1) l ( k) = h ( k) r ( k) h ( k 1) r ( k 1) + w ( k) S S h ( k) r ( k) r ( k 1) + w ( k) S = h ( k) r ( k) + w ( k) S (13) Th masurmt quato ca b drvd from th stmat xprsso of th TDCP obsrvabl from th output of th SDINS. Th basl vctor ca b xprssd as (1) trms of th atttud rror of th SDINS troducd (). r = C r = C C r = C I+ δψ C r b b b b = C C r + C δψ C r b b b b ( ) b b = C C r C r δψ (1) whr C b s th stmatd coordat trasformato b matrx from th body fram to th avgato fram; r ad r ar th basl vctor th body fram ad stmatd basl vctor th avgato fram, rspctvly. Th ovr bar rprsts a stmatd valu from th SDINS output. Th otato ( a ) mas th skw-symmtrc matrx of th a vctor as (1). ( a) α γ β γ β α = β = γ α (1) Dffrc of th basl vctor r ( k) ca b xprssd as (1) from (1) usg th assumpto ad 3 r ( k) = r ( k) r ( k 1) = C ( k) C ( k) r C ( k 1) C ( k 1) r b b b b ( ) δψ ( ) C ( k) r ( k) ( k) + C ( k 1) r ( k 1) δψ ( k 1) C ( k) Cb ( k) Cb ( k 1) r b ( ) ( ) C ( k) r ( k) r ( k 1) δψ ( k) ( ) b = C ( k) C ( k) r C ( k) r ( k) δψ ( k) b (1)

5 Sag Ho Oh, Dog-Hwa Hwag, Chask Park ad Sag Jog L 19 From (13) ad (1), th stmatd TDCP obsrvabl ca b xprssd as l ( k) = h ( k) r ( k) S = h ( k) C ( k) C ( k) r b b ( ) h ( k) C ( k) r ( k) δψ ( k) (17) whr th l S dots th stmatd valu of l S. I th drct Kalma fltr, stat varabls ad masurmt quato ar xprssd trms of SDINS rrors [18]. Th TDCP masurmt should b xprssd th SDINS atttud rror. From (1) ad (17), th masurmt quato ca b obtad as (18) ( ) S S z = l l = h C r δψ + v (18) Hc, th part of th masurmt quato rlatd to th TDCP s gv by z = H x+ v ( r ) ( k 1) H C 1 ( 1) 3 k ( k 1) 3 ( k 1) H C( r ) ( k 1) 3 ( k 1) 3 = x+ v ( r ) ( k 1) H C l ( k 1) 3 ( k 1) k ( ) ( ) ( ) T (19) T T T H = h ( k 1) 3 h h () whr k ad l dots umbr of satllts vw to a basl ad umbr of basl vctors, rspctvly. I spt that th masurmts oss ar crossly corrlatd wh th carrr phas obsrvabls ar procssd by trpl dffrc tchqu [8], t s assumd that th masurmt oss ar wht Gaussa radom varabls. Thrfor, t s xpctd that prformac of th tgrato Kalma fltr b dgradd. I ordr to tak to cosdrato of ths problm, valu of th masurmt os covarac matrx R should b carfully tud through smulatos ad post-msso data procssg. 3.3 Cycl slp dtcto Ev though th tgrato systm utlzs th TDCP obsrvabls, th cycl slp caot b avodd. Th cycl slp may gv rs to prformac dgradato tgratd avgato systms. I ordr to cop wth ths problm, a cycl slp dtcto algorthm usg rtal formato [] s cludd th proposd tgrato algorthm. Wh a cycl slp s dtctd, th tgrato Kalma fltr dos ot us th TDCP obsrvabls. If th atttud dtrmato GPS rcvr uss o commo clock, th sgl dffrc carrr phas obsrvabls btw rcvrs s gv by l ( k) = h ( k) r ( k) + λn + w ( k) (1) S S S whr h s th LOS vctor from th mastr ata to th satllt. Takg dffrc btw two coscutv pochs (1) ad usg th assumpto 1 th prvous scto gvs (). l ( k) h ( k) r ( k) + w ( k) () S S Th l S ca b stmatd from th stmatd basl vctor r. l ( k) h ( k) r ( k) (3) S Th masurmt of th tgrato Kalma fltr s gv by ls ( k) ls ( k) h ( k) r ( k) r ( k) + w S ( k) = h ( k) δ r ( k) + w ( k) S () whr δ r s rror of th stmatd basl vctor. Th cycl slp s dtctd by usg th followg qualty (). l ( k) l ( k) > ε () S S I th qualty (), a thrshold ε s slctd from th basl vctor rror ad masurmt os th carrr phas obsrvabls. Sc masurmt os s grally lss tha 1 mm ad th SDINS provds a vry accurat avgato soluto btw two coscutv pochs, t ca b xpctd that th cycl slp ca b ffctvly dtctd usg ().. Computr Smulato I ordr to vstgat ffctvss of th proposd algorthm, computr smulatos wr prformd. Error charactrstcs of a automotv grad IU ad L1 C/A cod GPS whch was gv Tabl 1 was usd for th smulato. Th Satllt Navgato Toolbox was usd to smulat moto of th GPS satllts ad grat th raw masurmts ad rrors. Th arragmt of th GPS atas s llustratd Fg.. A flght path for th smulato s show Fg. ad. Th vhcl s statoary for 3 scods ad acclratd

6 Atttud Dtrmato GPS/INS Itgrato Systm Dsg Usg Trpl Dffrc Tchqu toward th orth for 1 scods. Aftr that, t clmbs for 1 scods up toward.7 km alttud ad prforms two crcular flghts wth 1 bak agl. Roll (dg) - Tms ot-carlo Rsult RS Valu Tabl 1. Error Charactrstcs of IU ad GPS IU GPS Alttud (km) 1 Lattud (dg) 1 North (m/s). Roll (dg).1 1σ Error Sourc Gyro Bas ( /h) 3. Radom Walk ( / h). Accl Bas (mg) 1. Radom Walk (m/s/ h).1 Ioosphrc Advac (m). Troposphrc Dlay (m) 1. ultpath (Psudorag) (m) 1. ultpath (Carrr Phas) (m) Rcvr os (Psudorag) (m) 1. Rcvr os (Carrr Phas) (m) North (km) Flght Path Fg.. Flght path for smulato Logtud (dg) East (m/s).1. Ptch (dg) GPS Tm (s) Fg.. Fght path Alttud (m) Dow (m/s) Hadg (dg) 1 1 East (km) tms ot-carlo smulatos wr carrd out ad corrct tgr ambguty rsoluto was ttoally cludd to accss prformac of th proposd algorthm. At 1 scod (GPS tm), th tgr ambguty of th DDCP obsrvabls of basl 1 s corrctly rsolvd from - to -9 du to th cycl slp. At ths tm, th corrctly rsolvd tgr ambguty causs atttud rror th ADGPS rcvr as show Fg Ptch (dg) Hadg (dg) GPS Tm (s) Fg.. Atttud rror of ADGPS rcvr durg smulato axmum roll, ptch, ad hadg rrors ar 1., 1., ad.1 root-ma-squar (RS), rspctvly. I gral, atttud dtrmato ral-tm softwar of a ADGPS rcvr cluds a cycl slp dtcto algorthm ad a valdato rout for rsolvd tgr ambguty. It taks from fw scods to svral muts to dtct ad corrct th rror of th tgr ambguty rsoluto. I ths smulato, t s assumd that th ADGPS rcvr caot corrct th tgr ambguty rror for svral muts to valuat prformac of th proposd algorthm. Smulato rsults ar show Fg. 7 ad 8. Fgurs show rsults of th covtoal tghtly coupld GPS/INS tgrato, th ADGPS/INS tgrato wth DDCP obsrvabls, ad th ADGPS/INS tgrato wth TDCP obsrvabls proposd ths papr. I Fg. 7, th avgato rror s th root-sum-squar (RSS) valu calculatd from th RS rror of ach axs of th avgato fram. I Fg. 8, th IU bas stmato rror s ma valu of th RS rror of ach axs of th body fram. Each tgrato algorthm gvs smlar posto ad vlocty accuracy as Fg. 7. Th tghtly-coupld GPS/INS tgrato gvs larg atttud rror statoary stat sc th hadg rror gratly crass du to lack of obsrvablty. O th othr had, th ADGPS/INS tgratos provd mor accurat atttud rsult tha tghtly-coupld GPS/INS tgrato. Aftr cycl slp, th corrctly rsolvd tgr ambguty gvs rs to larg atttud rror th ADGPS/INS tgrato wth DDCP. Th proposd ADGPS/INS tgrato algorthm provds th most accurat atttud rsult sc t s ot affctd by th tgr ambguty rsoluto. I Fg. 8, t ca b obsrvd that th ADGPS/INS tgrato wth DDCP provds th bst bas stmato prformac bfor cycl slp ad th bas stmato rror crass wth tm aftr cycl slp. Th proposd tgrato algorthm gvs approxmatly two tms bttr bas stmato prformac tha th tghtly-coupld

7 Sag Ho Oh, Dog-Hwa Hwag, Chask Park ad Sag Jog L 1 Posto (m) 1 1 Bfor Cycl Slp GPS/INS(TC) ADGPS/INS(DDCP) ADGPS/INS(TDCP) Aftr Cycl Slp Vlocty (m/s) Atttud (dg) Fg. 9. Arragmt GPS atas for flght tst GPS Tm (s) GPS Tm (s) Fg. 7. Navgato rror Bfor Cycl Slp Aftr Cycl Slp Gyro Bas (dg/h) GPS/INS(TC) ADGPS/INS(DDCP) ADGPS/INS(TDCP) Accl Bas (mg) GPS Tm (s) Fg. 8. Bas stmato rror GPS/INS tgrato spt of cycl slp occurrc. 3. Flght Tst To valuat prformac of th proposd algorthm, a flght tst was prformd. A xprmtal stup was stalld a four-satd small arcraft. For atttud dtrmato, thr avato GPS atas (maufacturd by Ssor Systms Ic., S7-17-9) ar stup, wth.7m lgth of basl vctor as show Fg. 9. Fg. 1 shows stallato of A commrcal automotv grad IU whch was moutd o th logtudal axs of th fuslag. Th spcfcato of th IU s gv Tabl. A commrcal data acqusto systm was usd to rcord raw data of ssors (GPS, IU) th tst arcraft for post-msso data procssg ad prformac aalyss of th proposd algorthm. Th tst arcraft coductd svral typs of mauvrg as show Fg. 11. Total flght dstac was. km ad GPS Tm (s) Fg. 1. Istallato of IU Tabl. Spcfcato of IU Itm Dscrpto aufacturr Crossbow, USA odl DU-HX Grad Automotv Gyro Typ ES Gyro Bas ( /h) 3. Radom Walk ( / h). Accl Bas (mg) 1. Radom Walk (m/s/ h).1 Itrfac UART (RS-3) Output Rat (Hz) Sz (mm) Powr Cosumpto (W) < 3 flght tm 3 muts. Durg th tst, maxmum groud spd ad acclrato rachd km/h ad G, rspctvly. Aftr takoff, th tst arcraft wt up to m alttud for 1 scods wth 1 clmb agl to tr th mauvrg rgo. I th mauvrg rgo, th tst flght prformd sts of moto, bakg ad phugod. Durg th phugod moto, total alttud chag was approxmatly 1 m. Subsqutly, th tst arcraft dscdd to 3 m alttud ad coductd a straght ad lvl flght wth avrag 17 km/h groud spd for scods toward th vcty of arfld. Fally, t prformd 18 turg to approach th ruway ad ladd

8 Atttud Dtrmato GPS/INS Itgrato Systm Dsg Usg Trpl Dffrc Tchqu from th oppost drcto of takoff. Th tst flght profl s summarzd Tabl 3. atr Ata 8 11,88 111,8 111,8 111,8 111,8 111,88 11,8 11,71 Alttud (m) North (m) - - Fg. 11. Tst flght path East (m) Tabl 3. Typ of mauvrg durg flght tst Profl Typ of auvr GPS Tm (Durato) 1 ± ad ± Bakg 111,39 ~ 111,3 s (9 s) +/-1 ad +1/-1 111, ~ 111,99 s Phugod (7 s) 3 Straght ad Lvl Flght 111, ~ 111,899 s (37 s) Fg. 1 shows umbr of satllts vw at th mastr ata ad basls. It ca b s that satllt vsblty was good; maxmum umbr of satllts vw was 8. O th ruway, umbr of satllts vw was chagd frqutly du to sgal blockag by th hagar. Aftr takoff, th umbr of satllt vw was 8. Durg th profl 1, umbr of commo satllts vw of basls droppd to ad chagd to 7 durg th profl 3. Numbr of commo satllts vw of basls dcrasd tmporarly to wh th tst arcraft coductd a bakd tur to approach th ruway. Numbr of commo satllts vw of basls rcovrd rapdly to 8 durg ladg. Sc a hghly accurat avgato systm, whch ca b rgardd as a rfrc avgato systm for prformac valuato, could ot b stalld th tst arcraft, th proposd tgratd avgato systm was valuatd by obsrvg avgato output dffrcs btw th ADGPS rcvr ad ach tgrato algorthm. Th Basl 1 Basl 8 11,88 111,8 111,8 111,8 111,8 111,88 11,8 11, ,88 111,8 111,8 111,8 111,8 111,88 11,8 11,71 GPS Tm (s) Fg. 1. Numbr of satllts vw durg flght tst avgato output dffrcs btw th ADGPS rcvr ad tgrato algorthms ar gv Tabl. It ca b obsrvd that thr wr o sgfcat dffrcs avgato prformac. Roll ad ptch outputs wr compard wth thos of a vrtcal gyroscop. Th vrtcal gyroscop usd th valuato was th Arotc RVG-81E vrtcal gyroscop whch provds roll ad ptch agl at Hz wth ±. RS rror. Fg. 13 shows outputs of th avgato systms for ± ad ± roll moto. Th ADGPS rcvr doss ot provd accurat roll output du to corrctly rsolvd tgr ambguty durg - roll moto. I ths cas, th ADGPS/INS tgrato wth DDCP gvs maxmum. roll rror wth rspct to th output of th vrtcal gyroscop. O th othr had, th output of th proposd algorthm s ot affctd by tgr ambguty rsoluto rror. Outputs of th avgato systms for +/-1 ad +1/-1 ptch moto ar show Fg. 1. Th ADGPS/INS tgrato wth DDCP gvs maxmum 13. ptch rror wh th ADGPS rcvr provds corrct atttud. It ca b s that ptch rror of th proposd algorthm doss ot xcd.3. Fg. 1 shows th hadg output arly stag of th flght tst. It ca b obsrvd that th hadg rror of tghtly-coupld GPS/INS tgrato crass rapdly th statoary stat. Th rat of th hadg rror of th Tabl. Navgato output rsults Posto (m) Vlocty (m/s) GPS/INS (TC) ADGPS/INS (DDCP) ADGPS/INS (TDCP) a STD a STD a STD North East Dow North East Dow

9 Sag Ho Oh, Dog-Hwa Hwag, Chask Park ad Sag Jog L 3 Roll (dg) - - Vrtal Gyro ADGPS GPS/INS (TC) ADGPS/INS (DDCP) ADGPS/INS (TDCP) Itgr Ambguty Icorrctly Rsolvd proposd algorthm follows that of th ADGPS rcvr as sam cas as th ADGPS/INS tgrato wth DDCP. Th hadg outputs durg roll moto ar show Fg. 1. Dffrc of hadg output btw th tghtlycoupld GPS/INS tgrato ad th ADGPS rcvr crass gradually wh th tst arcraft prforms straght ad lvl flght from 111, to 111,3 scod (GPS tm). Th larg hadg rror ca b obsrvd th ADGPS/INS tgrato wth DDCP wh th ADGPS rcvr gvs corrct atttud output. It ca also b obsrvd that th proposd tgrato algorthm provds a accurat hadg output v ths harsh vromt ,3 111,3 111,3 111,38 111, 111, 111, 111, GPS Tm (s) Fg. 13. Outputs for ± ad ± roll moto ADGPS GPS/INS (TC) ADGPS/INS (DDCP) ADGPS/INS (TDCP) 1 Vrtcal Gyro ADGPS GPS/INS (TC) ADGPS/INS (DDCP) ADGPS/INS (TDCP) Hadg (dg) Ptch (dg) , 111,8 111,3 111,3 111, 111, 111, GPS Tm (dg) Fg. 1. Hadg output durg roll moto 111,37 111,39 111,1 111,3 111, 111,7 111,9 111,9 GPS Tm (s) Fg. 1. Output for +/-1 ad +1/-1 ptch moto (phugod) Hadg (dg) ADGPS GPS/INS (TC) ADGPS/INS (DDCP) ADGPS/INS (TDCP) 11,9 11,9 11,98 111, 111, 111,1 111,1 111,18111, GPS Tm (dg) Fg. 1. Hadg output arly stag of th flght tst proposd algorthm s rlatvly lowr tha that of th tghtly coupld GPS/INS tgrato v statoary stat. Aftr tal hadg moto, th hadg rsult of th. Cocludg Rmarks Ths papr has proposd a ADGPS/INS tgrato algorthm usg TDCP obsrvabls to avod prformac dgradato causd by th tgr ambguty rror ad th cycl slp. A w masurmt quato for th Kalma flr has b drvd for th TDCP obsrvabls. A cycl slp dtcto algorthm has b also cludd. Computr smulatos hav b prformd to valuat prformac of th proposd tgrato algorthm. Smulato rsults show that th proposd tgrato algorthm gvs a mor accurat avgato rsults v wh th ADGPS rcvr gvs rroous carrr phas obsrvabls du to cycl slp ad corrctly rsolvd tgr ambguty. A flght tst has b carrd out to dmostrat th ffctvss of th proposd algorthm wth a automotv grad IU ad multpl ata GPS rcvr. Th flght tst cludd roll ad ptch mauvrgs to valuat th prformac of th proposd algorthm a hgh dyamc vromt. Outputs of th proposd algorthm wr compard wth thos of a tghtly-coupld GPS/INS tgrato ad ADGPS/INS tgrato wth DDCP obsrvabls. Flght tst rsults show that th proposd tgrato algorthm gvs bttr avgato rsults tha othr tgrato algorthms wh th ADGPS rcvr

10 Atttud Dtrmato GPS/INS Itgrato Systm Dsg Usg Trpl Dffrc Tchqu provds rroous atttud outputs. Th proposd ADGPS/INS tgrato systm would also b wdly usd othr applcatos such as arcraft, mltary lad vhcl, ad spac vhcl, tc. Rfrcs [1] C. E. Coh, B. W. Parkso, Expadg th Prformac Evlop of GPS-basd Atttud Dtrmato, Procdgs of th ION GPS-91, pp 11-11, Albuqurqu, N, [] C. Park, I. Km, J. G. L., G. I. J, Effct Ambguty Rsoluto wth Costrats Equato, Procdgs of IEEE PLANS 9, Atlata, GO [3] J. Evas, S. Houck, G. cnutt, B. Parkso, Itgrato of a Chal GPS Rcvr for Automatc Cotrol Ito a Umad Arpla, Procdgs of th ION GPS-98, pp , Nashvll, TN, [] R. Wolf, G. W. H, B. Essfllr, E. Lohrt, A Itgratd Low Cost GPS/INS Atttud Dtrmato ad Posto Locato Systm, Procdgs of th ION GPS-9, pp , Kasas Cty, O, 199. [] H. C. Gldrloos, S. I. Shkh, B. W. Schppr, GPS Atttud Systm Itgratd wth a Irtal Systm for Spac Applcatos, Procdgs of th Dgtal Avocs Systms Cofrc, 1th DASC., AIAA/IEEE, vol : , [] D. Gbr-Egzabhr, D. R. Hayward, C. D. Powll CD, A Low-cost GPS/Irtal Atttud Hadg Rfrc Systm (AHRS) for Gral Avato Applcatos, Procdgs of th IEEE PLANS 98, pp 18-, [7] A. Lck, GPS Satllt Survyg, d d.:joh Wly & Sos, Ic., Nw York, 199. [8] B. Hofma-Wllhof, H. Lchtggr, J. Colls, Global Postog Systm: Thory ad Practc, d d.: Sprgr-Vrlag, W, 199. [9] C. Park, Atttud Dtrmato from GPS Carrr Phas asurmts: Ph.D. Thss: Soul Natoal Uvrsty, Fbruary [1] J. Wdl, O. str, R. oks, G. F. Trommr, Tm-Dffrcd Carrr Phas asurmts for Tghtly Coupld GPS/INS Itgrato, Procdgs of IEEE/ION PLANS, Apr. - 7,. [11] B. K. H. Soo, S. Schdg, H.-K. L, H.-K. L, H Durrat-Whyt, A approach to ad INS usg tmdffrcd GPS carrr phas (TDCP) masurmts, GPS Solutos, Vol., No., 8. [1] F. V. Graas, S.-W. L, Hgh-accuracy Dffrtal Postog for Satllt-basd Systms wthout usg Cod-phas asurmts, Joural of th Isttut of Navgato, vol., o., pp. -18, 199. [13]. art-nra, R. Lucas,. A. artz, Atttud Dtrmato wth GPS: Exprmtal Rsults, IEEE AES agaz, pp [1]. art-nra, R. Lucas, GPS Atttud Dtrmato of Sp Stablzd Satllts, Procdgs of th Isttut of Navgato GPS-9, Spt [1] I. Nsbo, P. Catr, GPS Atttud Dtrmato for Navgato, GPS World, 199. [1] F. V. Grass,. Brash, GPS Itrfromtrc Atttud ad Hadg dtrmato: Ital Flght Tst Rsults, Navgato: Joural of th ION, Vol. 38, No., 199. [17] J.-C. Juag, G.-S. Huag, Dvlopmt of GPS- Basd Atttud Dtrmato Algorthms, IEEE Tras. o AES. Vol. 33, No. 3, July [18] T. S. Bruggma, GPS L1 Carrr Phas Navgato Procssg: astr Thss: Quslad Uvrsty of Tchology,. [19] S. H. Oh, D.-H. Hwag, S. J. L, A Effct Itgrato Schm for th INS ad th Atttud Dtrmato GPS Rcvr, Procdgs of ION 7th Aual tg,, pp. 33-3, Albuqurqu, N, 1. [] C. Altmayr, Cycl Slp Dtcto ad Corrcto by as of Itgratd Systm, Procdgs of th Natoal Tchcal tg, pp. 13-1, Aahm, CA,. [1] D. Gosh-sk, I. Y. Bar-Itzhack, Ufd Approach to Irtal Navgato Systm Error odlg, Joural of Gudac, Cotrol, ad Dyamcs, vo1. 1, o. 3, pp. 8-3, 199. [] GPSoft, Satllt Navgato Toolbox Usr Gud: GPSoft LLC., Aths, OH, [3] G. Strag, K. Borr, Lar Algbra, Godsy, ad GPS: Wllsly-Cambrdg Prss, Wllsly, A, [] D Wlls, Gud to GPS Postog: Caada GPS Assocats, [] P. S. aybck, Stochastc odls, Estmato ad Cotrol: Acadmc Prss, Nw York, [] O. L. Colombo, U. V. Bhapkar, A. G. Evas, Irtal add Cycl-slp Dtcto/Corrcto for Prcs, Log-basl Kmatc GPS, Procdgs of th ION GPS-99, pp , Nashvll, TN, 199. Sag Ho Oh s a prcpal gr of th Itgratd Navgato Dvso of Hayag Navcom Co., Ltd., Kora. H rcvd Ph.D. dgr from Chugam Natoal Uvrsty. Hs rsarch trsts clud GPS/INS tgrato systm, Kalma fltrg, ad mltary applcato.

11 Sag Ho Oh, Dog-Hwa Hwag, Chask Park ad Sag Jog L Dog-Hwa Hwag s a profssor th Dpartmt of Elctrocs Egrg, Chugam Natoal Uvrsty, Kora. H rcvd hs B.S. dgr from Soul Natoal Uvrsty, Kora 198. H rcvd.s. ad Ph.D. dgr from Kora Advacd Isttut of Scc ad Tchology, Kora 1987 ad 1991, rspctvly. Hs rsarch trsts clud GNSS/INS tgratd avgato systm dsg ad GNSS applcatos. robust cotrol. Sag Jog L s a profssor th Dpartmt of Elctrocs Egrg, Chugam Natoal Uvrsty, Kora. H rcvd B.S.,.S. ad Ph.D. dgrs from Soul Natoal Uvrsty, Kora 1979, 1981, ad 1987, rspctvly. Hs rsarch trsts clud GNSS rcvr dsg ad Chask Park rcvd th B.S.,.S., ad Ph.D. dgrs Elctrcal Egrg from Soul Natoal Uvrsty 198, 198, ad 1997 rspctvly. H s currtly wth th Collg of Elctrcal ad Computr Egrg, Chugbuk Natoal Uvrsty, Chogju, Kora. Hs rsarch trsts clud GNSS, SDR, AJ, ITS ad WSN