Federated Information Mode-Matched Filters in ACC Environment

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1 Interntonl Journl o Control Federted Automton Inormton nd Mode-Mtched Systems vol. 3 Flters no. n pp. ACC 73-8 Envronment June 73 Federted Inormton Mode-Mtched Flters n ACC Envronment Yong-Shk Km nd Keum-Shk Hong* Abstrct: In ths pper trget trckng lgorthm or trckng mneuverng vehcles s presented. he overll lgorthm belongs to the ctegory o n nterctng multple-model (IMM) lgorthm used to detect multple trgets usng used normton rom multple sensors. Frst two knemtc models re derved: constnt velocty model or lner motons nd constnt-speed turn model or curvlner motons. Fpr the constnt-speed turn model nonlner normton lter s used n plce o the etended Klmn lter. Beng equvlent to the Klmn lter (KF) lgebrclly the normton lter s etended to -sensor dstrbuted dynmc systems. he model-mtched lter used n mult-sensor envronments tkes the orm o ederted nonlner normton lter. In mult-sensor envronments the normton-bsed lter s eser to decentrlze ntlze nd use thn KF-bsed lter. In ths pper the structurl etures nd normton shrng prncple o the ederted normton lter re dscussed. he perormnce o the suggested lgorthm usng Monte Crlo smulton under the two ptterns s evluted. Keywords: Inormton lter nterctng multple model etended Klmn lter ederted lter sensor uson.. IRODUCIO Recently the morty o vehcle compnes re developng vrous drver ssstnce systems to ncrese vehcle sety nd llevte drver worklod. he drver ssstnce systems nclude n dptve cruse control (ACC) lne-keepng support collson wrnng nd collson vodnce nd n sssted lne chnge. he eectveness o these drver ssstnt systems depends on the nterpretton o the normton rrvng rom sensors whch provde detls o the surroundng vehcle envronment nd o the drver-sssted vehcle tsel. In prtculr ll these systems rely on the detecton nd subsequent trckng o obects round the vehcle. Fg. shows the congurton o n ACC system. he ACC system conssts o drver nterce Mnuscrpt receved August 6 4; ccepted Jnury. Recommended by Edtor-n-Che Myung Jn Chung. hs work ws supported by the Mnstry o Scence nd echnology o Kore under progrm o the tonl Reserch Lbortory grnt number RL M J--3- nd Reserch Center or Logstcs Inormton echnology Pusn tonl Unversty. Yong-Shk Km s wth the Grdute School o Systems nd Inormton Engneerng Unversty o sukub -- ennod sukub Ibrk Jpn (e-ml: kyss@ roboken.cs.tsukub.c.p). Keum-Shk Hong s wth the School o Mechncl Engneerng Pusn tonl Unversty Sn 3 Jngeondong Gumeong-gu Busn Kore (e-ml: kshong@ pusn.c.kr). * Correspondng uthor. multsensors whch mesure the dstnce nd speed o precedng vehcle controller whch controls both the throttle nd brke nd ctutors [3]. hs blty to predct motons s dependent on how well the sensors o n ACC vehcle cn trck other vehcles. In order to trck other vehcles usng the obect normton obtned rom multple sensors trckng technques bsed on the Byesn pproch re usully used []. A number o multple-model technques to trck mneuverng trget hve been proposed n the lterture [94]. Generlly trget moton models cn be dvded nto two subctegores: the unorm moton model nd the mneuverng model. A mneuverng trget movng t constnt turn-rte nd speed s usully modeled s mneuverng model nd s clled coordnted turn model [7-94]. For pplcton to r trc control ed structure IMM lgorthm wth sngle constnt velocty model nd two coordnted turn models ws nlyzed [4]. Semerdev nd Mhylov [7] dscussed vrble- nd ed-structure ugmented IMM lgorthms wheres ed-structure lgorthm only ws dscussed n L nd Br-Shlom Mult-Sensors (Sensor Dt) Mult-Sensor Dt Fuson Reltve Velocty Reltve Dstnce IMM Algorthm (Federted Inormton Flter) Drver Interce (Swtch/LCD) ACC Vehcle Controller Brke Actutor Fg.. Congurton o the ACC system. hrottle Actutor

2 74 Yong-Shk Km nd Keum-Shk Hong [4] nd ws ppled to mneuverng shp trckng problem by ugmentng the turn rte error. Dt uson technques re used to employ number o sensors nd to use the normton rom ll o these sensors n centrl processor []. In dstrbuted system the processng o rw dt s perormed t locl sensors nd the results re trnsmtted to dt uson center or trck processng n order to obtn the nl results. As n lterntve method to mprove the trck uson the normton lter (IF) [6] whch s clmed to be the lgebrc equvlent to the Klmn lter (KF) ws developed. he IF s essentlly KF epressed n mesures o normton bout stte estmtes nd ther ssocted covrnces. In ddton decentrlzed IF (DIF) ws developed by [6]. Crlson [] nd Crlson nd Berrducc [3] consdered ederted structure s nother mens o dt uson. It s known tht the ederted KF (FKF) hs the dvntges o smplcty nd ult-tolernt cpblty over other decentrlzed lter technques. he contrbutons o ths pper re s ollows. Frst the IMM lgorthm s ppled to drvng lgorthm or n ACC vehcle n drvng on rod n multsensor envronments. Second two knemtc models or the possble nvgton ptterns o vehcle re derved: A constnt velocty model or lner motons nd constnt-speed turn model or curvlner motons. hrd ederted normton lter (FIF) or lner moton nd ederted nonlner normton lter (FIF) or curvlner moton were used n multsensor envronments. Fourth n ths study unlke the FKF there re no gn or nnovton covrnce mtrces nd the mmum dmenson o mtr to be nverted s the stte dmenson. Fth ths pper shows tht n normton shrng the FIF/FIF s equl to the centrlzed IF/IF (CIF/CIF). hs pper s orgnzed s ollows. In Secton stochstc hybrd system s ormulted nd two knemtc models re dscussed. In Secton 3 we ormulte n FIF or constnt velocty model nd n FIF or constnt-speed turn model n n IMM lgorthm n multsensor envronments. In Secton 4 we evlute the perormnce o these lters usng Monte Crlo smulton under the vrous ptterns. Secton concludes the pper.. PROBLEM FORMULAIO he vrous drvng ptterns o vehcle such s strght lne nd curve cut-n/out u-turn nd n nterchnge were descrbed n []. In ths secton ccordng to such drvng ptterns stochstc hybrd system n the orm o n IMM lgorthm to detect other vehcle usng mult-sensors s ormulted. Also two knemtc models representng the nlyzed drvng ptterns re ntroduced... Stochstc hybrd system Followng the work o L nd Br-shlom [4] stochstc hybrd system wth ddtve nose s consdered s ollows: ( = [ k ( k ) m( ] + g[ k ( k ) ν[ k m( ] m( ] wth nosy mesurements () z = h[ k m] + w [ k m] () n where k ( ) R s the stte vector ncludng the poston velocty nd yw rte o the vehcle t dscrete tme k m( s the sclr-vlued modl stte (drvng mode nde) t nstnt k whch s homogeneous Mrkov chn wth probbltes o trnston gven by Pm { ( k+ ) m} = π m m M (3) where P{} denotes the probblty nd M s the set o modl sttes tht s constnt velocty constnt ccelerton constnt ngulr rte turnng wth constnt rdus o curvture mong others. he consdered system s hybrd snce the dscrete event m( ppers n the system. In the drvng o ACC vehcle m( denotes the drvng mode o the precedng vehcle n eect durng the smplng perod endng t k tht s the tme perod ( tk tk]. he event or whch mode m s n eect t tme k s denoted s m { m = m }. (4) n zk ( ) R z s the vector-vlued nosy mesurement rom the sensor t tme k whch s mode-dependent. n ν[ k m] R ν s the mode-dependent process nose sequence wth men ν [ k m] nd n covrnce Q[k- m(]. w [ k m] R z s the mode-dependent mesurement nose sequence wth men wk [ mk ( )] nd covrnce R[k m(]. Fnlly g nd h re nonlner vector-vlued unctons... wo knemtc models he concept o usng nose-drven knemtc models comes rom the ct tht noses wth derent levels o vrnce cn represent derent motons. A model wth hgh vrnce nose cn cpture mneuverng motons whle model wth low vrnce nose represents unorm motons. he multple-models pproch ssumes tht model cn mmedtely cpture the comple system behvor better thn others. wo knemtc models or rectlner nd curvlner

3 Federted Inormton Mode-Mtched Flters n ACC Envronment 7 motons re now derved. Frst ssumng tht ccelertons n the stedy stte re qute smll (.e. brupt motons lke sudden stop or collson re not covered) lner ccelertons or decelertons cn be resonbly well covered by process noses wth the constnt velocty model. ht s the constnt velocty model plus zero-men nose wth n pproprte covrnce representng the mgntude o ccelerton cn hndle unorm motons on the rod. In dscretetme the constnt velocty model wth nose s gven by ( ) ( ) k = k + ν ( k ) () where s the smplng tme (.e.. sec n ths pper) ( s the stte vector ncludng the poston nd velocty o the precedng vehcle n the longtudnl (ξ ) nd lterl (η ) drectons t dscrete tme k tht s = [ ξ ξ η( η( ] (6) wth ξ nd η denotng the orthogonl coordntes o the horzontl plne; nd ν s zero-men Gussn whte nose representng the ccelertons wth n pproprte covrnce Q. I ν s the ccelerton ncrement durng the k th smplng perod the velocty durng ths perod s clculted by ν ( k ) nd the poston s ltered by ν ( k ) /. Second dscrete-tme model or turnng s derved rom contnuous-tme model or the coordnted turn moton [ p. 83]. A constnt speed turn s turn wth constnt yw rte long rod o constnt rdus o curvture. However the curvtures o ctul rods re not constnt. Hence rly smll nose s dded to constnt-speed turn model or the purpose o cpturng the vrton o the rod curvture. he nose n the model represents the modelng error such s the presence o ngulr ccelerton nd non-constnt rdus o curvture. For vehcle turnng wth constnt ngulr rte nd movng wth constnt speed (the mgntude o the velocty vector s constnt) the knemtc equtons n the ( ξ η ) plne re ξ( t) = ω η( t) η ( t) = ω ξ ( t) (7) where ξ () t s the norml (longtudnl) ccelerton nd η ( t) denotes the tngentl ccelerton nd ω s the constnt yw rte ( ω > mples counterclockwse turn). he tngentl component o the ccelerton s equl to the rte o chnge o the speed tht s η( t) = d η( t) / dt = d( ωξ( t)) / dt nd the norml component s dened s the squre o the speed n the tngentl drecton dvded by the rdus o the curvture o the pth tht s ξ () t = η ()/ t ξ() t =ω ξ ()/ t ξ() t where η ( t) = ωξ () t. he stte spce representton o (7) wth the stte vector dened by ( t) = [ ξ ( t) ξ ( t) η( t) η( t) ] becomes ( t) = A( t) (8) where ω A =. ω he stte trnsent mtr o the system Eq. (8) s gven by e At = sn ωt ω cosωt cosωt ω sn ωt cosωt ω sn ωt sn ωt. (9) ω cosωt It hs been remrked tht the ngulr rte ω n (7) s tme-vryng (9) would be no longer true. In the sequel ollowng the pproch n [ p. 466] nerly constnt-speed turn model n dscrete-tme domn s ntroduced. In ths pproch the model tsel s motvted rom (9) but the ngulr rte s llowed to vry. A new stte vector by ugmentng the ngulr rte ω to the stte vector o (7) s dened s ollows: = [ ξ ξ η( η( ω( ] () where superscrpt denotes the ugmented vlue. hen the nerly constnt-speed turn model s dened s ollows [ p. 467]: = snω( k ) ω( k ) cosω( k ) cosω( k ) ω( k ) snω( k ) cosω( k ) ω( k ) snω( k ) snω( k ) ω( k ) cosω( k ) ( ) k + ν ( k ). () Evdently both () nd () re specl orms o ().

4 76 Yong-Shk Km nd Keum-Shk Hong In ddton t s resonble to ssume tht the trnston between the drvng modes o n ACC vehcle hs the Mrkovn probblty governed by (3). 3. FIF FOR CURVILIEAR MOIOS he concept (structure) o n IMM lgorthm s reerred to n Br-Shlom et l. [ p.44] nd L nd Br-Shlom [4]. In ths study two models n the IMM lgorthm were used: one or rectlner motons nd the other or curvlner motons. he trckng procedure o the vehcle n rectlner moton usng () s crred out by n FIF. However n trckng curvlner motons whch requres the estmton o ω wth new ugmented model (8) n Secton n FIF s used. 3.. he decentrlzed normton lter We wll begn by revewng the CIF equtons [6] s mens o ntroducng notton nd or lter comprson wth the FIF equtons to be suggested n Secton 3.3. Denote the normton mtr s Y ( k = P ( k nd the normton stte s y( k = P ( k ( k respectvely. hen t the mster lter ssmlton equtons to produce the globl normton stte nd normton mtr wth ll the sensor dt re gven s ) me updte (predcton) y ( k k ) = L( k k ) y( k k ) Yk ( k ) = [ Fk ( ) Y F ( k) () + Qk ( )]. ) Mesurement updte y ( k ( k k ) + H ( R z( Y ( k = Y ( k k ) + H ( R H (3) where the normton predcton coecent L ( k k ) s gven by L ( k k ) = Y ( k k ) F( k ) Y ( k k ).(4) Remrk : It s preerble to employ n IF snce n mult-sensor structures the IF s eser to employ thn the KF [6]. he IF s more drect nd nturl method o delng wth mult-sensor dt uson problems thn the conventonl covrnce-bsed KF. he ttrctve etures o the IF re s ollows. Frst there re no gn or nnovton covrnce mtrces nd the mmum dmenson o mtr to be nverted s the stte dmenson. In mult-sensor systems the stte dmenson s generlly smller thn the observton dmenson. Hence t s preerble to employ the IF nd to nvert smller normton mtrces thn to use the KF nd nvert lrger nnovton covrnce mtrces. Second ntlzng the IF s much eser thn the KF. hs s becuse normton estmtes (mtr nd stte) re esly ntlzed to zero normton. hrd the IF s eser to dstrbute nd use thn s the KF. For locl estmte by th sensor the decentrlzed estmton equtons re gven by ) me updte (predcton) y ( k k ) = L ( k k ) y ( k k ) () ( k k ) = [ F( k ) Y ( k k ) F ( k ) + Q( k )]. Y ) Mesurement updte y ( k ( k k ) + H R z Y ( k = Y ( k k ) + H R H (6) where the normton predcton coecent L ( k k ) s gven by L ( k k ) = Y ( k k ) F( k ) Y ( k k ) (7) nd y ( k nd Y ( k denote the prtl normton stte nd ts normton mtr bsed only on the th sensor s own observton. hen the ssmlton equtons to produce globl normton estmtes re s ollows: ) Inormton stte y( k ( k k ) + ) Inormton mtr Y ( k = Y ( k k ) + = = { y ( k y { Y ( k Y ( k k )} (8) ( k k )}. (9) Remrk : As n lterntve lterng method o the CIF the DIF ws suggested []. In ths study however contrry to the ully connected decentrlzed estmton lgorthm o Mutmbr [6] there ws no communcton between sensors n the lter structure. In Chong et l. [6] nd Zhu et l. [8] Klmnlterng uson wth eedbck rom centrl processor n decentrlzed rchtecture s shown. It s composed o multple structures nvolvng mster lter t hgh level nd locl lters t low level. A locl lter relted to ech observton sensor estmtes the locl stte vrble. he mster lter combnes the estmtes trnsmtted rom the locl lters nd deduces the globlly optml stte estmte. A decentrlzed lter presented n ths pper employs the rchtecture proposed n Chong et l. [6] nd Zhu et l. [8]. As eplned erler the decentrlzed estmton lgorthm hs the sme orm s the

5 Federted Inormton Mode-Mtched Flters n ACC Envronment 77 centrlzed estmton lgorthm n rel-tme mplementton snce the mster model ncludes estmtes. In generl however n the event tht the system models t locl lters re ll the sme nd the observton model s decomposed to ech locl lter the lter structure s not optml. he estmte o locl lter s ected by the overlppng use o the system model. he end result s tht the computtonl lod cn be sgncntly reduced by ths decentrlzed technque. Although the decentrlzed lterng technque hs been recognzed s n eectve method o reducng the typclly hgh computtonl lod n stndrd centrlzed lterng ts potentlly hgh ult-tolernce perormnce cpblty hs not been wdely nvestgted. 3.. he FIF or the constnt velocty model An FKF cn be consdered specl orm o decentrlzed KF [3]. he ederted lter tkes the decentrlzed technque one step urther by employng the normton-shrng prncple. he ederted lter cn obtn the globlly optml estmte by pplyng the normton-shrng prncple to ech locl lter nd then usng the estmtes o these locl lters. For the systems o locl lter structure such s () nd (6) the globl normton mtr nd normton stte equtons re s ollows: Y ( k = Y ( k + + Y ( k () mster y ( k ( k. () mster = heorem : For the system () nd () nd the locl lter structure () nd (6) the soluton o the FIF () nd () s equl to the soluton o the CIF () nd (3) condtons ) - c) re stsed. ) he ntl vlue o the normton mtr the ntl normton stte nd the process nose covrnce re dstrbuted to locl lters s ollows: Y ( ) = Y ( ) = () γ y ( ) Y ( ) Y = ( ) y( ) = (3) Q = γ Q( =. (4) b) he normton stte nd ts normton mtr whch re clculted usng () nd () re dstrbuted to the locl lters s ollows: Y ( k = Ymster ( k = γ () y ( k mster ( k =. (6) c) An normton-shrng ctor s dened s ollows: = γ = γ. (7) Proo: we shll prove ths hypothess usng mthemtcl nducton. Frst we ssume tht t the k- tme epoch the normton stte nd the normton mtr o the mster lter s dentcl to those o the CIF s ollows: Y mster ( k k ) = Y ( k k ) = (8) y mster ( k k ) ( k k ) = (9) where ŷ nd Y re the normton stte nd ts normton mtr o the CIF respectvely. he used normton stte nd ts normton mtr re sent to the locl lters s ollows: Y( k k ) = Ymster (3) γ y ( k k ) = y mster ( k k ). (3) he predcton procedure t ech locl lter usng () nd (3) o the CIF s rewrtten s ollows: Y( k k ) = [ F( k){ Y} F ( k ) + Q ( k)] = [ Fk ( ){ Ymster ( k k)} F ( k ) + γ Qk ( )] γ [ ( ) ( ) ( ) ( )] = Fk Ymster k k F k + Qk γ [ ( ) ( ) ( ) ( )] = Fk Y k k F k + Qk γ = Y ( k k ) = (3) γ y ( k k ) = L( k k ) y ( k k ) = L( k k ) y mster( k k ) = L ( k k ) y ( k k ) ( k k ). (33) he mesurement updte o the normton mtr t ech locl lter cn be obtned s ollows: Y( k Y( k k ) H R H = Ymster ( k k ) + H R H. γ = + (34) Hence the ssmlton equton n the mster lter s epressed s ollows: Y mster ( k = Y ( k = Y γ = = mster ( k k ) + H R = H

6 78 Yong-Shk Km nd Keum-Shk Hong = Y ( k k ) + H ( R H (3) = Y ( k. = he mesurement updte o the normton stte t the locl lters cn be wrtten s y ( k ( k k ) + H ( R z. (36) hereore the ssmlton equton n the mster lter s gven by mster + + y = y ( k = = [ y ( k k ) + H R = ( k k ) + H R = y ( k. z ] z (37) Remrk 3: Accordng to () nd (4) o the suggested lterng scheme the system process normton s dstrbuted mong the mster nd locl lters n the proporton o γ. he ssue n the suggested lter desgn s to determne how the totl normton s to be dvded mong the ndvdul lters to cheve hgher ult-tolernce perormnce nd mprovement n throughput nd ecency. In the suggested lter contrry to the other decentrlzed lters the mster lter combnes only the ltered normton stte nd ts normton mtr o locl lters. hereore the number o vrbles trnsmtted rom the locl lters to the mster lter s dmnshed. he FIF structure s shown n Fg he FIF or the constnt-speed turn model Snce the model n () s nonlner the estmton o the stte equton () wll be perormed v the FIF. he nerly constnt-speed turn model o () cn be rewrtten s ollows: Reerence Sensor # Sensor # Sensor # z z z Fg.. FIF structure. d R ŷ γ Y mster mster LF# ŷ Y ŷ γ Y mster mster LF # ŷ Y Mster Flter (Fuson) ŷ γ Y mster mster ŷ mster LF# ŷ Y Y mster = [ ( k ) ω ( k )] + G( k ) ν ( k ) (38) where the uncton ( ) s known nd remns unchnged durng the estmton procedure. he nose trnston mtr G ( k ) s the sme orm s tht gven n (). o obtn the predcted stte ( k k ) the nonlner uncton n (38) s epnded n ylor seres round the ltest estmte ( k k ) wth terms up to rst order to yeld the rst-order EKF. he vector ylor seres epnson o (38) up to rst order s = [ ω( k )] + ( k) [ ( k) ( k k)] + HO + Gk ( ) ν ( k) where HO represents the hgher-order terms nd = ( k ) = [ sn ( ω k ) ( ω k ) cos ( ω k ) cos ( ω k ) ( ω k ) sn ( ω k ) ( ω) ] = ( k k) cos ( ω k ) ( ω k ) sn ( ω k ) sn ( ω k ) ( ω k ) cos ( ω k ) ω ω ω3 ω4 (39) ( k ) ( k ) ( k ) ( k ) (4) s the Jcobn o the vector evluted wth the ltest estmte o the stte. he prtl dervtves wth respect to ω re gven by ξ( k k )cos ω( k ) ω = ( ω k ) ξ( k k )sn ω( k ) ( ω k ) η( k k )sn ω( k ) ( ω k ) η( k k )( + cos ω( k ) ) ( ω k ) ω = ξ( k k )sn ω( k ) η( k k )cos ω( k ) (4) ξ( k k )sn ω( k ) ω3 = ( ω k ) ξ( k k )(cos ω( k ) ) ( ω k ) η( k k )cos ω( k ) + ( ω k )

7 Federted Inormton Mode-Mtched Flters n ACC Envronment 79 η( k k )sn ω( k ) ( ω k ) ω4 = ξ( k k )cos ω( k ) η( k k )sn ω( k ) where Q s the covrnce o the process nose n (38). For locl estmte by the th sensor the decentrlzed nonlner estmton equtons re gven by ) me updte (predcton) y ( k k ) = Y ( k k ) [ ( k k ) ω ( k )] Y ( k k ) = [ ( k ) Y ( k k ) ( k ) (4) + Q ( k )]. ) Mesurement updte y ( k ( k k ) + h R [ υ + h ( k k )] (43) Y ( k = Y ( k k ) + h R h where h = [ h ( ω ) ] s the = ( k k) Jcobn o the vector h evluted t the predcted stte ( k k ) nd υ ( s the nnovton gven by υ = z( h ( k ( k k ) w( ). hen the ssmlton equtons to produce globl normton estmtes re s ollows: ) Inormton stte y mster ( k = = y ( k (44) ) Inormton mtr Y ( k = Y ( k + + Y ( k. (4) mster Remrk 4: Ultmtely the locl lters n the FIF produce the sme results s the normton stte nd normton mtr o the DIF () nd (6). However the ssmlton equtons o the mster lter produce the globl optml vlue by usng only the updted vlue o ech locl lter. 4. SIMULAIOS As descrbed n ths secton we consdered stte estmton problem o vehcle n two dmensons. Smultons were eecuted to compre the perormnce o the IMM lgorthms usng centrlzed EKF () ederted EKF () centrlzed nonlner IF (CIF) nd n FIF respectvely or curvlner motons. he perormnce o these our lgorthms ws compred wth the use o Monte Crlo smultons. he mneuverng vehcle trectores were generted usng the vrous ptterns mentoned n []. wo knemtc models were used to trck the mneuverng vehcle: A constnt-velocty model or rectlner motons nd constnt-speed turn model or curvlner motons. We then compred the perormnce o the our derent IMM lgorthms wth these two models. 4.. he drvng scenros It ws ssumed tht the vehcle moves rectlnerly n the begnnng. he trget ntl postons nd veloctes were derently set or ech scenro. he sngle-trget trck o the mneuverng vehcle ws lso ssumed to hve been prevously ntlzed nd tht trck mntennce ws the gol o the IMM lgorthms. he results or the 4 selected scenros re presented ccordng to the drvng ptterns. ) Scenro or strght lne nd curve: he trget ntl postons nd veloctes were ( = m; y = m; y =8 m/s; ω = /s). Its trectory ws =8 m/s; constnt velocty between s nd 8 s wth speed o 8 m/s; turn wth constnt yw rte o ω =.4 /s between 8 s nd s; constnt velocty between s nd 36 s; turn wth constnt yw rte o ω =.4 /s between 36 s nd 437 s; constnt velocty between 437 s nd 6 s. ) Cut-n/out scenro: he trget ntl postons nd veloctes were ( = m; y = m; = 8 m/s; y = m/s; ω= /s). Its trectory ws strght lne between s nd 73 s wth speed o 8 m/s; turn wth constnt yw rte o ω =.6 /s between 73 s nd 8 s; constnt velocty between 8 s nd 4 s wth speed o 8 m/s; turn between 4 s nd 3 s wth yw rte o ω =.6 /s; strght lne between 3 s nd 49 s wth speed o 8 m/s; turn wth constnt yw rte o ω =.6 /s between 49 s nd 8 s; constnt velocty between 8 s nd 8 s wth speed o 8 m/s; turn between 8 s nd 89 s wth yw rte o ω =.6 /s nd strght lne between 89 s nd 6 s. ) U-turn scenro: he trget ntl postons nd veloctes were ( = m; y = m; =8 m/s; y = m/s; ω = /s). hs scenro ncluded nonmneuverng drvng mode durng scns rom s to 73 s wth speed o 8 m/s 8 turn lstng rom scn 73 s to 7 s wth yw rte o ω=9.3 /s nd non-mneuverng drvng mode rom scn 7 s to 78 s. v) Interchnge scenro: he trget ntl postons nd veloctes were ( = m y = m =8 m/s y = m/s ω = /s). hs scenro ncluded nonmneuverng drvng mode durng scns rom s to 44 s wth speed o 8 m/s 7 -turn lstng rom scn 44 s to 48 s wth yw rte o ω =. 4 /s nd

8 8 Yong-Shk Km nd Keum-Shk Hong non-mneuverng drvng mode rom scn 48 s to 64 s. he mneuverng vehcle speed ws 8 m/s. 4.. Prmeters used n the desgn he prmeters used n the desgn re lsted here. Subscrpts CV nd CS stnd or constnt velocty nd constnt speed turn respectvely. he ntl yw rte o ech nvgton scenro ws ω () =-.4 /s -.6 /s 9.3 /s nd.4 /s respectvely. he ntl vlues o normton mtr were s ollows: CV mode: Y ( ) = dg{..} CS mode: Y ( ) = dg{.. σ ω } where σ ω = (.) /s. he normton shrng ctors used or the two sensors were / γ = / γ =.. he ntl mode probblty vectors µ were chosen s ollows:. µ = Perormnce evluton nd nlyss he RMS error o ech stte component ws chosen s the mesure o perormnce. he comprson results o the IMM lgorthms usng n CIF nd n FIF respectvely or the curvlner moton re shown n Fgs. 3-4 where the RMS error n the poston nd the velocty re plotted by Fgs nd 4. Fgs nd show comprsons o the true poston nd the estmted ones wth the the the CIF nd the FIF respectvely. he results presented here re bsed on Monte Crlo runs. It s evdent tht the two lgorthms hve lmost equl poston nd velocty estmton ccurcy or ll scenros. hs conrms the lgebrc equvlence whch s mthemtclly proven nd estblshed n the dervton o the normton lter rom the Klmn lter. hese conclusons were conrmed by the RMS error plots presented n Fgs. 3-4 respectvely. Longtudnl poston (m) rue trectory CIF FIF RMS poston error (m) CIF FIF me (s) Fg. 4. Comprson o poston errors n the cse o strght lnes nd curves. RMS velocty error (m/s) 3 CIF FIF me (s) Fg.. Comprson o velocty errors n the cse o strght lnes nd curves. Longtudnl poston (m) rue trectory CIF FIF Lternl poston (m) Fg. 6. Comprson o poston estmtes n the cse o cut-n/out. RMS poston error (m) CIF FIF Lternl poston (m) Fg. 3. Comprson o poston estmtes n the cse o strght lnes nd curves.. me (s) Fg. 7. Comprson o poston errors n the cse o cut-n/out.

9 Federted Inormton Mode-Mtched Flters n ACC Envronment 8 RMS velocty error (m/s) 3 CIF FIF me (s) Fg. 8. Comprson o velocty errors n the cse o cut-n/out. Longtudnl poston (m) rue trectory CIF FIF Lternl poston (m) Fg.. Comprson o poston estmtes n the cse o nterchnge. Longtudnl poston (m) 3 3 rue trectory CIF FIF Lternl poston (m) Fg. 9. Comprson o poston estmtes n the cse o u-turn. RMS poston error (m) CIF FIF me (s) Fg. 3. Comprson o poston errors n the cse o nterchnge. RMS poston error (m) CIF FIF RMS velocty error (m/s) 3 3 CIF FIF me (s) Fg.. Comprson o poston errors n the cse o u-turn. RMS velocty error (m/s) CIF FIF me (s) Fg.. Comprson o velocty errors n the cse o u-turn me (s) Fg. 4. Comprson o velocty errors n the cse o nterchnge.. COCLUSIOS In ths pper trckng lgorthm to trck mneuverng vehcle on rod n n dptve cruse control envronment ws desgned. he trckng lgorthm detects nd trcks other mneuverng vehcle on rod by two knemtc models derved n ths pper. For the constnt-speed turn model ederted nonlner normton lter ws used n plce o the etended Klmn lter n mult-sensor systems. Besdes t ws mthemtclly shown tht n vew o the normton shrng ctor the ederted normton lter s equl to the centrlzed normton lter. Comprson nd nlyss o the

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