Distributed Fusion and Tracking in Multi-Sensor Systems

Transcription

1 Dsrbued Fuso d Trckg Mul-Sesor Sysems Deepk Khosl, Jmes Gullocho, Howrd Choe HRL Lborores LLC, Mlbu, CA, USA Ryheo Sysems Compy, NCS, Plo, TX, USA ABSTRACT The gol of sesor fuso s o ke observos of evrome from mulple sources d combe hem o he bes possble rck pcure. For smplcy, hs s usully doe by sedg ll mesuremes o sgle ode whose sole sk s o fuse mesuremes o cohere rck pcure. Ths pper roduces ew frmework, Dsrbued Fuso Archecure for Clssfco d Trckg (DFACT), h does o rely o sgle full-wreess ode o fuse observos, bu rher urs every sesor o fuso ceer. Movg ework from cerlzed o dsrbued rchecure complces sesor fuso, bu provdes my gble beefs. Sce ech sesor s boh source d sk of formo, he loss of y dvdul compoe mes h oly oe of my possble formo chels hs bee desroyed. I hs pper, we dscuss how o fuse boh rckg d clssfco observos dsrbued ework, d compre s performce o cerlzed frmework. ch rck hs boh kemc se d belef se ssoced wh. Compoes ulze he formo form of he Klm fler for kemc rckg, whle rge ype s deermed usg herrchcl belef srucure o deerme objec clssfco, recogo, d defco. ch compoe he ework ms s ow depede pcure of he evrome, d formo s exchged bewee compoes v queued messgg sysem. Ths pper compres he performce of cerlzed rchecures o dsrbued rchecures, d her respecve commuco d compuo coss. Keywords: Sesor fuso, fuso rchecures, dsrbued fuso, dsrbued rckg, mul-level clssfco. INTRODUCTION Mul-sesor sysems provde cresed ccurcy d relbly for rckg d defyg rges beyod he cpbles of soled sesors. Oher dvges clude greer re coverge d robusess o flure. However, he use of mul-sesor sysems hve led o remedous crese he mou of d requrg processg. Fuso d resource mgeme plys crcl role hese sysems. The gol of sesor fuso s o ke observos of evrome from mulple sesors d combe hem o he bes possble rck pcure. Fuso rchecure c be brodly clssfed o wo dsc cegores - cerlzed d decerlzed fuso. I cerlzed mesureme fuso, mesuremes from sesors re se o sgle ode whose sole sk s o fuse mesuremes o cohere globl rck pcure. Ths ode s globl fuso ceer (Full-wreess odes, or FAN) d ms he curre globl rck se, d updes he se wh comg mesuremes from sesors or he pssge of me. Ths ew se c ow be used o deerme fuure ses. Sce cerlzed eworks rely o sgle fuso ceer, hs mkes hem hghly suscepble o csrophc flure. I decerlzed fuso, dvdul sesors combe d from oher sesors o cree her locl rck pcure. I sychroous decerlzed rchecure, he mesuremes rsmed from ech sesor re sychroous. ch ode s se s oly depede o h ode s pror se, pu from he evrome, d process ose, jus lke y oher Mrkov process. ch ode ms s ow dvdul pcure of he se spce, bu sce er-ode commuco s mperfec, hese se represeos re ofe drmclly dffere from ode o ode. Movg ework from cerlzed o dsrbued rchecure complces sesor fuso, bu provdes my gble beefs. Sce ech sesor s boh source d sk of formo, he loss of y dvdul compoe mes h oly oe of my possble formo chels hs bee desroyed. The m dvge of dsrbued eworks s her robusess d modulr ure. Our lerure survey cludes umber of ppers h propose eresg mehods for performg sesor fuso. There hs bee much wre o he opc of cerlzed fuso. Thomopoulos e l. provde geerl proof h he opml soluo o dsrbued fuso mous o Neym-Perso es he fuso ceer d lkelhood-ro es he dvdul sesors. Archecures c use eher d fuso or decso fuso, dscusso of he pros d cos of ech s provded by Brooks e l., D Cos d Syeed 3, d Clouqueuer e l. 4 Zhg e l. 5 d Wg e l. 6 propose

2 herrchcl decso fuso: As decsos re pssed up ree of ermede levels, cer odes re gve hgher weghs h oher odes depedg o he quly of he fused formo. We he cosder he work doe dsrbued fuso, whch s subslly less developed. Sroupe e l. 7 pply dsrbued fuso o ework of depede robos, d expl how o properly fuse mesuremes receved from dffere frmes of referece. A mehod proposed by Xo e l. 8 volves ech ode updg s ow d wh weghed verge of s eghborg odes. Q e l. 9 del sysem of moble ges whch rvel bewee locl d ses by rsmg hemselves from oe ode o he ex. Ths hs he dvge of oly hvg o rsm he ge self, rher h he d, whch could be severl mes lrger sze. Thrmrs e l. 0 descrbe dsrbued rchecure wh mulple fuso ceers; however, her model sll res sesors d fuso ceers s sepre odes he ework. Durr-Whye e l. prese mehod for rckg rges dsrbued frmework; we use her formo fler for he dsrbued rchecure we prese hs pper. A umber of ppers hve explored herrchcl clssfco echques. Vly e l descrbe sysem for orgzg vco mges o herrchcl cegores effor o mprove mge rerevl bsed o mge coe. Koller d Shm 3 use herrchcl Byes clssfers o sor web pges o groups bsed o her respecve opcs. McKy 4 dels he pros d cos of usg Byes clssfer models of vryg complexy. I hs pper we mpleme ew rchecure o ddress he shorcomgs of prevous dsrbued fuso models: Dsrbued Fuso Archecure for Clssfco d Trckg, or DFACT. Ths rchecure brgs ogeher severl dffere cug-edge echologes o sgle mul-fucol pckge, cludg some ew echologes uque o hs work. The echologes we corpore from oher sources clude he formo fler descrbed Myk d Durr-Whye 5 d lgorhm for debsg polr mesuremes proposed by Mo e l 6. We lso roduce brd ew mehod for performg mul-level clssfco h s fredly o dsrbued evrome (see seco..3). We demosre he combo of hese echologes hrough smulo es-bed wre Mlb d C++ usg he MX erfce. The srucure of hs pper s s follows. Seco descrbes wo dffere rchecure for sesor fuso: Cerlzed (CFACT) d dsrbued (DFACT). Ths seco dels how rge rckg, ssoco, d clssfco re performed, d he compuol d commuco coss ssoced wh ech rchecure. Seco 3 dels he smulo es bed used o es d compre he rchecures preseed seco, d cludes he sesor models used d descrpo of he mesure used o compre performce. Seco 4 preses smulo resuls hghlghg he performce dffereces bewee he rchecures.. Flly Seco 5 preses cocluso of hs work d fuure drecos.. ARCHITCTURS FOR SNSOR FUSION Sesor fuso rchecures hve wo resposbles - rge rckg d rge clssfco. ch rck hs kemc se (h rcks, for exmple, poso d velocy wo dmesos) d clssfco se bsed o herrchcl clssfco scheme descrbed Seco..3. The sesors c observe eher or boh of hese depedg o her mode of opero.. Cerlzed Fuso Archecure for Clssfco d Trckg (CFACT) I cerlzed rckg, he overll rck pcure s med by sgle ode clled he full-wreess ode (FAN). Ths ode collecs observos from ll he sesors d merges he formo o upded globl rck pcure, d he reurs hs upded rck pcure o he sesors. The cerlzed rchecure ulzes he sdrd Klm fler, we shll refer o hs s he bsc form of he Klm fler. We mke he ssumpo h he FAN hs models of ll he sesors he ework, d lso kows ech sesor s curre poso. Ths mes h he sesors do o hve o sed redud formo wh ech pcke. A hgh-level dgrm of he rchecure s workgs s provded below.

3 Cerlzed Fuso Archecure for Clssfco d Trckg (CFACT) Full-Awreess Node Sesor (FAN). Mke 3. Fuse. Sed Mesuremes Mesuremes Mesuremes. Mke mesuremes - All sesors mke observos of he evrome. The kemc mesureme s represeed by he vecor z d he mrx R, whle he clssfco mesureme s represeed by ID umber.. Sed mesuremes - The formo ghered sep s se by ech sesors o he FAN. 3. Fuse mesuremes - Frs, he rck pcures re upded due o he pssge of me. Ths volves dvcg he esmed se x, he covrce mrx P, d he belef se b of ech of he rcks usg equo. z, R, d c re he used o geere upded se pcure. Ths process s repeed for ech sesor h reurs mesureme... Trckg Fgure. Cerlzed rchecure for sesor fuso. I hs work, we ssume smplfed rge model. All rges hve cos velocy, d re subjec o rdom perurbo due o whe ose. Ths llows us o use smple Klm fler o m he kemc se. However, we use dffere forms of he fler for cerlzed d dsrbued fuso. I would be relvely srghforwrd o exed hs work o oher rge models. The dymcs of he ler dymcl sysem re govered by x = " x + w, w ~ N(0, Q). ()!! Here, x s he se of oe of he rges me. (If s ecessry o refer o he se of prculr rge,, superscrp wll be dded: x ) Φ s he se rso mrx d Q s he process ose, d N(m, Σ) deoes he mulvre orml dsrbuo wh me vecor m d covrce mrx Σ. If he rge s observble me by sesor j (whch depeds o he se of he rck d he co seleced for he sesor), he kemc observo (z,j ) wll be geered ccordg o z = H x + v, v ~ N(0, R ). (), j, j, j, j, j H,j s he mesureme rsfer mrx d R,j s mesure of he ccurcy of he mesureme. We ke Z o be he se of ll he kemc observos of rck me. Sce x s uobservble, mus be esmed hrough he use of Klm fler 7. The Klm fler ms les-squres esme x( ) = [x Z,, Z ] d covrce mrx P( ) = [x( )x T ( ) Z,, Z ] of he error. Ths s recursvely med hrough he followg ses of equos xˆ ( ) ˆ! = " x! (3) P (!) = " P " + Q (4) T!!!! xˆ = xˆ (!) + K [ z! H xˆ (!)] (5) K P H H P H R! T T = (!) [ (!) + ] (6) P = [ I! K H ] P (!) (7) where x s he curre rck esme d P ˆ s he covrce ssoced wh h esme, Lke ll vecors hs pper, hs s colum vecor.

4 .. Assoco Idvdul mesuremes re o ssoced wh prculr rck whe hey re geered d eed o be ssoced wh exsg rcks (We do o cree or delee rcks rume, ll rcks re creed bsed o rge groud ruhs = 0). We hve lso cluded flse lrms our model, whch re deeco eves h rse from rdom ose d o due o he presece of rge. These wo ssues mke ecessry o perform rck ssoco. For hs sk, we hve chose o use he Hugr mehod, he mplemeo of whch s kow s Mukres lgorhm 8. Assume here re M workers d N sks, d ech combo MN hs ssoced cos C MN. The lgorhm deermes whch workers should perform whch sks o mmze he ol cos. For our problem, he workers re he exsg rcks, d he sks re he mesuremes. The cos C MN s defed by he Mhlobs dsce r r r r r r d x y x y x y. (8) M T! (, ) = (! ) " (! ) Ths s smlr o he uclde dsce; he dfferece beg he cluso of he covrce!. The covrce used s h of he mesureme self. Ths mes h f wo mesuremes re equds from exsg rck, bu ech mesureme hs dffere!, he mesureme wh he smlles covrce wll be ssoced wh he rck. Assoco c be performed by eher he sedg ode or he receve ode, depedg o he ype of Klm fler beg used. The cerlzed rchecure exhbed hs pper requres sesor odes o forwrd ll formo o he FAN, whch he performs he ssoco...3 Clssfco As wh he kemc se, he defco of he rck c be resoed bou umber of wys; we pply Byes resog o he problem. We model he sesors usg cofuso mrces; he klh eleme of Θ j gves he probbly me h sesor j repors he rck s ype k whe s ype l. Ths mrx s geered for ech sesor/rge combo by he FAN CFACT, so he sesors oly eed o commuce umber lbelg he ppropre row of he mrx o be used he belef se upde. The ucery s modeled s muloml dsrbuo; he kh eleme of he belef se b() s he belef (.e. probbly) me h he rck s ype k, gve ll he observos h hve come up o (d cludg) me. If he rck s observble me by sesor j, he defco observo (o j ) wll be produced. We ke O o be he se of ll he defco observos of rck me. The belef se c he be upded wh b! oj b = b o"! j. (9) We ow descrbe he process o compue he elemes of he cofuso mrx Frs, we deerme he probbly h objec wll be defed s clss k gve h s clss k. The probbly of correc defco P(k k) s gve by Johso s crer, foud Hrey 9 : ( N N50) + ( N N ) N P( k k) =, = N 50 N s he umber of resoluo elemes o he rge whe he mesureme s ke, d N 50 specfes he umber of resels requred for 50% chce of ssocg he objec wh he correc ype. The vlue of N s depede o he sesor beg used; our es bed, oly elecro-opcl sesors re cpble of performg clssfco. N 50 depeds o he percepo level oe s eresed. Tble shows he dffere levels of percepo. We mke he ssumpo h ll correc defcos re equprobble. Therefore, he probbly h clss k s defed s beg clss l, ssumg h k l, s ( ) ( ) 50 P( k l! k) = " P( k k) C " () where C s he umber of possble clsses. I rely, k s more lkely o be msclssfed s dffere ype of k rher h ype of cr; he sgle-level clssfco model does o reflec hs. Ths leds us o mul-level clssfco. (0)

5 Tble. Johso s crer for dffere percepo levels (from Hrey 9 ). The more resels we hve o he rge, he hgher he percepo level we re ble o cheve..5 resels (0.75 cycles) per crcl dmeso 50% deeco probbly 3 resels (.5 cycles) per crcl dmeso 50% clssfco probbly 6 resels (3 cycles) per crcl dmeso 50% recogo probbly resels (6 cycles) per crcl dmeso 50% defco probbly Mul-level clssfco ebles more geerl formo o be exrced from objec. The rchecures we demosre hs pper corpore herrchcl clssfco srucure o provde exr coexul formo bou ech rge. A exmple belef se s show Fgure. Noce h he form of he belef se for mul-level clssfco rems oe-dmesol. The dfferece rses how he cofuso mrces re cosruced. Frs, cofuso mrces for ech cegory d subcegory re cosruced v he process deled bove, whch ssumes h ll correc clssfcos re equprobble. Whe cosrucg he cofuso mrces, we mke he ssumpo h ech subcegory ssumes h he sesor hs reured mesureme h he objec belog o he cegores bove. Usg recursve mehod, we geere cofuso mrces for ech percepo level. Afer we hve cosruced he cofuso mrces, he belef se s upded usg equo (9), excly s would uder sgle-level clssfco. Clssfco Recogo Idefco Belef Se. M Tk Fredly Neurl Hosle.05 M09 Humvee. M707.0 M Sed Cr. V. T7 Tk Fgure. Belef se orgzo. We use he cofuso mrx ssoced wh he percepo level of he observos reured from he sesor. The cofuso mrx s cosruced recursvely, srg wh he mos bsc objec cegores d progressg hrough more d more specfc clssfcos hrough ech ero (s he objec rcked vehcle? s he rge k? s he rge T7 k?). I he smulos we ru ler, 3 percepo levels re used (Clssfco, recogo, d defco). If oe ws o exrc cegorcl formo from he belef se, ll h s requred s smple sum of ll clsses h belog o h prculr cegory. Le s sy we w o deerme he chce h objec s k. The belef se dces here s 0% chce he objec s T7 k, 0% chce s M k, d 5% chce s M09 k. Therefore, he chce h he objec s k s smply 0% + 0% + 5% = 45%...4 Compuol Requremes The CFACT rchecure uses he bsc Klm fler o m he rck ses. The bsc fler s srghforwrd, d s suble for rchecures where here s oly oe fuso ceer.. T90. Sed Cr. V Tble. Number of flog-po operos requred o predc d upde ech rck s se cerlzed fuso. N s he umber of sesors, K s he legh of he Klm se, C s he legh of he belef se, d M s he umber of mesured vrbles. Sep Flops Predco 3 Upde Tol..5 Commuco Requremes 3K K 3K MK + 4KM + M! ( K + 3MK) + (3C! ) N(K + 6MK + 4KM + M + 3C! ( K + 3MK + )) A ech cycle, ech sesor seds s mesuremes o he FAN, whch requres 4(M + )(N FA + N D ) byes of bdwdh, where N FA s he umber of flse lrm eves, d N D s he umber of deeco eves.

6 Cerlzed rchecures mke beer use of vlble commuco resources evromes where here s lle cvy. Sce he FAN hs locl models of ll he sesors he ework, ech mesureme requres relvely lle d rsfer; oly he mesureme vecor d clss defco umber eed o be se for ech eve. For exmple, mesureme of rck s poso hree dmesos wh hree possble clssfcos requres mesureme sze of 3 (M = 3, C = 3). Les ssume he verge umber of flse lrm eves s 0, d he umber of deeco eves s 0. If sesor mkes mesureme every 00 ms, d here re 0 sesors, ech sesor mus be cpble of sedg.6 klobyes/sec (.8 kbps), d he FAN mus be ble o hdle 6 klobyes/sec (8 kbps) of comg d rsfer. Now ssume h he flse lrm re s 90. Now ech sesor mus be cpble of sedg 3 klobyes/sec (56 kbps), d he FAN mus be ble o hdle 30 klobyes/sec (.56 Mbps) of comg d rsfer.. Dsrbued Fuso Archecure for Clssfco d Trckg (DFACT) The bsc gol behd dsrbued rchecure s o mke sysem of sesors robus he cse of dvdul sesor flures. The loss of sgle sesor decerlzed evrome does o subslly mpc he overll helh of he sysem. For sce, ssume h our sesors re moble plforms rugged evrome. I such suo, cer sesors my fd hemselves res where hey co coc some of he oher sesors. If he sesor h flls ou of coc s solely resposble for mg he rck pcure, he sesor ework s rouble. The loss of mpor ode cerlzed ework c drop sysem effcecy from 00% o 0%. I decerlzed sysem, he loss of y ode mgh oly reduce he sysem effcecy oly mrglly. I ddo, he dsrbued rchecure hs lgher commuco requremes evromes wh dese cluer. Ths s becuse ech sesor performs rck ssoco pror o sedg mesuremes o he oher sesors. Sce he ssoco lgorhm wll remove y mesuremes h re o ssoced wh y currely exsg rcks, hese flse lrms ever hve o be se o he oher sesors o he ework. The mou of commucos requred s oly depede o he umber of rcks, d wll o crese wh cresg cluer. Ulke CFACT, DFACT ssumes h o sesor hs y pror formo bou y oher sesor. Ths llows sesors o be dded o he ework y me, d eve llows for ew ypes of sesors o jo lredy exsg ework. However, hs requres some more formo o be se bewee he sesors every me hey commuce. Ths ddol overhed s descrbed seco..5. Dsrbued Fuso Archecure for Clssfco d Trckg (DFACT). Mke Mesuremes A sesor mkes observo of he evrome.. Geere Iformo Mesuremes re covered o Cres coordes, d he mesuremes re ssoced o pre-exsg rcks. The mesuremes re he used o geere he formo vecors I d. 3. Shre Iformo The formo vecors geered sep d he clssfco mesureme re rsmed o ll oher sesors. 4. Fuse Iformo All sesors, cludg he sesor h mde he mesureme, upde her ow rck pcures... Trckg Fgure 3. Dsrbued rchecure for sesor fuso. Our dsrbued model uses he Iformo form of he Klm fler, derved Grocholsky e l 0. Ths form s mhemclly decl o he bsc Klm fler, bu he equos hve bee mpuled o reduce he complexy of updg he kemc se wh ew mesureme. The seps of he Iformo fler re show below. = H R z, I T! j, j, j, = H R H () T! j, j,

7 y (!) = Y (!)" Y (!) y (3)!! Y (!) = [" Y " + Q ] (4)! T!!!!! N y y ( ) =! +" (5) j, j= N Y Y ( ) I =! +" (6) j, j= The dvge of hs form of he Klm fler les he j, d I j, vecors, kow s he formo vecors. If plform hs mulple sesors d receves mulple mesuremes from he sme rck, hs plform c fuse he mesuremes o oe se of formo vecors before pssg o oher odes o he ework. A cve of hs echque s h mesuremes mus be ssoced wh rcks before beg se. The reso for hs s h he formo vecors hemselves co o po of referece; hey represe he djusme requred for he curre se bsed o he ew mesuremes. A smple D exmple: Our curre esme for rck s poso s x = 5. A sesor produces mesureme, ssoces he mesureme wh hs prculr rck, d he geeres he formo vecor. The formo vecor specfes h he curre se mus be djused by -.. Thus, fer he upde, he ew esme s x = 3.8. Whou kowg whch rck we re modfyg beforehd, s mpossble o ssoce formo vecor wh y gve rck... Assoco Trck ssoco s performed fer he mesuremes hve bee rsmed o he full-wreess ode he cerlzed rchecure. DFACT does he verse: The mesuremes re ssoced by ech sesor o rck pror o beg se. Sce he formo vecors used by he dsrbued rchecure mus be ched o specfc rck, ssoco hs o be doe pror o commuco. Ths sves bdwdh sce mesuremes h re o ssoced wh y of he rcks do o eed o be se. The mehod of ssoco s decl o he cerlzed model, see seco Clssfco DFACT uses he sme mul-level clssfco process deled seco..3; however, here s dfferece how he mesureme s commuced bewee he odes. Sce he cerlzed rchecure hs locl models of ll he sesors he ework, oly eeds o receve he d umber ssoced wh he clss mesureme reured by ech sesor. Nodes DFACT re gor of he oher sesors he ework, so more d s requred o properly upde he belef se. The odes mus sed he ppropre row from he cofuso mrx ssoced wh rge he mesureme s poso. Ths row wll hve dmeso xc, where C s he umber of clsses he belef se...4 Compuol Requremes Sce DFACT uses he formo form of he Klm fler, he recepo of messge from oher sesor ode uses he compuolly smple IKF upde equos (5). Sep Tble 3. Flog-po operos requred by he formo-form of he Klm fler used DFACT. Flops Iformo Geero 3 M + MK + 4KM! ( K + K) Predco 3 0K! (K! K ) Upde K + (3C! ) Tol 3 3 0K + M + K M + 4KM + KM + N(K + 3C! )! (3K + K)

8 Ths requres fr fewer flog-po operos h he upde procedure used he bsc Klm fler. For smll umber of sesors, hs dfferece s eglgble, bu s N becomes lrge, he effec s subsl...5 Commuco Requremes ch sesor mus sed ol of 8(N )(K + K + C + )N D byes per cycle. I dsrbued rchecures, ech ode seds d o every oher ode, d lso receves formo from every oher ode. Ths mulples he umber of pckes requred by fcor of (N ). Sce ech ode s depede d does o hve model of he oher sesors he ework, more formo mus be se ech commuco cycle. For dsrbued rchecure usg he bsc Klm fler, sesors would eed o clude her curre poso, he mesureme rsfer mrx H, d he mesureme covrce R wh every rsmsso. DFACT does o eed o clude y of hese mrces s rsmssos! Ths formo s sed compcly represeed by he vecors d I. A dvge DFACT hs over CFACT s h rck ssoco s doe pror o messge pssg. Ths mes h DFACT wll o sed mesuremes h wll eveully be hrow wy by he rck ssoco lgorhm. Cosequely, lo less d s se per commuco cycle, especlly osy evromes. To compre, le us clcule he bdwdh requred o ru he exmple preseed he cerlzed seco uder DFACT sed: For K = 6, C = 3, N = 0, DFACT requres 33. klobyes/sec (65 kbps) per sesor ode. I he cse where here re o flse lrm eves, he cerlzed rchecure requres oly y frco of he bdwdh requred by DFACT. As he flse lrm re creses, he gp bewee he wo rchecures shrks, d eveully DFACT requres less bdwdh h CFACT. Aoher dvge s h mulple kemc observos of sgle rck c be combed pror o beg se o oher ode o he ework. Ths s becuse boh he d I vecors c be summed pror o be se o oher odes. Ths mes oe c reduce he commuco frequecy d herefore overll commuco requremes. Sce rge kemc ses re dymc, kemc mesuremes become less ccure over me. A soluo o hs problem c be foud Br-Shlom e l. Clssfco observos c lso be combed. For ech observo, ll h s se s sgle row of he cofuso mrx. If we look he form of equo (9), we oce h we c combe dvdul o j vecors o sgle vecor d perform jus sgle upde. Ths mes h ech ode c smply m vecor of ew clssfco formo, d sed hs vecor y desred frequecy. However, we do o combe mesuremes our smulo es-bed sce we ssume h ech observo s se dvdully. 3. SIMULATION TST-BD Our smulo es-bed mplemes boh he cerlzed d dsrbued rchecures for he purpose of comprso. The es-bed s Grphcl User Ierfce (GUI) s wre Mlb, whle he uderlyg fucoly s wre C++. The wo lguges erc v he MX erfce, whch fcles he pssge of formo. We chose hs seup becuse our gol ws o cree powerful evrome h s lso esy o cofgure d ssss debuggg d d colleco. The smulo es-bed llows us o geere vrous sesor d rge sceros cludg evromel codos, ru fuso rchecures, d lyze he resuls. The es-bed llows us o cree scero wh vrble umber of rges wh dffere srg locos d veloces. The rges re modeled s movg he xy ple (z=0) srgh le wh cos velocy d whe process ose. Sce rges move he xy ple, ech rge oly hs four-dmesol kemc se (comprsg he poso d velocy of he rge log wo dmesos spce). The rges s lso ssged Swerlg ype (I-V), d ls of clssfers h defy rge clss, recogo, d defco. The ls of clssfers s smply ls of cegores h he objec belogs o. For sce, hosle T-7 k would be lzed wh Hosle s s clss, Tk s s recogo, d T-7 s s defco. The es-bed lso llows us o model vrble umber of rdr d elecro-opcl (O) sesors wh dffere locos d prmeers (see 3.. d 3..). Whle movg sesor models re llowed, he smulos preseed here ssumed fxed sesor posos. Boh sesors reur mesuremes D polr coordes, d hese mesuremes re covered o Cres sysem v he mehod descrbed Mo e l 6. The es-bed lso llows us o model 3D polygol-shped occlusos such s buldgs. Ths effecs boh he sesor mesureme zoes d he messge pssg bewee sesors/fans sce we ssume h ll occlusos re compleely opque. Ths mes h objecs c oly be mesured/commuced wh f hey re wh Le of Sgh (LOS). The

9 geered err s frly smple, d cosss of projecos of D polygos o he 3rd dmeso. I ddo, commucos re subjec o smple expoelly decyg pcke loss fucos I order o compre performce of cerlzed d dsrbued fuso rchecures, we hve developed severl quve mercs. I ddo o he obvous kemc d clssfco errors w.r.. groud ruh, we lso use formo heory mesures such s eropy for mesures of overll performce. These mesures llow us o compre jo rckg d clssfco performce cross he rchecures. They c lso be used o judge how much formo s ged whe rsog from oe se o oher. We lso keep rck of compuo d commuco resource ulzo. 4. XPRIMNTAL RSULTS We used he bove smulo es-bed o geere vrous sceros d compred rckg d clssfco performces of CFACT d DFACT pproches. We expec h he wo rchecures preseed bove should yeld smlr rckg/clssfco performce whe esed sde-by-sde decl evromes. The resuls demosre hs smlry performce bewee CFACT d DFACT. 4. Trckg Performce Frs, we wsh o compre he kemc rckg performce of boh rchecures. To do hs, we se up scero wh squre Are Of Ieres (AOI) of km x km. Ths AOI cos 6 rdr sesors, oe FAN, d 50 rges. The FAN s loced he ceer of he AOI. The sesors re sory d plced rdomly 3D spce wh rdom prmeers (so some rdr odes wll be more effecve h ohers). The rges re cofed o move he xy ple d ssged rdom Swerlg ypes (I-V). The rdr sesors oly mesure rge poso, herefore M =. Fgure 4 shows hs prculr cofguro. We frs r he CFACT pproch o hs scero. As descrbed Seco., he sesors mke mesuremes o ech rge d sed hese rw mesuremes o he FAN. The FAN performs d ssoco d fuses hese mesuremes o upde he globl rck pcure. The sesors he perform mesuremes he ex me sep d he process s repeed. A ech me sep, we compue he eropy of ech rck d he ol kemc eropy cross ll rcks usg he formuls preseed seco Fgure 4. vrome seup. The crcles represe rdr sesors, he crosses represe rges, d he FAN s represeed by dmod. There re 6 rdr sesors, oe FAN, d 50 rges. I DFACT, we sr wh he sme l scero d codos. As descrbed Seco., ech sesor mkes mesuremes o he rges, performs d ssoco d geeres he formo mesures descrbed 3.3. ch ) ) sesor lso K cs s fuso ode. I combes s formo mesures K wh hose receves from oher sesors/odes o / / upde Jhe rck pcure. Uder delyed d lossy commuco, J s expeced h sesor odes wll hve some ( ( dffereces her rck pcures. y p o r c m e K Sesor Sesor Sesor 3 Sesor 4 Sesor 5 Sesor 6 Cerlzed y p o r c m e K Sesor Sesor Sesor 3 Sesor 4 Sesor 5 Sesor 6 Cerlzed Tme lpsed (s) Tme lpsed (s) Fgure 5. Kemc eropy vs. me for ech ode wh expoel pcke loss. Fgure 6. Kemc eropy vs. me for ech ode wh o pcke loss.

10 Sce he formo form of he Klm fler s mhemclly equvle o he bsc Klm fler, oe would expec wo fuso ceers usg hese wo forms of he fler wh oherwse decl chrcerscs should perform excly he sme. The oly dffereces we expec bewee he wo lgorhms should be due o he lossy commuco d posog of he dvdul odes he ework. The resuls Fgure 5 show h he FAN performs beer h some sesors, d worse h ohers. Ths resul s expeced: Sce we hve show h he performce dfferece bewee he bsc d formo forms of he Klm flers re eglgble, ll h mers s ode poso. I our exmple, he FAN s loced he ceer of he evrome, plcg close o he ceer of mss of he ework. The reso h cer sesors perform beer h he FAN s h hey re closer o he ceer of mss, prly due o beg oe of he sources of formo hemselves. Fgure 6 shows he resuls of rug he sme es wh zero pcke loss. As expeced, ll odes ow perform declly. Ths s becuse ech ode ow receves he sme mou of formo, regrdless of s loco. Ths resul demosres he mhemcl equvlece of he bsc form d formo forms of he Klm fler. 4. Mul-Level Clssfco Performce To es he mul-level clssfco resuls, we used smlr scero o he prevous seco, excep ow we use elecro-opcl sesors sed of rdr sesors o observe he rges. o c f s s l C Sesor Sesor Sesor 3 Sesor 4 Sesor 5 Sesor 6 Cerlzed o c f s s l C Sesor Sesor Sesor 3 Sesor 4 Sesor 5 Sesor 6 Cerlzed Fgure 7. Clssfco eropy vs. me for ech ode wh pcke loss. Fgure 8. Clssfco eropy vs. me for ech ode wh o pcke loss. Ths s doe becuse he rdr sesors co clssfy rges. The O sesors mke observos he hghes percepo level possble, whch hs cse s rck defco. To compre performce, we use seup decl o he oe preseed Fgure 4, replcg he rdr sesors wh elecro-opcl. The resuls re smlr o he resuls we obed whe comprg rckg performce. We prese he cse wh pcke loss Fgure 7 d whou pcke loss Fgure 8. The ceer of mss rgume offered he prevous seco serves o expl hese resuls s well. 5. CONCLUSION Ths pper roduced Dsrbued Fuso Archecure for Clssfco d Trckg (DFACT), h does o rely o sgle full-wreess ode o fuse observos, bu rher urs every sesor o fuso ceer. We dscussed how o fuse boh rckg d clssfco observos dsrbued frmework d compre s performce o cerlzed frmework (CFACT). We mplemeed smulo es-bed o es, vlde d compre he CFACT d DFACT pproches. For he sceros preseed here, he resuls demosre h DFACT performs jus s well s s cerlzed couerpr erms of rck d clssfco performce. I ddo o decl performce, DFACT uses less compuol resources, d osy evromes, DFACT hs mlder commuco requremes. We lso hve show h our mul-level clssfco lgorhm works he coex of hese rchecures. The curre desg of he es-bed s useful ool for lyss d desg of fuso rchecures, bu c beef from ehcemes. Fuure work wll volve exedg our es-bed o exme he flueces of more relsc commuco models, beer rckg lgorhms such s MHT s well s dymc ework opology mgeme.

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