Multiple Target Tracking With a 2-D Radar Using the JPDAF Algorithm and Combined Motion Model

Transcription

1 Mulple Targe Trang Wh a -D Radar Ung he JPDAF Algorhm and Combned Moon Model Alabar Gor Daronolae, Mohammad Bagher Menha, Al Doomohammad ABSTRACT Mulple arge rang (MTT aen no aoun a one of he mo mporan op n rang arge wh radar. In h paper, he MTT problem ued for emang he poon of mulple arge when a -D radar employed o gaher meauremen. To do o, he Jon Probabl Daa Aoaon Fler (JPDAF approah appled o rang he poon of mulple arge. To haraerze he moon of eah arge, wo model are ued. Fr, a mple near onan veloy model ondered and hen o enhane he rang performane, peally, when arge mae maneuverng movemen a varable veloy model propoed. In addon, a ombned model alo propoed o mgae he maneuverng movemen beer. Th new model gve an advanage o explore he movemen of he maneuverng obe whh ommon n many rang problem. Smulaon reul how he uperory of he new moon model and effe n he rang performane of mulple arge. KEYWORDS Mulple arge rang, JPDAF algorhm, daa aoaon, maneuverng movemen. ITRODUCTIO The problem of emang he poon of a arge n phyal envronmen an mporan problem n he mlary feld. Indeed, beaue of he nrn error embedded n he daa olleed by meauremen enor, here range and bearng fnder, ome operaon hould be ondued on he rude daa o reah more aurae nowledge abou he poon of a arge. owaday, varou algorhm are propoed o modfy he auray of loalzaon algorhm. In he feld of arge rang, he Kalman fler approah [] play a gnfan role. Th approah ue a uggeed model derbng he arge movemen and he meauremen olleed by a -D radar and, hen, provde an aurae emaon of he arge poon. ow, he Kalman fler grealy ued n many rang problem []. Alhough h fler ha provded a general raegy o olve loalzaon problem, uffer from ome weanee. The mo gnfan problem of he Kalman mehod weane o he ae emaon of many real yem n he preene of evere nonlneare. Aually, n general nonlnear yem, he poeror probably deny funon of ae gven meauremen anno be preened by a Gauan deny funon and, herefore, he Kalman mehod may reul n unafaory repone. Moreover, he Kalman fler very enve o he nal ondon of ae. Aordngly, Kalman baed mehod do no provde aurae reul n many ommon global loalzaon problem. More reenly, parle fler have been nrodued o emae non-gauan, non-lnear dynam proee [5].The ey dea of parle fler o repreen he ae by e of ample (or parle. The maor advanage of h ehnque ha an repreen mul-modal ae dene, a propery whh ha been hown o nreae he robune of he underlyng ae emaon proe. Moreover, parle fler are le enve o he nal value of ae han he Kalman mehod. Th problem very onderable n applaon n whh he nal value of ae are no nown uh a global loalzaon problem. The aforemenoned power of parle fler n he ae emaon of nonlnear yem ha made hem be appled wh grea ue o dfferen ae emaon problem nludng vual rang [6], moble robo loalzaon [7], onrol and hedulng [8], arge rang [9] and dynam probabl newor []. Mulple arge rang anoher arave ue n he feld of aeropae engneerng. Th problem an be Correpondng Auhor, Al A.Gor wh he Deparmen of Eleral And Compuer Engneerng, MMaer Unvery, Hamlon, Canada (e-mal: gorda@mmaer.a. M. B. Menha wh he Deparmen of Eleral Engneerng, Amrabr Unvery of Tehnology, Tehran, Iran (e-mal:menha@au.a.r. Al Doomohammad wh he Deparmen of Eleral Engneerng, Amrabr Unvery of Tehnology, Tehran, Iran. Amrabr / MISC / Vol. 4 / o. / Fall 9 43

2 nrodued a rang arge poon by daa reeved from a -D radar. Alhough h problem appear mlar o he ommon loalzaon algorhm n whh he dynamal model of he arge nown, he radonal approahe anno be ued beaue he radar doe no have ae o he nernal enor daa of eah arge ued n loalzaon algorhm o pred he fuure poon of he arge. Moreover, ung he parle fler o emae he poon of all arge, nown a ombned ae pae, no raable beaue he omplexy of h approah grow exponenally wh he number of obe beng raed. To reolve he problem of he la of nernal enor daa, varou moon model have been propoed. The mple model propoed he near onan veloy model. Th model ha been grealy ued n many rang applaon uh a arraf rang [], people rang [] and ome oher arge rang applaon [3]. Bede h model, ome oher ruure have been propoed uable n ome oher peal applaon. ear onan aeleraon model a modfed veron of he prevou model whh an be appled o rang maneuverng obe [4]. Alo, nerave mulple model (IMM fler repreen anoher ool o ra he movemen of hghly maneuverng obe where he former propoed approahe are no relable [5]. Reenly, many raege have been alo propoed n he leraure o addre he dffule aoaed wh mularge rang. The ey dea of he leraure o emae eah obe poon eparaely. To do o, he meauremen hould be agned o eah arge. Therefore, daa aoaon ha been nrodued o relae eah arge o aoaed meauremen. By ombnng daa aoaon onep wh flerng and ae emaon algorhm, he mulple arge rang ue an be deal wh eaer han applyng ae emaon proedure o he ombned ae pae model. Among he varou mehod, Jon Probabl Daa Aoaon Fler (JPDAF algorhm aen no aoun a one of he mo arave approahe. The radonal JPDAF [6] ue Exended Kalman Flerng (EKF on wh he daa aoaon o emae ae of mulple obe. However, he performane of he algorhm degrade a he nonlneare beome more evere. To enhane he performane of he JPDAF agan he evere nonlneary of dynamal and enor model, reenly, raege have been propoed o ombne he JPDAF wh parle ehnque nown a Mone Carlo JPDAF, o aommodae general nonlnear and non-gauan model [7]. The newer veron of he above-menoned algorhm ue an approah named a of gang o redue he ompuaonal o whh one of he mo erou problem n onlne rang algorhm [7]. Bede he Mone Carlo JPDAF algorhm, ome oher mehod have been propoed n he leraure. In [7], a omprehenve urvey ha been preened on he mo well-nown algorhm applable n he feld of mulple arge rang. In h paper, he Mone Carlo JPDAF algorhm ued for he mulple arge rang problem. A a modfaon o he reen leraure, dfferen moon model are eed o evaluae he performane of rang. Bede he radonal near onan veloy model, we wll e he effeny of he oher wo model a well n he paper. Fr, a varable veloy model ued o haraerze he movemen of arge. Then, we propoe a ombned approah n whh he moon model a lnear ombnaon of onan and varable veloy model. In addon, a mple algorhm repreened o deermne he wegh agned o eah moon model. I hown ha ome nformaon of he JPDAF algorhm an be ued o deermne he aforemenoned faor. The goal, here, o ufy he effeny of he JPDAF algorhm ung ombned model ompared wh eah ndvdual model. The re of h paper organzed a follow. Seon II derbe he Mone Carlo JPDAF algorhm for mulple arge rang. The JPDAF for mulple arge rang he op of eon III. In h eon, we wll preen how he moon of arge n a real envronmen an be derbed. To do o, near onan veloy and aeleraon model are nrodued o derbe he movemen of moble arge. Then, wll be hown how daa reeved from a -D radar an be ued for rang movng obe. In eon IV, varou mulaon reul are preened o uppor he performane of he algorhm. In h eon, he maneuverng movemen of he arge alo ondered. The reul ealy approve he uable performane of he JPDAF algorhm n rang he moon of moble arge n he mulaed envronmen. Fnally, eon V onlude he paper.. THE JPDAF ALGORITHM FOR MULTIPLE TARGET TRACKIG Th eon preen he JPDAF algorhm ondered a he mo ueful and wdely appled raegy for mul-arge rang under daa aoaon unerany. The Mone Carlo veron of he JPDAF algorhm ue ommon parle fler approah o emae he poeror deny funon of ae gven meauremen p ( x y :. ow, onder he problem of rang obe. x denoe he ae of hee obe a me where,,.., he he arge number. Furhermore, he movemen of eah arge an be ondered by a general nonlnear ae pae model a follow: x f ( x + v + ` y g( x + w ( 44 Amrabr / MISC / Vol. 4 / o. / Fall 9

3 where v and w are whe noe wh he ovarane mare Q and R, repevely. Alo, n he above equaon, f and g are he general nonlnear funon repreenng he dynam behavor of he arge and he enor model. The JPDAF algorhm reurvely updae he margnal flerng drbuon for eah arge p ( x y :,,,.., nead of ompung he on flerng drbuon p ( X y :, X x,..., x. To ompue he above drbuon funon, ome pon have o be aen no onderaon a follow: - I very mporan o now how o agn eah arge ae o a meauremen. Indeed, he enor provde a e of meauremen a eah me ep. The oure of hee meauremen an be he arge or he durbane alo nown a luer. Therefore, a peal proedure needed o agn eah arge o aoaed meauremen. Th proedure degnaed a Daa Aoaon ondered a he ey age of he JPDAF algorhm whh derbed n he nex eon. - Beaue he JPDAF algorhm reurvely updae he emaed ae, a reurve oluon hould be appled o updae ae a eah ample me. Tradonally, Kalman flerng ha been a rong ool for reurvely emang ae of he arge n mul-arge rang enaro. Reenly, parle fler on wh he daa aoaon raegy have provded beer emaon, peally, when he enor model nonlnear. Wh regard o he above pon, he followng eon derbe how parle fler paralleled wh he daa aoaon onep an deal wh he mul-arge rang problem. A. The Parle Fler For Onlne Sae Emaon Conder he problem of onlne ae emaon a ompung he poeror probably deny funon p ( x y :. To provde a reurve formulaon for ompung he above deny funon, he followng age are preened: - Predon age: he predon ep done ndependenly for eah arge a: x y x x x y dx ( : x - Updae age: he updae ep an be derbed a follow: p ( x y : y x x y: (3 The parle fler emae he probably deny funon x y : by amplng from a pef drbuon funon a follow: (4 x y w~ δ ( x x : Amrabr / MISC / Vol. 4 / o. / Fall 9 where,,..., he ample number, w ~ he normalzed mporane wegh and δ he dela dra funon. In he above equaon, he ae x ampled from he propoal deny funon q( x x, y :. By ubung he above equaon n ( and he fa ha he ae are drawn from he propoal funon q, he reurve equaon for he predon ep an be wren a follow:, x x (5 α α, q( x x, y: where x, he -h ample of x.ow, by ung (3 he updae age an be expreed a he reurve adumen of mporane wegh a follow: w α y x (6 By repeang he above proedure a eah me ep he equenal mporane amplng (SIS for onlne ae emaon preened below: The SIS Algorhm. For : nalze he ae x, predon weghα and mporane wegh w.. A eah me ep proeed he followng age: 3. Sample he ae from he propoal deny funon a follow: x ~ q( x x, y : (7 4. Updae predon wegh ung (5. 5. Updae mporane wegh ung (6. 6. ormalze mporane wegh a follow: w (8 w~ w 7. Se + and go o ep 3. In he above, for mply, he ndex,, ha been elmnaed. The man falure of he SIS algorhm he degeneray problem. Tha, afer a few eraon one of he normalzed mporane rao end o, whle he remanng rao go o zero. Th problem aue he varane of he mporane wegh o nreae ohaally over me [9]. To avod he degeneray of he SIS algorhm, a eleon (re-amplng age may be ued o elmnae ample wh low mporane wegh and mulply ample wh hgh mporane wegh. There are many approahe o mplemen re-amplng age [9]. Among hem, he redual re-amplng provde a raghforward raegy o remedy he degeneray problem n he SIS algorhm. The redual reamplng on wh he SIS algorhm an be preened a 45

4 he SIR algorhm a follow: The SIR Algorhm. For : nalze he ae x, predon weghα and mporane wegh w.. A eah me ep, do he followng: 3. perform he SIS algorhm o ample ae x and ompue normalzed mporane wegh w ~. 4. Che he re-amplng reron: a. If eff > hreh follow SIS age Ele b. Implemen redual-reamplng approah o mulply/uppre ae wh hgh/low wegh.. Se new normalzed mporane wegh a w~. 5. Se + and go o ep 3. In above, eff a reron heng he degeneray of algorhm whh an be wren a: (9 eff ( w 46 In [9], a omprehenve duon ha been made on how o mplemen he redual re-amplng age. Bede he SIR algorhm, ome oher approahe have been propoed n he leraure o enhane he qualy of he SIR algorhm uh a Marov Chan Mone Carlo parle fler, Hybrd SIR and auxlary parle fler []. Alhough hee mehod are more aurae han he ommon SIR algorhm, ome oher problem uh a he ompuaonal o are he mo gnfan reaon ha, n many real me applaon uh a onlne rang, he radonal SIR algorhm appled o reurve ae emaon. B. Daa Aoaon In he la eon, he SIR algorhm wa preened for onlne ae emaon. However, he maor problem of he propoed algorhm how o ompue he lelhood funon p ( y x. To do o, an aoaon hould be made beween he meauremen and arge. Brefly, he aoaon an be aegorzed no arge o meauremen and meauremen o arge: Defnon : A arge o meauremen aoaon denoed a ( T M defend by ~ λ { ~ r, M, M T } where ~ r ~ r,..., ~ r K wh: If he -h arge undeeed r If he -h arge ha generaed he -h meauremen where,,...,m and m he number of meauremen a eah me ep and,,..,k whh K he number of arge. Defnon : n a mlar fahon, he meauremen o arge aoaon ( M T defned by λ { r, M, M T } where r r,..., rm and r gven below. If he -h meauremen no aoaed wh any arge r If he -h arge In he boh above equaon, aoaed wh he -h arge meauremen due o arge and m T he number of m he number of luer. I very eay o how ha boh defnon are equvalen, however he dmenon of he arge o meauremen aoaon le han ha of he meauremen o arge aoaon. Therefore, n h paper, he arge o meauremen aoaon ued. ow, he lelhood funon for eah arge an be wren a: m ( y x β + β y x In he above equaon, β defned a he probably ha he h meauremen agned o he h arge. Hene, β wren a: β p ( ~ r y : ( Before elaborang more on he above equaon, he followng defnon needed. Defnon 3: We defne he e Λ ~ a all poble agnmen whh an be made beween meauremen and arge. For example, onder a 3-arge rang problem. Aume ha followng aoaon are reognzed beween arge and meauremen: r, r 3, r 3 ow, he e Λ ~ an be led a gven n able I. TABLE ALL POSSIBLE ASSOCIATIOS BETWEE TARGETS AD MEASUREMETS FOR EXAMPLE TARGET TARGET TARGET Amrabr / MISC / Vol. 4 / o. / Fall 9

5 Here, mean ha he arge ha no been deeed. By ung he above defnon, Eq.( an be rewren a: ~ p ( ~ r y : ~ ~ Λ ~ r p y, ( λ ( λ : The rgh de of he above equaon wren a follow: ~ ~ ~ y y:, λ y:, λ λ y: y: (3 ~ ~ y y:, λ λ where we have ued he fa ha he aoaon veor ~ λ no dependen on he hory of meauremen. Eah of he deny funon n he rgh de of he above equaon aed a follow: - ~ λ The above deny funon beome ~ p ( λ ( ~ ( ~ p r, M, M T (4 p r M, M M M T The ompuaon of eah deny funon n he rgh de of he above equaon raghforward a fully dued n [7]. ~ - y y :, λ Beaue he arge are uppoed o be ndependen, he above deny funon an be wren a follow: ~ M r (5 y y, λ V p y y T ( max ( : : Γ where Vmax he maxmum volume whh n he lne of gh of he enor, Γ he e of all vald r meauremen o arge aoaon and p ( y y : he predve lelhood for he r h arge. ow, onder r. The predve lelhood for he -h arge an be formulaed a: p ( y y y x x y dx (6 : : Boh deny funon n he rgh hand de of he above equaon are emaed ung he ample drawn from he propoed deny funon. However, he man problem how o deermne he aoaon beween meauremen ( y and arge. To do o, a of gang mehod propoed n he followng algorhm:. Conder x, Sof Gang,,,,, a ample drawn from he propoed deny funon.. For :m, do he followng ep for he -h meauremen. 3. For :K, do he followng ep: 4. Compue µ a follow: µ ~α g( x,, where g he enor model and wegh a preened n he SIR algorhm. 5. Compue σ a: σ R +, ~ α he normalzed (, (, g( x µ g( x ~ α µ T (7 (8 6. Compue he dane o he -h arge by: T (9 d ( y µ ( σ ( y µ 7. If d < ε, agn he -h meauremen o he -h arge. I eay o how ha he predve lelhood gven n (6 an be approxmaed by: p ( y y : ( µ, σ ( µ, σ a normal drbuon wh mean where ( µ and he ovarane marx σ. By ompung he predve lelhood, he lelhood deny funon ealy emaed. In he nex ubeon, he JPDAF algorhm preened for mul-arge rang problem. C. The JPDAF Algorhm The mahemaal foundaon of he JPDAF algorhm were dued n he la eon. ow, we are ready o propoe he full JPDAF algorhm for he problem of mulple arge rang. To do o, eah arge haraerzed by he dynamal model nrodued n (. The JPDAF algorhm preened below. The JPDAF Algorhm x,. Inalzaon: nalze ae for eah arge a where,,.., and,,...,k, he predve mporane wegh α and mporane wegh w,,.. A eah me ep, proeed a: 3. For :, do he followng ep. 4. For :K, ondu he followng proedure for eah arge. 5. Sample he new ae from he propoed deny funon a follow: (, x x, y, x ~ q : ( Amrabr / MISC / Vol. 4 / o. / Fall 9 47

6 6. Updae he predve mporane wegh a: (,,,, p x x α α,, q x x, y ( : ( Then, normalze he predve mporane wegh. 7. Ue he ampled ae and new obervaon, y, o onue he aoaon veor for eah arge a R { m, y } where ( refer o he aoaon beween he -h arge and he -h meauremen. To do o, ue he of gang proedure derbed n he prevou ubeon. 8. Conue all poble aoaon for he arge and eablh he e Γ ~ a derbed n defnon Ue (3 and ompue β for eah meauremen where l,,..,m and m he number of meauremen.. Ue ( o ompue he lelhood rao for eah arge a (, p y x.. Compue he mporane wegh for eah arge a:,, (, w α p y x (3 Then, normalze he mporane wegh a follow:, w (4 w~,, w. Proeed wh he re-amplng age. To do o, mplemen he mlar proedure derbed n he SIR algorhm. Aferward, for eah arge he reampled ae an be preened a follow: {,, m (5 w~ (,, x }, x 3. Se he me a + and go o ep 3. In he nex eon, he JPDAF algorhm for mulple ae an be ued for mulple arge rang. In addon, ome well-nown moon model are hen preened o ra he moon of a moble arge. 3. THE JPDAF ALGORITHM FOR MULTIPLE TARGET TRACKIG WITH A -D RADAR ow, we wan o ue he JPDAF algorhm for he problem of mulple arge rang wh a -D radar. To do o, Radar yem ue modulaed waveform and dreve anenna o ranm Eleromagne energy no a pef volume n pae o earh for arge. Obe (arge whn a earh volume wll refle poron of h energy (radar reurn or ehoe ba o he radar. Thee ehoe are hen proeed by he radar reever o exra arge nformaon uh a range, veloy, angular poon and oher arge denfyng haraer. To emae he poon of eah arge by daa olleed va a -D radar, we need a moon model o derbe he behavor of he arge. The mple mehod near onan veloy model, preened a: X + AX + Bu (6 X [ x x y y ] where he yem marxe are defned a: T A T T (7 T B T T where T refer o he ample me. In he above equaon, u whe noe wh zero mean and an arbrary ovarane marx. Beaue he model ondered a a near onan veloy, he ovarane of he addve noe anno be o large. Indeed, h model uable for he movemen of arge wh a onan veloy, whh ommon n many applaon uh a ommeral arraf pah rang [8] and people rang []. The movemen of a arge an be modeled by he above model n many ondon. However, n ome peal ae, he arge movemen anno be haraerzed by a mple near onan veloy model. For example, n many problem, arge may ondu a maneuverng movemen. Therefore, he moon raeory of he arge o omplex ha he elemenary onan veloy model wll no reul n afaory repone. To overome h problem, he varable veloy model propoed. The ey dea behnd h model o ue he arge aeleraon a anoher ae varable whh hould be emaed a well a ompung he veloy and poon of he arge. In oher word, he new ae veor defned a, X x y [ x x a y y a ], where a and are he arge aeleraon along wh he x and y ax, repevely. ow, he near onan aeleraon model an be wren a wha menoned n (7, exep for he yem marxe are defned a follow [4]: x a y 48 Amrabr / MISC / Vol. 4 / o. / Fall 9

7 T a T a a A a ex T (8 ex T b b b B b b3 b3 where parameer of he above equaon are defned a follow: b3 ( ex T a b3, b ( T a, a b (9 T b a In he above equaon, a onan value. The above model an be ued o ra he moon raeory of a maneuverng obe. Moreover, ombnng he reul of he propoed model may enhane he performane of rang. Th dea an be preened a follow: ~ ~ a ~ v X αx + ( α X (3 where X ~ a and X ~ are he emaon of he near onan v aeleraon and near onan veloy model, repevely, and α a number beween and. Bede he above approahe, ome oher mehod have been propoed o deal wh rang of maneuverng obe uh a IMM fler [5] whh very applable n mlary heme where arraf hange her aeleraon uddenly. 4. SIMULATIO RESULTS To evaluae he effeny of he JPDAF algorhm, a 3- arge rang enaro ondered. To prepare he enaro and mplemen mulaon, he parameer are preened for arge ruure and mulaon envronmen a TABLE II. ow, he followng expermen are ondued o evaluae he performane of he JPDAF algorhm n varou uaon. TABLE II SIMULATIO PARAMETERS Parameer Derpon n umber of enor R The maxmum range of max mulaon envronmen Q The ovarane marx of he enor addve noe Sample me for runnng mulaon Smulaon maxmum max runnng me A. Loal Trang for on-maneuverng Movemen The nal poon of he radar e a 5,5, π. 8,4,π, Alo, he poon of arge are ondered a [ ],3, π π 3,,9,, 4 repevely. To run he mulaon, ample me,, and mulaon maxmum runnng me, max, are e a and, repevely. Fg. how he raeore generaed for eah arge. The radar provde he dane from he a obe, wall or obale, and he dynam arge. The radar daa an be repreened a a par of [ r,φ] where φ he angle beween he enor and he referene oordnaon whoe relaonhp wh he arge poon o o [ x x + ( y y ] ( r o (3 y y φ aran o x x o o where [ x, y ] denoe he poon of he enor. Alo, he ovarane of he enor noe uppoed o be:. 5 4 (3 ow, he JPDAF framewor ued o ra he raeory of eah arge. In h mulaon, he luer are aumed o be unformly drbued over he oal volume of he envronmen. To apply he near onan veloy model a derbed n (7, he nal value of he veloy hoen unformly beween and - a follow: x u(, y u(, (33 where u(. he unform drbuon funon. Fg. preen he mulaon reul ung he JPDAF algorhm Amrabr / MISC / Vol. 4 / o. / Fall 9 49

8 wh 5 parle for eah arge rang. Smulaon reul ufy he ably of he JPDAF algorhm n modfyng he nrn error embedded n he daa olleed from he meauremen enor. Fg.. The generaed raeory for arge 5. COCLUSIOS In h paper, he JPDAF algorhm wa fully developed for mulple arge rang. Afer nrodung he mahemaal ba of he JPDAF algorhm, we howed how o apply he JPDAF algorhm o he problem of mulple arge rang; h led o hree dfferen model propoed n he paper. ear onan veloy model, near onan aeleraon model were fr derbed and, hen, a ombnaon of he wo former approahe wa preened o enhane he rang auray. Aferward, mulaon reul were arred ou n wo dfferen enaro. Fr, rang he nonmaneuverng moon of arge wa explored. Laer, he JPDAF algorhm wa eed on rang he moon of arge wh maneuverng movemen. Smulaon reul howed ha he ombned approah provde beer performane han he oher wo propoed raege. Fg.. The emaed raeory ung he JPDAF algorhm B. Loal Trang for Maneuverng Movemen ow, onder a maneuverng movemen for eah arge. Therefore, a varable veloy model ondered for eah arge movemen. Fg. 3 how he generaed raeory for eah arge. ow, we apply he JPDAF algorhm for rang eah arge poon. To do o, 3 approahe are mplemened. ear onan veloy model, near onan aeleraon model and ombned model derbed n he la eon are ued o emae he ae of he arge. Fg. 4-6 how he reul for eah arge eparaely. To ompare he effeny of eah raegy, he obaned error preened for eah approah n able III, IV where he followng reron ued for emang he error: max z ~ z ( e z max, z, { x y } (3 The reul how beer performane of he ombned mehod ompared wh he oher approahe. Fg. 3. The generaed raeory for maneuverng arge Fg. 4. The emaed raeory for arge TABLE III THE ERROR FOR ESTIMATIG x Robo um Conan Conan Combned Aeleraon Veloy Amrabr / MISC / Vol. 4 / o. / Fall 9

9 TABLE IV THE ERROR FOR ESTIMATIG y Robo um Conan Conan Combned Aeleraon Veloy Fg. 6. The emaed raeory for arge 3 Fg. 5. The emaed raeory for arge 6. REFERECES [] R. E. Kalman, and R. S. Buy, ew Reul n Lnear Flerng and Predon, Tran. Ameran Soey of Mehanal Engneer, Sere D, Journal of Ba Engneerng, Vol. 83D, pp. 95 8, 96. [] Brano R, Saneev Arulampalam, and el Gordon, Beyond he Kalman Fler: Parle Fler for Trang Applaon, Areh Houe, Boon, London, 4. [3] R. Segwar and I. R. ourbahh, Inoduon o Auonomou Moble Robo, MIT Pre, 4. [4] A. Howard, Mul- robo Smulaneou Loalzaon and Mappng ung Parle Fler, Robo: Sene and Syem I, pp. 8, 5. [5].J. Gordon, D.J. Salmond, and A.F.M. Smh, A ovel Approah o onlnear/non-gauan Bayean Sae Emaon, IEE Proeedng F, 4(:7 3, 993. [6] M. Iard, and A. Blae, Conour Trang by Soha Propagaon of Condonal Deny, In Pro. of he European Conferene of Compuer Von, 996. [7] D. Fox, S. Thrun, F. Dellaer, andw. Burgard, Parle Fler for Moble Robo Loalzaon, Sequenal Mone Carlo Mehod n Prae. Sprnger Verlag, ew Yor,. [8] C. Hue, J. P. L. Cadre, and P. Perez, Sequenal Mone Carlo Mehod for Mulple Targe Trang and Daa Fuon, IEEE Tranaon on Sgnal Proeng, Vol. 5, O., February. [9] B. R, S. Arulampalam, and. Gordon, Beyond he Kalman Fler, Areh Houe, 4. [] K. Kanazawa, D. Koller, and S.J. Ruell, Soha Smulaon Algorhm for Dynam Probabl ewor, In Pro. of he h Annual Conferene on Unerany n AI (UAI, Monreal, Canada, 995. [] F. Guafon, F. Gunnaron,. Bergman, U. Forell, J. Janon, R. Karlon, and P. J. ordlund, Parle Fler for Poonng, avgaon, and Trang, IEEE Tranaon on Sgnal Proeng, Vol. 5, o., February. [] D. Shulz, W. Burgard, D. Fox, and A. B. Cremer, People Trang wh a Moble Robo Ung Sample-baed Jon Probabl Daa Aoaon Fler, Inernaonal Journal of Robo Reearh (IJRR, (, 3. [3] M. S. Arulampalam, S. Maell,. Gordon, and T. Clapp, A Tuoral on Parle Fler for Onlne onlnear/on-gauan Bayean Trang, IEEE Tranaon on Sgnal Proeng, Vol. 5, o., February. [4]. Ioma,. Ihmura, T. Hguh, and H. Maeda, Parle Fler Baed Mehod for Maneuverng Targe Trang, IEEE Inernaonal Worhop on Inellgen Sgnal Proeng, Budape, Hungary, May 4-5, pp.3 8,. [5] R. R. Pre, V. P. Jlov, and X. R. L, A omparave udy of mulple model algorhm for maneuverng arge rang, Pro. 5 SPIE Conf. Sgnal Proeng, Senor Fuon, and Targe Reognon XIV, Orlando, FL, Marh 5. [6] T. E. Formann, Y. Bar-Shalom, and M. Sheffe, Sonar Trang of Mulple Targe Ung Jon Probabl Daa Aoaon, IEEE Journal of Oean Engneerng, Vol. 8, pp , 983. [7] J. Vermaa, S. J. Godll, and P. Perez, Mone Carlo Flerng for Mul-Targe Trang and Daa Aoaon, IEEE Tranaon on Aeropae and Eleron Syem, Vol. 4, o., pp , January 5. [8] O. Fran, J. eo, J. Guvan, and S. Shedng, Mulple Targe Trang Ung Sequenal Mone Carlo Mehod and Saal Daa Aoaon, Proeedng of he 3 IEEE/IRSJ, Inernaonal Conferene on Inellgen Robo and Syem, La Vega, evada, Oober 3. [9] Jao F. G. de Frea, Bayean Mehod for eural ewor, PhD he, Trny College, Unvery of Cambrdge, 999. [] P. D. Moral, A. Doue, and A. Jara, Sequenal Mone Carlo Sampler, J. R. Sa. So. B, 68, Par 3, pp , 6. Amrabr / MISC / Vol. 4 / o. / Fall 9 5