Novel Rao-Blackwellized Particle Filter for Mobile Robot SLAM Using Monocular Vision
|
|
- Jeffry Little
- 6 years ago
- Views:
Transcription
1 Inernaonal Journal of Compuer and Informaon Engneerng Novel Rao-Blackwellzed Parcle Fler for Moble Robo SLAM Usng Monocular Vson Maoha L Bngrong Hong esu Ca and Ronghua Luo Inernaonal Scence Index Compuer and Informaon Engneerng waseorg/publcaon/15275 Absrac hs paper presens he novel Rao-Blackwellsed parcle fler (RBPF) for moble robo smulaneous localzaon and mappng (SLAM) usng monocular vson he parcle fler s combned wh unscened Kalman fler (UKF) o exendng he pah poseror by samplng new poses ha negrae he curren observaon whch drascally reduces he uncerany abou he robo pose he landmark poson esmaon and updae s also mplemened hrough UKF Furhermore he number of resamplng seps s deermned adapvely whch serously reduces he parcle depleon problem and nroducng he evoluon sraeges (ES) for avodng parcle mpovershmen he 3D naural pon landmarks are srucured wh machng Scale Invaran Feaure ransform (SIF) feaure pars he machng for mul-dmenson SIF feaures s mplemened wh a KD-ree n he me cos of O(log 2 N ) Expermen resuls on real robo n our ndoor envronmen show he advanages of our mehods over prevous approaches Keywords Moble robo smulaneous localzaon and mappng Rao-Blackwellsed parcle fler evoluon sraeges scale nvaran feaure ransform I INRODUCION key prerequse for a ruly auonomous robo s ha can A smulaneously localze self and accuraely map s surroundngs [1] he problem of achevng hs s one of he mos acve areas n moble robocs research whch s known as Smulaneous Localzaon and Mappng (SLAM) One of he popular successful aemps a he SLAM problem was he exended Kalman fler (EKF)[23] One of he lmaons of he EKF s her compuaonal complexy [4] he sandard EKF approach requres me quadrac n he number of feaures n he map for each ncremenal updae he oher s ha requres ha feaures n he envronmen be unquely denfable oherwse hs can cause excessve daa assocaon dffculy [5] Recenly parcle flers have been a he core of soluons o hgher dmensonal robo problems such as SLAM whch when phrased as a sae esmaon problem Murphy Manuscrp receved March hs research s suppored by he Naonal Naural Scence Foundaon of Chna ( ) and he Naonal H-ech Research and Developmen Program of Chna (2002AA735041) Maoha L s wh he Deparmen of Compuer Scence and echonology Harbn Insue of echonology CO Chna (e-mal: lmaoha@ heducn) Bngrong Hong s wh he Deparmen of Compuer Scence and echonology Harbn Insue of echonology CO Chna esu Ca s wh he Deparmen of Compuer Scence and echonology Harbn Insue of echonology CO Chna Ronghua Luo s wh he Deparmen of Compuer Scence and echonology Harbn Insue of echonology CO Chna adoped Rao-Blackwellzed parcle flers (RBPF) [6] as an effecve way of represenng alernave hypoheses on robo pahs and assocaed maps Monemerlo e al [7] exended hs mehod o effcen landmark-based SLAM usng Gaussan represenaons of he landmarks and were he frs o successfully mplemen on real robos More recenly RBPF s used wdely o buld map [8910] Daley descrbe he applcaon of FasSLAM usng a rnocular sereo camera [11] Se e al [12] demonsrae he use of Scale Invaran Feaure ransform (SIF) pon feaures as landmarks for he SLAM problem usng a rnocular sereo camera Davson e al [13] demonsrae a sngle-camera SLAM algorhm capable of learnng a se of 3D pon feaures Mos of hese vson-based mehods use he sereo camera o oban sraghly he 3D feaure and he assocaon problem eher beween feaures n successve camera frames or beween observed feaures and map feaures s solved ambguously In hs paper we presen an nvesgaon no he use of monocular vson for SLAM n ndoor envronmen wh 3D feaure landmarks whch are srucured from he SIF feaure machng pars hese 2D SIF feaures are used o srucure 3D landmarks because hey are nvaran o mage scale roaon and ranslaon as well as parally nvaran o llumnaon changes and affne or 3D projecon and her descrpon s mplemened wh mul-dmensonal vecor [14] hs combnaon can resul n many hghly dsncve landmarks from envronmen whch smplfes he daa assocaon problem o only dsngushng unque landmarks We presens a fas and effcen algorhm for machng feaures n a KD-ree n he me cos of O(log 2 N ) [15] Followng [67] our approach apples RBPF o esmae a poseror of he pah of he robo where each parcle has assocaed wh an enre map n whch each landmark s esmaed and updaed by he unscened Kalman fler (UKF) [16] and UKF s used o sample new poses ha negrae he curren observaon whch drascally reduces he uncerany abou he robo pose Furhermore he number of resamplng seps s deermned adapvely [17] whch serously reduces he parcle depleon problem and nroducng he Evoluon sraeges (ES) for avodng parcle mpovershmen [18] All of hese specales can make daa assocaon n hs paper more robus han oher mehods and he bul precse map only need a small number of parcles he paper s organzed as follows: In he nex secon he RBPF for SLAM problem s brefly revewed and hen he novel RBPF mehod s descrbed n deal and secon 3 Inernaonal Scholarly and Scenfc Research & Innovaon 2(3) scholarwaseorg/ /15275
2 Inernaonal Journal of Compuer and Informaon Engneerng Inernaonal Scence Index Compuer and Informaon Engneerng waseorg/publcaon/15275 provdes a dealed s mplemenaon for monocular vson-based SLAM n unknown ndoor envronmen Expermen resuls and dscussons are presened n secon 4 wh concluson n secon 5 II NOVEL RAO-BLACKWELLIED PARICLE FILER FOR SLAM Consder he case of a moble robo movng hrough an unknown envronmen conssed of a se of landmarks he landmark n s denoed θ n he robo moves accordng o a known probablsc moon model p(s u s -1 ) where s denoes he robo sae a me and he conrol npu u carred ou n he me nerval [-1 ] As he robo moves around akes measuremens z of s envronmen hrough observaon model p(z s θn ) where θ s he se of all landmarks and n s he ndex of he parcular landmark observed a me he SLAM problem s o recover he poseror dsrbuon p(s θ 1 θ M z u n ) where M s he number of landmarks observed so far and he noaon s denoes s 1 s (and smlarly for oher varables) In [6] Murphy e al provde an mplemenaon of RBPF for SLAM: M θ1 θm θ n 1 n p( s z u n ) p( s z u n ) p( s z n ) (1) hs can be done effcenly snce he facorzaon decouples he SLAM problem no a pah esmaon problem and ndvdual condonal landmark locaon problems and he quany p(θ n s z n ) can be compued analycally once s and z are known and he amoun of compuaon needed for each ncremenal updae says consan regardless of he pah lengh Each map s consruced gven z and he rajecory s represened by he correspondng parcle Each parcle s of he form S () {s () µ () 1 Σ () 1 µ () M Σ () M } where () ndcaes he ndex of he parcle; s () () s s pah esmae µ m () and Σ m are he mean and varance of he Gaussan represenng he m-h landmark locaon Our novel RBPF updae s performed n he followng seps: Pror Lkelhood Fg 1 Movng he samples n he pror o regons of hgh lkelhood s mporan f he lkelhood les n one of he als of he pror A Samplng New Poses Usng UKF Here we need o calculae he poseror over robo pahs p(s u z n ) approxmaed by a parcle fler Each parcle n he fler represens one possble robo pah s from me 0 o me Snce he map landmark esmaes p(θ n s z n ) depend on he robo pah he parcles samplng sep s very mporan However mos mehods use he sae ranson pror p(s u s -1 ) o draw parcles Because he sae ranson does no ake no accoun he mos recen observaon z especally when he lkelhood happens o le n one of he als of he pror dsrbuon or f s oo narrow as showed n Fg 1 If an nsuffcen number of parcles are employed here may be a lack of parcles n he vcny of he correc sae leadng o dvergence of he fler hs s known as he parcles depleon problem In our mehods he -h new pose s () s drawn from he poseror p(s s -1() u z n ) whch akes he measuremen z no consderaon along wh he landmark n and s -1() s he pah up o me -1 of he -h parcle An effecve approach o accomplsh hs s o use he unscened ransformaon (U) generaed Gaussan approxmaon: ps s u z n Ns s% P N (2) 1() () () ( ) ~ ( ; ) 12 U can compue he mean and covarance up o he hrd order of he aylor seres expanson of he nonlnear observaon funcon g(θ n s ) Le L be he dmenson of s he U compues mean and covarance as follows: 1) Deermnscally generae 2L+1 sgma pons S {χ W }: χ0 s% χ s% + ( ( L+ λ) Ps ) 1 L χ s% ( ( L+ λ) Ps ) 12 L+ L (3) m c m 2 W0 λ ( L+ λ) W0 W0 + (1 α + β) m 2 W 1 (2 ( L+ λ)) 12 L λ α ( L + γ) L (4) Where γ s a scalng parameer ha conrols he dsance beween he sgma pons and he mean s α s a posve scalng parameer ha conrols he hgher order effecs resuled from he non-lnear funcon g β s a parameer ha conrols he weghng of he 0-h sgma pon α0 β0 and γ2 are he opmal values for he scalar case ( (L+λ) P s ) s he -h column of he marx square roo 2) Propagae he sgma pons hrough he nonlnear ransformaon: g( θ χ ) 02 L (5) n 3) Compue he mean and covarance of as follows: 2L m 2L c 0 z 0 z % W P W ( z % )( z % ) (6) Now we follow UKF algorhm o exend he pah s () by samplng he new poses s () from he poseror p(s s -1() u z n ): 1) Calculae he sgma pons: χ { s% s% ± ( L+ λ) P } (7) () () () () ) Usng moon model o predc: Inernaonal Scholarly and Scenfc Research & Innovaon 2(3) scholarwaseorg/ /15275
3 Inernaonal Journal of Compuer and Informaon Engneerng Inernaonal Scence Index Compuer and Informaon Engneerng waseorg/publcaon/15275 *() () () () 2L m() *() -1 f 1 u s% 1 W j 0 j j -1 χ ( χ ) χ () 2 L c () *() () *() () 1 [ 0 j χ j -1- % 1 ][ χ j -1- % 1] j P W s s 3) Incorporang new observaon z : *( ) *( ) ( ) 2L m( ) *( ) 1 ( χ -1 θn ) j j j () 2 L c() *( ) () *( ) () zz [ ][ -1-1] Wj j z% j j z% () 2 L c () *( ) () *( ) () sz W [ ][ -1-1] j j χ j s% j z% () () () 1 () () () () () % sz zz % () () () () () 1 z z g z% W (9) P P K P ( P ) s s K ( z z ) P P K P K 4) Samplng new pose s () and exendng he pah s () : s ~ p( s s u z ) N( s ; s% P ) s s s () 1() () () ( ) 1( ) ( ) ( ) (8) (10) (11) (12) B Updang he Observed Landmark Esmae In hs sep we updae he poseror over he landmark esmaes represened by he mean µ () n-1 and he covarance Σ () n-1 he updaed values µ () n and Σ () n are hen added o he emporary parcle se ψ along wh he new samplng pose s () he updae depends on wheher or no a landmark n was observed a me For n n he poseror over he landmark remans unchanged: µ () n µ () n-1 Σ () n Σ () n-1 For he observed feaure nn he updae s specfed hrough he followng Equaon: p( θ s n z ) ( ) n ( ) 1 ( ) 1 θn θ n ( ) 1 pz ( s n z ) () 1() 1 1 pz n s n p n s n z ( ) ( ) ( ) ~ N( z; g( θn s ) R) ~ N ( θ n ; µ Σ ) n 1 n 1 p( z s n z ) p( s n z ) η ( θ ) ( θ ) (13) he probably p(θ n s -1() z -1 n -1 ) a me -1 s represened by a Gaussan wh mean µ n-1 () and covarance Σ n-1 () For he new esmae a me o also be Gaussan we need generae Gaussan approxmaon for he percepual model p(z θ n s () n ) Our mehods also use U o approxmae he non-lnear measuremen funcon g(θ n s () ): 1) Calculae he sgma pons: ξ { µ µ ± ( L + λ) Σ (14) () () () () n 1 n 1 n 1 n 1 2) Usng observaon model o compue he mean and covarance of he observaon as follows: () () () () 2L m() () n ξn 1 n j 0 j j n () 2 L c() () () () () [ 0 - ][ z - ] n j j j n n j n n g( s ) z W P W z z (15) 3) Under hs approxmaon he poseror for he locaon of landmark n s ndeed Gaussan he new mean and covarance are obaned usng he followng measuremen updae: K Σ P ( P Σ P + R ) () () () () () () 1 n 1 zn zn n 1 zn () () () () n 1 ( ) n + K zz () () () () n ( ) 1 I K Pzn n µ µ Σ Σ C Adapve Resamplng (16) Nex we resample from emporary se of parcles ψ hen form he new parcle se ψ Resamplng s a common echnque n parcle flerng o correc for such msmaches and avodng parcles degeneracy By weghng parcles n ψ and resamplng accordng o hose weghs he resulng parcle se ndeed approxmaes he arge dsrbuon Afer he resamplng all parcle weghs are hen rese o w () 1/N However resamplng can delee good parcles from he sample se n he wors case he fler dverges Accordngly s mporan o fnd a creron when o perform a resamplng sep Lu [19] nroduced he so-called number of parcles N eff 1/Σ 1 N (w () ) 2 o esmae how well he curren parcle se represens he rue poseror Our approach deermnes wheher or no a resamplng should be carred ou accordng o N eff We resample each me N eff drops below a gven hreshold whch was se o 06N where N s he number of parcles In our expermens we found ha hs echnque drascally reduces he rsk of replacng good parcles because he resamplng operaons are only performed when needed D Inroducng Evoluon Sraegy he resamplng sep descrbed before helps o avod parcle degeneracy bu also leads o an undesrable loss of parcle dversy as resamplng may resul n mulple copes of only a few or n he lm only one parcle In hs case here s a severe depleon of samples In order o nroduce sample varey afer resamplng whou affecng he valdy of he approxmaon we nroduce he ES Because he evoluon operaor can search for opmal parcles he samplng process s more effcen and he number of parcles requred o represen he poseror densy can be reduced consderably he wo operaors: crossover and muaon work drecly over he floang-pons o avod he rouble brough by bnary codng and decodng he crossover and muaon operaor are defned as followng: Crossover: selec wo paren parcles (s (p1) w (p1) ) and (s (p2) w (p2) ) randomly from populaon ψ he crossover operaor maes hem by he followng equaon o generae wo chldren parcles: Inernaonal Scholarly and Scenfc Research & Innovaon 2(3) scholarwaseorg/ /15275
4 Inernaonal Journal of Compuer and Informaon Engneerng (1) c ( p1) ( p2) (1) c (1) c s κs + (1 κ) s + τ w p( z s ) ( c2) ( p2) ( p1) ( c2) ( c2) (17) s κs + (1 κ) s + τ w p( z s ) Where κ~u[01] τ~n(0σ) and U[01] represens unform dsrbuon and N(0Σ) he normal dsrbuon hen replace he parens {s (p1) s (p2) } by hers chldren{s (c1) s (c2) }accordng o he followng creron: he chld s (c1) would be acceped f p(z s (c1) )>max(p(z s (p1) )p(z s (p2) ))value else would be acceped wh probably Haa!Haa! In he smlar form s acceped or rejeced he chld s (c2) Muaon: selec one paren parcle (s (p) w (p) ) he muaon operaor on s defned as followng: mached SIF feaure pars of successve mages capured a relavely close posons along he robo s pah by a monocular vson sysem Gven a SIF key-pons se E and a arge key-pon vecor d hen a neares neghbor of d d s defned as: k 2 ( ) 1 d" E d d' d d" d d' d d' (20) Where d s he -h componen of d We mplemen he SIF key-pons machng algorhm whch based on neares neghbor search algorhm n a KD-ree Inernaonal Scence Index Compuer and Informaon Engneerng waseorg/publcaon/15275 s s + σ w p( z s ) σ ~ N(0 Σ ) (18) ( c) ( p) ( c) ( c) hen he new parcle s (c) s acceped f p(z s (c) )>p(z s (p) ) else s acceped wh probably p(z s (c) )/p(z s (p) ) For more effcen he crossover operaor wll perform adapvely wh probably p c and muaon operaor wll perform adapvely wh probably p m : ( pc 1 pc2)( fc favg) pc 1 fc favg c max avg p f f pc 1 fc < favg ( pm 1 pm2)( fmax fm) pm 1 fm favg pm fmax favg pm 1 fm < favg (19) Where f max s he bgges fness value n he populaon and f avg s he fness average value f c s he bgger fness value of wo crossover ndvduals f m s he fness value of muaon ndvdual In hs paper we se p c1 085 p c2 065 p m1 01 p m III IMPLEMENAION DEAILS OF USING MONOCULAR VISION A SIF Feaure Exracon he Scale Invaran Feaure ransform (SIF) was proposed n [14] as a mehod of exracng and descrbng key-pons whch are robusly nvaran o common mage ransforms he SIF algorhm has four major sages: 1) Scale-space exrema deecon 3) Orenaon assgnmen 4) Key-pon descrpor An mporan aspec of he algorhm s ha generaes a large number of hghly dsncve feaures over a broad range of scales and locaons he number of feaures generaed s dependen on mage sze and conen as well as algorhm parameers For a more dealed dscusson see [14] In hs paper we use he vecors wh 128 elemens as key-pon descrpor Fg 2 shows an example of SIF feaure exracon B KD-ree Based Feaure Machng hs secon descrbes KD-ree algorhm for deermnng he Fg 2 ypcal exraced SIF feaures wh her locaons represened by + he radus of he crcle represens her scales: he pxel es mage aken a (a) 1618mm; (b) 756mm; and he resul s (a) 278 key-pons; (b) 267 key-pons Fg 3 he SIF feaure maches based on KD-ree and he machng pars are represened by red and he dsance of he key-pons s represened usng he Eucldean dsance beween her accordng 128 dmensonal descrpor vecor (Equaon 20) and we can use he followng equaon o judge he machng for wo key-pons: kp kp kp kp < λ (21) 1 2 Where λ s consan and 0<λ<1(n hs paper λ s evaluaed as 07) f hs equaon s sasfed hen he machng s successful and smulaneously elmnaes he false machng Fg 3 shows an example of SIF feaure machng for a par mage from he labor corner wh dfferen scale and drecon and we oban 67 mached pars whch he machng accurae rae s hgher han 80% C 3D Srucure Afer he SIF feaure machng we oban he 2D SIF mage feaure machng pars along he robo s rajecory In Inernaonal Scholarly and Scenfc Research & Innovaon 2(3) scholarwaseorg/ /15275
5 Inernaonal Journal of Compuer and Informaon Engneerng Inernaonal Scence Index Compuer and Informaon Engneerng waseorg/publcaon/15275 hs secon we use hese feaure pars o srucure he 3D spaal landmarks whch are n a sngle world model Le p 1 (u 1 v 1 ) and p 2 (u 2 v 2 ) be he machng par ha observed from wo dfferen vewpons and p 1 p 2 assocae he 3D spaal pon landmark P(X w Y w w ) as shown n Fg 4 usng he pnhole camera model: [ ] [ ] [ ] [ ] z 1 u 1 M 1 1 v1 X Y (22) c w w w z 1 M 1 c2 u2 v2 Xw Yw w (23) he soluon of hree unknown varans X w Y w and w can be obaned hrough he leas square mehod and he projecon marx M: α x 0 u0 0 R M 0 α y v (24) Where moon model provdes exrnsc camera roaons R and ranslaons for each mage Offlne calbraon [23] yelds he camera s nrnsc parameers α x α y u 0 v 0 as shown n able 1 D Moon Model he moon model p(s u s -1 ) predcs he movemen and saus over me of he robo As shown n prevous mehods O C 1 W Y X X p 1 e 1 when a conrol u conssng of forward and angular velocy s appled o he robo: ps ( u s 1) f( u s 1) + ε x 1 x + v cos( ϕ + ω ) (25) y+ 1 + ε y + v sn( ϕ + ω ) + ε ϕ + 1 ϕ ϕ + ω Where (x y φ ) s he robo s locaon and bearng a me for all parcles 1 N v s he lne velocy ω s he angular eppolar lne Y e 2 baselne X O C 2 Y Fg 4 wo vewpons geomery and he eppolar consran ABLE I HE INRINSIC PARAMEERS AND EXRINSIC PARAMEERS OF CAMERA Inrnsc Parameers P p 2 Exrnsc Parameers α x x cr mm α y z cr mm u θ cr 90 v velocy a me s he me sep and ε are nose n erms of a normal dsrbuon N(0P ) E Observaon Model Every me he robo s rggered he CCD camera vson sysem capures he consecuve dgal mages and afer SIF feaure exracng machng curren observed SIF feaure wh he map daabase conaned wh 3D spaal naural landmarks hrough KD-ree based neares neghbor search algorhm Le F {f 1 f k } be he k SIF feaure key-pons observed a me n whch here are n key-pons machng wh he 3D landmarks n he map daabase: n l {f 1 ~L f1 f n ~L fn } and here are m key-pons machng he 2D SIF feaure key-pons whch observed a me -1 and are no reconsruced and added o he map daabase: n v {f n+1 ~V fn+1 f n+m ~V fn+m } hen he lkelhood of he observaon z beng obaned s: pz s θ n pz s θ n pz s θ n (26) () l () l v () v ( ) ( ) ( ) l v Where z represens he observaon F l {f 1 f n } and z represens he observaon F v {f n+1 f n+m } p(z l s () n l ) l represens he lkelhood of he observaon z gven he machng relaon n l and p(z l s () n v ) represens he lkelhood of he observaon z v gven he machng relaon n v hese wo lkelhood can be calculaed separaely as follows: l () n () θ j 1 j fj ln pz ( s ) ln p( f s L) (27) v () n + m () θ j n+ 1 j fj ln pz ( s ) ln p( f s V) (28) Where p(f j s () L fj ) represens he lkelhood of he () observaon beng f j when robo a pose s observng he landmark L fj and p(f j s () V fj ) represens he lkelhood of he observaon beng f j when robo a pose s () observng he SIF feaure V fj Le he 3D coordnaes of he landmark L fj be (x (j) w y (j) w z (j) w ) hen we can oban lnp(f j s () L fj ) as follows: $ $ () 1 ln p( f j s Lfj) 05mn( l( I j I j) S ( I j I j)) S J( RG fjr ) J (29) Where J s he Jacoban marx of he observaon equaon G fj s he covarance of L fj he maxmum observaon nnovaon l s consan (n our case 30) whch s seleced so as o preven ouler observaons from sgnfcanly affecng he observaon lkelhood Whle he feaure V fj has no 3D spaal nformaon lnp(f j s () V fj ) s only calculaed accordng o eppolar consran: () ln p( f j s V fj) 05( ds( I j H fj) ds( I fj H j)) + (30) Inernaonal Scholarly and Scenfc Research & Innovaon 2(3) scholarwaseorg/ /15275
6 Inernaonal Journal of Compuer and Informaon Engneerng Where I fj s he mage coordnae of he feaure V fj H fj s he eppolar lne on he mage plane correspondng o V fj a me and H j s he eppolar lne on he mage plane correspondng o he feaure f j a me -1 ds( ) s he funcon of he dsance beween pon and lne Afer calculang he observaon model p(z s θn ) whch can be used o evaluae he -h parcle wegh w () and w () s aken as he fness value n evoluonary process: robo s movng ahead he mage frames are capured and processed buldng he map of he wall Fg 6 shows some frames of sze (38 frames n oal) A he end a oal of 1468 SIF landmarks wh 3D posons are gahered n he map whch are relave o he nal coordnaes frame w pz s θ n (31) ( ) () () ( ) N () pz 1 s j θ n Inernaonal Scence Index Compuer and Informaon Engneerng waseorg/publcaon/15275 IV EXPERIMENAL RESULS AND DISCUSSION he expermens are performed on a Poneer 3-DX moble robo ncorporang an 800 MHz Inel Penum processor as shown n Fg 5a Moor conrol s performed on he on-board compuer whle a 3 GHz PC conneced o he robo by a wreless lnk provdes he man processng power for vson processng and he SLAM sofware A monocular color CCD camera mouned a he fron of he robo s used for deecng he landmarks he es envronmen s a robo laboraory wh lmed space shown n Fg 5b For llusrang he advanages of our mehods over prevous approaches we mplemen SLAM wh our novel RBPF and prevous mehod he expermen s descrbed as follows (a) (b) Fg 5 (a) Poneer 3 moble robo; (b) expermenal envronmen Fg 6 he mage sequence of he wall Frsly he robo s se a he dsance of 2m from he lab wall and he robo orenaon s parallel wh he wall a he same me le he CCD camera vson face wh he wall Whle he (1a) (1b) (2a) (2b) Fg 7 Expermen resuls of map buldng based on (1) convenonal RBPF: (a) 100 parcles (b) 500 parcles; (2) novel RBPF: (a) 50 parcles (b) 100 parcles Fg 7 shows he expermen resuls In he map S represens he sar pon of robo pah and E represens he end pon of robo pah he red pon represens he pah parcle he 2D vew of 3D landmarks n he map s represened wh blue pons As shown n Fg 7 (1) f we ncrease he number of parcles he performance of convenonal RBPF wll be mproved largely however he sorage requremen and calculaon burden s severely aggravaed ownng o each parcle assocaed wh a vew of he map Fg 7 (2) shows he bul map wh he novel RBPF whch adops separaely 50 parcles and 100 parcles and 8 evoluonary seps For execung he evoluon sraeges he mos parcles can be convergen o he regon hgh wegh and approxmae he poseror only wh few parcles he performance of he novel RBPF changes a lle wh ncreasng he number of parcles specfcally we can buld precse map only wh few parcles he more deal comparson of performance wh dfferen numbers of parcles s shown as Fg 8 obvously he robo pose and landmark esmaon error s largely reduced and we only need a few parcles o reach remarkable resuls by means of ncorporang curren observaon and hnkng abou evoluon sraegy and adapve resamplng as well as he effecve managemen srucure based on Kd-ree However ES sep can aggravae he compuaon burden hs negave mpac can be largely reduced for less and less parcles wh he runnng process he resuls are compared wh prevous mehods ndcae superor performance of presened mehod Inernaonal Scholarly and Scenfc Research & Innovaon 2(3) scholarwaseorg/ /15275
7 Inernaonal Journal of Compuer and Informaon Engneerng Anoher expermen was carred ou n our sngle lab room where he compac map s bul wh our mehod and 186 mage frames of sze are capured Fg 9 shows he brd s-eye vew of he 3D spaal map he robo pah and UKF for esmang he map Furhermore he number of resamplng seps s deermned adapvely whch serously reduces he parcle depleon problem and nroducng ES sep afer he resamplng for avodng parcle mpovershmen Expermen resuls on real robo n our ndoor envronmen show he advanages of our mehods over prevous approaches Inernaonal Scence Index Compuer and Informaon Engneerng waseorg/publcaon/15275 Fg 8 Resuls of our novel RBPF SLAM algorhm compared wh convenonal RBPF Fg 9 Brd s-eye vew of he SIF landmarks n he map S ndcaes he nal robo poson E ndcaes he pah end he do lne ndcaes he esmaed robo pah and ndcaes he robo movng drecon V CONCLUSION hs arcle descrbed a novel algorhm for SLAM problem usng monocular CCD camera Lke many prevously publshed SLAM algorhms our mehod calculaes poseror probably dsrbuons over 3D SIF feaured maps and robo locaons I does so recursvely based on a key propery of he SLAM problem: he condonal ndependence of feaure esmaes gven he vehcle pah hs condonal ndependence gves rse o a facored represenaon of he poseror usng a combnaon of parcle flers for esmang REFERENCES [1] D Korenkamp RP Bonasso and R Murphy edors AI-based Moble Robos: Case sudes of successful robo sysems MI Press Cambrdge 1998 pp [2] R C Smh P Cheeseman On he Represenaon and Esmaon of Spaal Uncerany Inernaonal Journal of Robocs Research vol 5 no 4 pp [3] J Leonard J D ard os S hrun and H Chose edors Workshop Noes of he ICRA Workshop on Concurren Mappng and Localzaon for Auonomous Moble Robos n Proc IEEE In Conf Robocs and Auomaon Washngon DC 2002 [4] J E Guvan E M Nebo Opmzaon of he smulaneous localzaon and map-buldng algorhm for real-me mplemenaon IEEE rans Robocs and Auomaon vol 17 no 3 pp [5] A J Davson and D W Murray Smulaneous localzaon and map buldng usng acve vson IEEE rans Paern Analyss and Machne Inellgence vol 24 no 7 pp [6] K Murphy and S Russell Rao-blackwellzed parcle flerng for dynamc bayesan neworks n Sequenal mone carlo mehods n pracce Sprnger Verlag 2001 [7] M Monemerlo and S hrun Smulaneous localzaon and mappng wh unknown daa assocaon usng FasSLAM n Proc IEEE In Conf Robocs and Auomaon ape 2003 [8] A J Davson Real-me smulaneous localsaon and mappng wh a sngle camera n Proc of he Nnh In Conf on Compuer Vson ICCV'03 Nce France 2003 pp [9] C Sachnss G Grse and W Burgard Recoverng Parcle Dversy n a Rao-Blackwellzed Parcle Fler for SLAM Afer Acvely Closng Loops n Proc IEEE In Conf Robocs and Auomaon 2005 pp Barcelona Span [10] R Sm P Elnas M Grffn and J Lle Vson-based SLAM usng he Rao-Blackwellzed Parcle Fler n Workshop Reasonng wh Uncerany n Robocs Ednburgh Scoland 2005 [11] M N Daley and M Parnchkun Landmark-based smulaneous localzaon and mappng wh sereo vson n Proc of he 2005 Asan Conf on Indusral Auomaon and Robocs 2005 [12] S Se D Lowe and J Lle Moble robo localzaon and mappng wh uncerany usng scale-nvaran vsual landmarks Inernaonal Journal of Robocs Research 21(8): [13] A Davson Y Cd and N Ka Real-me 3D SLAM wh wde-angle vson n Proceedngs of he IFAC Symposum on Inellgen Auonomous Vehcles 2004 [14] D Lowe Dsncve mage feaures from scale-nvaran keypons In J of Compuer Vson vol 60 no 2 pp [15] A W Moore An nroducory uoral on kd-rees Robocs Insue Carnege Mellon Unversy Psburgh echncal Repor No 209 Compuer Laboraory Unversy of Cambrdge 1991 [16] R Merwe A Douce N Freas and E Wan he Unscened Parcle Fler echncal Repor CUED/FINFENG /R 380 Cambrdge Unversy Engneerng Deparmen 2000 [17] A Douce On sequenal smulaon-based mehods for Bayesan flerng echncal repor Sgnal Processng Group Deparemen of Engeneerng Unversy of Cambrdge 1998 [18] Ducke A genec algorhm for smulaneous localzaon and mappng n Proc of he IEEE Inernaonal Conference on Robocs and Auomaon 2003 pp [19] J S Lu and R Chen Sequenal Mone Carlo mehods for dynamcal sysems J Amer Sas Assoc vol 93 pp [20] hang Flexble camera calbraon by vewng a plane from unknown orenaons Proc ICCV pp Inernaonal Scholarly and Scenfc Research & Innovaon 2(3) scholarwaseorg/ /15275
Fall 2010 Graduate Course on Dynamic Learning
Fall 200 Graduae Course on Dynamc Learnng Chaper 4: Parcle Flers Sepember 27, 200 Byoung-Tak Zhang School of Compuer Scence and Engneerng & Cognve Scence and Bran Scence Programs Seoul aonal Unversy hp://b.snu.ac.kr/~bzhang/
More informationComputer Robot Vision Conference 2010
School of Compuer Scence McGll Unversy Compuer Robo Vson Conference 2010 Ioanns Rekles Fundamenal Problems In Robocs How o Go From A o B? (Pah Plannng) Wha does he world looks lke? (mappng) sense from
More informationCHAPTER 10: LINEAR DISCRIMINATION
CHAPER : LINEAR DISCRIMINAION Dscrmnan-based Classfcaon 3 In classfcaon h K classes (C,C,, C k ) We defned dscrmnan funcon g j (), j=,,,k hen gven an es eample, e chose (predced) s class label as C f g
More informationRobustness Experiments with Two Variance Components
Naonal Insue of Sandards and Technology (NIST) Informaon Technology Laboraory (ITL) Sascal Engneerng Dvson (SED) Robusness Expermens wh Two Varance Componens by Ana Ivelsse Avlés avles@ns.gov Conference
More informationCS434a/541a: Pattern Recognition Prof. Olga Veksler. Lecture 4
CS434a/54a: Paern Recognon Prof. Olga Veksler Lecure 4 Oulne Normal Random Varable Properes Dscrmnan funcons Why Normal Random Varables? Analycally racable Works well when observaon comes form a corruped
More informationWiH Wei He
Sysem Idenfcaon of onlnear Sae-Space Space Baery odels WH We He wehe@calce.umd.edu Advsor: Dr. Chaochao Chen Deparmen of echancal Engneerng Unversy of aryland, College Par 1 Unversy of aryland Bacground
More informationVariants of Pegasos. December 11, 2009
Inroducon Varans of Pegasos SooWoong Ryu bshboy@sanford.edu December, 009 Youngsoo Cho yc344@sanford.edu Developng a new SVM algorhm s ongong research opc. Among many exng SVM algorhms, we wll focus on
More informationV.Abramov - FURTHER ANALYSIS OF CONFIDENCE INTERVALS FOR LARGE CLIENT/SERVER COMPUTER NETWORKS
R&RATA # Vol.) 8, March FURTHER AALYSIS OF COFIDECE ITERVALS FOR LARGE CLIET/SERVER COMPUTER ETWORKS Vyacheslav Abramov School of Mahemacal Scences, Monash Unversy, Buldng 8, Level 4, Clayon Campus, Wellngon
More informationOn One Analytic Method of. Constructing Program Controls
Appled Mahemacal Scences, Vol. 9, 05, no. 8, 409-407 HIKARI Ld, www.m-hkar.com hp://dx.do.org/0.988/ams.05.54349 On One Analyc Mehod of Consrucng Program Conrols A. N. Kvko, S. V. Chsyakov and Yu. E. Balyna
More informationGenetic Algorithm in Parameter Estimation of Nonlinear Dynamic Systems
Genec Algorhm n Parameer Esmaon of Nonlnear Dynamc Sysems E. Paeraks manos@egnaa.ee.auh.gr V. Perds perds@vergna.eng.auh.gr Ah. ehagas kehagas@egnaa.ee.auh.gr hp://skron.conrol.ee.auh.gr/kehagas/ndex.hm
More informationBayes rule for a classification problem INF Discriminant functions for the normal density. Euclidean distance. Mahalanobis distance
INF 43 3.. Repeon Anne Solberg (anne@f.uo.no Bayes rule for a classfcaon problem Suppose we have J, =,...J classes. s he class label for a pxel, and x s he observed feaure vecor. We can use Bayes rule
More informationJohn Geweke a and Gianni Amisano b a Departments of Economics and Statistics, University of Iowa, USA b European Central Bank, Frankfurt, Germany
Herarchcal Markov Normal Mxure models wh Applcaons o Fnancal Asse Reurns Appendx: Proofs of Theorems and Condonal Poseror Dsrbuons John Geweke a and Gann Amsano b a Deparmens of Economcs and Sascs, Unversy
More informationParticle Filter Based Robot Self-localization Using RGBD Cues and Wheel Odometry Measurements Enyang Gao1, a*, Zhaohua Chen1 and Qizhuhui Gao1
6h Inernaonal Conference on Elecronc, Mechancal, Informaon and Managemen (EMIM 206) Parcle Fler Based Robo Self-localzaon Usng RGBD Cues and Wheel Odomery Measuremens Enyang Gao, a*, Zhaohua Chen and Qzhuhu
More informationThis document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore.
Ths documen s downloaded from DR-NTU, Nanyang Technologcal Unversy Lbrary, Sngapore. Tle A smplfed verb machng algorhm for word paron n vsual speech processng( Acceped verson ) Auhor(s) Foo, Say We; Yong,
More informationDynamic Team Decision Theory. EECS 558 Project Shrutivandana Sharma and David Shuman December 10, 2005
Dynamc Team Decson Theory EECS 558 Proec Shruvandana Sharma and Davd Shuman December 0, 005 Oulne Inroducon o Team Decson Theory Decomposon of he Dynamc Team Decson Problem Equvalence of Sac and Dynamc
More informationSolution in semi infinite diffusion couples (error function analysis)
Soluon n sem nfne dffuson couples (error funcon analyss) Le us consder now he sem nfne dffuson couple of wo blocks wh concenraon of and I means ha, n a A- bnary sysem, s bondng beween wo blocks made of
More informationKernel-Based Bayesian Filtering for Object Tracking
Kernel-Based Bayesan Flerng for Objec Trackng Bohyung Han Yng Zhu Dorn Comancu Larry Davs Dep. of Compuer Scence Real-Tme Vson and Modelng Inegraed Daa and Sysems Unversy of Maryland Semens Corporae Research
More informationOutline. Probabilistic Model Learning. Probabilistic Model Learning. Probabilistic Model for Time-series Data: Hidden Markov Model
Probablsc Model for Tme-seres Daa: Hdden Markov Model Hrosh Mamsuka Bonformacs Cener Kyoo Unversy Oulne Three Problems for probablsc models n machne learnng. Compung lkelhood 2. Learnng 3. Parsng (predcon
More informationFoundations of State Estimation Part II
Foundaons of Sae Esmaon Par II Tocs: Hdden Markov Models Parcle Flers Addonal readng: L.R. Rabner, A uoral on hdden Markov models," Proceedngs of he IEEE, vol. 77,. 57-86, 989. Sequenal Mone Carlo Mehods
More informationFTCS Solution to the Heat Equation
FTCS Soluon o he Hea Equaon ME 448/548 Noes Gerald Reckenwald Porland Sae Unversy Deparmen of Mechancal Engneerng gerry@pdxedu ME 448/548: FTCS Soluon o he Hea Equaon Overvew Use he forward fne d erence
More informationHEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD
Journal of Appled Mahemacs and Compuaonal Mechancs 3, (), 45-5 HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD Sansław Kukla, Urszula Sedlecka Insue of Mahemacs,
More informationdoi: info:doi/ /
do: nfo:do/0.063/.322393 nernaonal Conference on Power Conrol and Opmzaon, Bal, ndonesa, -3, June 2009 A COLOR FEATURES-BASED METHOD FOR OBJECT TRACKNG EMPLOYNG A PARTCLE FLTER ALGORTHM Bud Sugand, Hyoungseop
More informationDepartment of Economics University of Toronto
Deparmen of Economcs Unversy of Torono ECO408F M.A. Economercs Lecure Noes on Heeroskedascy Heeroskedascy o Ths lecure nvolves lookng a modfcaons we need o make o deal wh he regresson model when some of
More informationComputing Relevance, Similarity: The Vector Space Model
Compung Relevance, Smlary: The Vecor Space Model Based on Larson and Hears s sldes a UC-Bereley hp://.sms.bereley.edu/courses/s0/f00/ aabase Managemen Sysems, R. Ramarshnan ocumen Vecors v ocumens are
More informationMANY real-world applications (e.g. production
Barebones Parcle Swarm for Ineger Programmng Problems Mahamed G. H. Omran, Andres Engelbrech and Ayed Salman Absrac The performance of wo recen varans of Parcle Swarm Opmzaon (PSO) when appled o Ineger
More informationEffect of Resampling Steepness on Particle Filtering Performance in Visual Tracking
102 The Inernaonal Arab Journal of Informaon Technology, Vol. 10, No. 1, January 2013 Effec of Resamplng Seepness on Parcle Flerng Performance n Vsual Trackng Zahdul Islam, Ch-Mn Oh, and Chl-Woo Lee School
More informationSingle and Multiple Object Tracking Using a Multi-Feature Joint Sparse Representation
Sngle and Mulple Objec Trackng Usng a Mul-Feaure Jon Sparse Represenaon Wemng Hu, We L, and Xaoqn Zhang (Naonal Laboraory of Paern Recognon, Insue of Auomaon, Chnese Academy of Scences, Bejng 100190) {wmhu,
More informationGray-dynamic EKF for Mobile Robot SLAM in Indoor Environment
Gray-dynamc EKF for Moble obo SLAM n Indoor Envronmen Peng Wang, Qbn Zhang, Zongha hen Deparmen of Auomaon, Unversy of Scence and echnology of hna, Hefe, 6, hna grapesonwang@gmalcom, zqb@malusceducn, chenzh@usceducn
More informationLinear Response Theory: The connection between QFT and experiments
Phys540.nb 39 3 Lnear Response Theory: The connecon beween QFT and expermens 3.1. Basc conceps and deas Q: ow do we measure he conducvy of a meal? A: we frs nroduce a weak elecrc feld E, and hen measure
More informationRobust and Accurate Cancer Classification with Gene Expression Profiling
Robus and Accurae Cancer Classfcaon wh Gene Expresson Proflng (Compuaonal ysems Bology, 2005) Auhor: Hafeng L, Keshu Zhang, ao Jang Oulne Background LDA (lnear dscrmnan analyss) and small sample sze problem
More information( t) Outline of program: BGC1: Survival and event history analysis Oslo, March-May Recapitulation. The additive regression model
BGC1: Survval and even hsory analyss Oslo, March-May 212 Monday May 7h and Tuesday May 8h The addve regresson model Ørnulf Borgan Deparmen of Mahemacs Unversy of Oslo Oulne of program: Recapulaon Counng
More informationApproximate Analytic Solution of (2+1) - Dimensional Zakharov-Kuznetsov(Zk) Equations Using Homotopy
Arcle Inernaonal Journal of Modern Mahemacal Scences, 4, (): - Inernaonal Journal of Modern Mahemacal Scences Journal homepage: www.modernscenfcpress.com/journals/jmms.aspx ISSN: 66-86X Florda, USA Approxmae
More informationClustering (Bishop ch 9)
Cluserng (Bshop ch 9) Reference: Daa Mnng by Margare Dunham (a slde source) 1 Cluserng Cluserng s unsupervsed learnng, here are no class labels Wan o fnd groups of smlar nsances Ofen use a dsance measure
More informationTime-interval analysis of β decay. V. Horvat and J. C. Hardy
Tme-nerval analyss of β decay V. Horva and J. C. Hardy Work on he even analyss of β decay [1] connued and resuled n he developmen of a novel mehod of bea-decay me-nerval analyss ha produces hghly accurae
More informationIn the complete model, these slopes are ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL. (! i+1 -! i ) + [(!") i+1,q - [(!
ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL The frs hng o es n wo-way ANOVA: Is here neracon? "No neracon" means: The man effecs model would f. Ths n urn means: In he neracon plo (wh A on he horzonal
More informationCubic Bezier Homotopy Function for Solving Exponential Equations
Penerb Journal of Advanced Research n Compung and Applcaons ISSN (onlne: 46-97 Vol. 4, No.. Pages -8, 6 omoopy Funcon for Solvng Eponenal Equaons S. S. Raml *,,. Mohamad Nor,a, N. S. Saharzan,b and M.
More informationObject Tracking Based on Visual Attention Model and Particle Filter
Inernaonal Journal of Informaon Technology Vol. No. 9 25 Objec Trackng Based on Vsual Aenon Model and Parcle Fler Long-Fe Zhang, Yuan-Da Cao 2, Mng-Je Zhang 3, Y-Zhuo Wang 4 School of Compuer Scence and
More information5th International Conference on Advanced Design and Manufacturing Engineering (ICADME 2015)
5h Inernaonal onference on Advanced Desgn and Manufacurng Engneerng (IADME 5 The Falure Rae Expermenal Sudy of Specal N Machne Tool hunshan He, a, *, La Pan,b and Bng Hu 3,c,,3 ollege of Mechancal and
More informationLecture 11 SVM cont
Lecure SVM con. 0 008 Wha we have done so far We have esalshed ha we wan o fnd a lnear decson oundary whose margn s he larges We know how o measure he margn of a lnear decson oundary Tha s: he mnmum geomerc
More information( ) () we define the interaction representation by the unitary transformation () = ()
Hgher Order Perurbaon Theory Mchael Fowler 3/7/6 The neracon Represenaon Recall ha n he frs par of hs course sequence, we dscussed he chrödnger and Hesenberg represenaons of quanum mechancs here n he chrödnger
More informationAn introduction to Support Vector Machine
An nroducon o Suppor Vecor Machne 報告者 : 黃立德 References: Smon Haykn, "Neural Neworks: a comprehensve foundaon, second edon, 999, Chaper 2,6 Nello Chrsann, John Shawe-Tayer, An Inroducon o Suppor Vecor Machnes,
More informationPARTICLE FILTER BASED VEHICLE TRACKING APPROACH WITH IMPROVED RESAMPLING STAGE
ISS: 0976-910(OLIE) ICTACT JOURAL O IMAGE AD VIDEO PROCESSIG, FEBRUARY 014, VOLUME: 04, ISSUE: 03 PARTICLE FILTER BASED VEHICLE TRACKIG APPROACH WITH IMPROVED RESAMPLIG STAGE We Leong Khong 1, We Yeang
More informationAttribute Reduction Algorithm Based on Discernibility Matrix with Algebraic Method GAO Jing1,a, Ma Hui1, Han Zhidong2,b
Inernaonal Indusral Informacs and Compuer Engneerng Conference (IIICEC 05) Arbue educon Algorhm Based on Dscernbly Marx wh Algebrac Mehod GAO Jng,a, Ma Hu, Han Zhdong,b Informaon School, Capal Unversy
More informationNew M-Estimator Objective Function. in Simultaneous Equations Model. (A Comparative Study)
Inernaonal Mahemacal Forum, Vol. 8, 3, no., 7 - HIKARI Ld, www.m-hkar.com hp://dx.do.org/.988/mf.3.3488 New M-Esmaor Objecve Funcon n Smulaneous Equaons Model (A Comparave Sudy) Ahmed H. Youssef Professor
More informationGENERATING CERTAIN QUINTIC IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS. Youngwoo Ahn and Kitae Kim
Korean J. Mah. 19 (2011), No. 3, pp. 263 272 GENERATING CERTAIN QUINTIC IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS Youngwoo Ahn and Kae Km Absrac. In he paper [1], an explc correspondence beween ceran
More informationAlgorithm Research on Moving Object Detection of Surveillance Video Sequence *
Opcs and Phooncs Journal 03 3 308-3 do:0.436/opj.03.3b07 Publshed Onlne June 03 (hp://www.scrp.org/journal/opj) Algorhm Research on Movng Objec Deecon of Survellance Vdeo Sequence * Kuhe Yang Zhmng Ca
More informationTesting a new idea to solve the P = NP problem with mathematical induction
Tesng a new dea o solve he P = NP problem wh mahemacal nducon Bacground P and NP are wo classes (ses) of languages n Compuer Scence An open problem s wheher P = NP Ths paper ess a new dea o compare he
More informationMachine Learning Linear Regression
Machne Learnng Lnear Regresson Lesson 3 Lnear Regresson Bascs of Regresson Leas Squares esmaon Polynomal Regresson Bass funcons Regresson model Regularzed Regresson Sascal Regresson Mamum Lkelhood (ML)
More informationOn computing differential transform of nonlinear non-autonomous functions and its applications
On compung dfferenal ransform of nonlnear non-auonomous funcons and s applcaons Essam. R. El-Zahar, and Abdelhalm Ebad Deparmen of Mahemacs, Faculy of Scences and Humanes, Prnce Saam Bn Abdulazz Unversy,
More informationLecture 6: Learning for Control (Generalised Linear Regression)
Lecure 6: Learnng for Conrol (Generalsed Lnear Regresson) Conens: Lnear Mehods for Regresson Leas Squares, Gauss Markov heorem Recursve Leas Squares Lecure 6: RLSC - Prof. Sehu Vjayakumar Lnear Regresson
More informationFiltrage particulaire et suivi multi-pistes Carine Hue Jean-Pierre Le Cadre and Patrick Pérez
Chaînes de Markov cachées e flrage parculare 2-22 anver 2002 Flrage parculare e suv mul-pses Carne Hue Jean-Perre Le Cadre and Parck Pérez Conex Applcaons: Sgnal processng: arge rackng bearngs-onl rackng
More informationSampling Procedure of the Sum of two Binary Markov Process Realizations
Samplng Procedure of he Sum of wo Bnary Markov Process Realzaons YURY GORITSKIY Dep. of Mahemacal Modelng of Moscow Power Insue (Techncal Unversy), Moscow, RUSSIA, E-mal: gorsky@yandex.ru VLADIMIR KAZAKOV
More informationA Bayesian algorithm for tracking multiple moving objects in outdoor surveillance video
A Bayesan algorhm for racng mulple movng obecs n oudoor survellance vdeo Manunah Narayana Unversy of Kansas Lawrence, Kansas manu@u.edu Absrac Relable racng of mulple movng obecs n vdes an neresng challenge,
More informationBoosted LMS-based Piecewise Linear Adaptive Filters
016 4h European Sgnal Processng Conference EUSIPCO) Boosed LMS-based Pecewse Lnear Adapve Flers Darush Kar and Iman Marvan Deparmen of Elecrcal and Elecroncs Engneerng Blken Unversy, Ankara, Turkey {kar,
More informationSupplementary Material to: IMU Preintegration on Manifold for E cient Visual-Inertial Maximum-a-Posteriori Estimation
Supplemenary Maeral o: IMU Prenegraon on Manfold for E cen Vsual-Ineral Maxmum-a-Poseror Esmaon echncal Repor G-IRIM-CP&R-05-00 Chrsan Forser, Luca Carlone, Fran Dellaer, and Davde Scaramuzza May 0, 05
More informationChapter 6: AC Circuits
Chaper 6: AC Crcus Chaper 6: Oulne Phasors and he AC Seady Sae AC Crcus A sable, lnear crcu operang n he seady sae wh snusodal excaon (.e., snusodal seady sae. Complee response forced response naural response.
More informationA NEW TECHNIQUE FOR SOLVING THE 1-D BURGERS EQUATION
S19 A NEW TECHNIQUE FOR SOLVING THE 1-D BURGERS EQUATION by Xaojun YANG a,b, Yugu YANG a*, Carlo CATTANI c, and Mngzheng ZHU b a Sae Key Laboraory for Geomechancs and Deep Underground Engneerng, Chna Unversy
More informationA Novel Object Detection Method Using Gaussian Mixture Codebook Model of RGB-D Information
A Novel Objec Deecon Mehod Usng Gaussan Mxure Codebook Model of RGB-D Informaon Lujang LIU 1, Gaopeng ZHAO *,1, Yumng BO 1 1 School of Auomaon, Nanjng Unversy of Scence and Technology, Nanjng, Jangsu 10094,
More informationVolatility Interpolation
Volaly Inerpolaon Prelmnary Verson March 00 Jesper Andreasen and Bran Huge Danse Mares, Copenhagen wan.daddy@danseban.com brno@danseban.com Elecronc copy avalable a: hp://ssrn.com/absrac=69497 Inro Local
More informationRelative controllability of nonlinear systems with delays in control
Relave conrollably o nonlnear sysems wh delays n conrol Jerzy Klamka Insue o Conrol Engneerng, Slesan Techncal Unversy, 44- Glwce, Poland. phone/ax : 48 32 37227, {jklamka}@a.polsl.glwce.pl Keywor: Conrollably.
More informationMachine Learning 2nd Edition
INTRODUCTION TO Lecure Sldes for Machne Learnng nd Edon ETHEM ALPAYDIN, modfed by Leonardo Bobadlla and some pars from hp://www.cs.au.ac.l/~aparzn/machnelearnng/ The MIT Press, 00 alpaydn@boun.edu.r hp://www.cmpe.boun.edu.r/~ehem/mle
More informationCH.3. COMPATIBILITY EQUATIONS. Continuum Mechanics Course (MMC) - ETSECCPB - UPC
CH.3. COMPATIBILITY EQUATIONS Connuum Mechancs Course (MMC) - ETSECCPB - UPC Overvew Compably Condons Compably Equaons of a Poenal Vecor Feld Compably Condons for Infnesmal Srans Inegraon of he Infnesmal
More information( ) [ ] MAP Decision Rule
Announcemens Bayes Decson Theory wh Normal Dsrbuons HW0 due oday HW o be assgned soon Proec descrpon posed Bomercs CSE 90 Lecure 4 CSE90, Sprng 04 CSE90, Sprng 04 Key Probables 4 ω class label X feaure
More informationSingle-loop System Reliability-Based Design & Topology Optimization (SRBDO/SRBTO): A Matrix-based System Reliability (MSR) Method
10 h US Naonal Congress on Compuaonal Mechancs Columbus, Oho 16-19, 2009 Sngle-loop Sysem Relably-Based Desgn & Topology Opmzaon (SRBDO/SRBTO): A Marx-based Sysem Relably (MSR) Mehod Tam Nguyen, Junho
More informationA New Approach for Large-Scale Localization and Mapping: Hybrid Metric-Topological SLAM
27 IEEE Inernaonal Conference on Robocs and Auomaon Roma, Ialy, -14 Aprl 27 ThB1.5 A New Approach for Large-Scale Localzaon and Mappng: Hybrd Merc-Topologcal SLAM Jose-Lus Blanco, Juan-Anono Fernández-Madrgal,
More informationIntroduction ( Week 1-2) Course introduction A brief introduction to molecular biology A brief introduction to sequence comparison Part I: Algorithms
Course organzaon Inroducon Wee -2) Course nroducon A bref nroducon o molecular bology A bref nroducon o sequence comparson Par I: Algorhms for Sequence Analyss Wee 3-8) Chaper -3, Models and heores» Probably
More informationFI 3103 Quantum Physics
/9/4 FI 33 Quanum Physcs Aleander A. Iskandar Physcs of Magnesm and Phooncs Research Grou Insu Teknolog Bandung Basc Conces n Quanum Physcs Probably and Eecaon Value Hesenberg Uncerany Prncle Wave Funcon
More informationJ i-1 i. J i i+1. Numerical integration of the diffusion equation (I) Finite difference method. Spatial Discretization. Internal nodes.
umercal negraon of he dffuson equaon (I) Fne dfference mehod. Spaal screaon. Inernal nodes. R L V For hermal conducon le s dscree he spaal doman no small fne spans, =,,: Balance of parcles for an nernal
More informationExistence and Uniqueness Results for Random Impulsive Integro-Differential Equation
Global Journal of Pure and Appled Mahemacs. ISSN 973-768 Volume 4, Number 6 (8), pp. 89-87 Research Inda Publcaons hp://www.rpublcaon.com Exsence and Unqueness Resuls for Random Impulsve Inegro-Dfferenal
More informationDEEP UNFOLDING FOR MULTICHANNEL SOURCE SEPARATION SUPPLEMENTARY MATERIAL
DEEP UNFOLDING FOR MULTICHANNEL SOURCE SEPARATION SUPPLEMENTARY MATERIAL Sco Wsdom, John Hershey 2, Jonahan Le Roux 2, and Shnj Waanabe 2 Deparmen o Elecrcal Engneerng, Unversy o Washngon, Seale, WA, USA
More informationTackling the Premature Convergence Problem in Monte Carlo Localization Gert Kootstra and Bart de Boer
Tacklng he Premaure Convergence Problem n Mone Carlo Localzaon Ger Koosra and Bar de Boer Auhors: Ger Koosra (correspondng auhor) Arfcal Inellgence Unvesy of Gronngen, The Neherlands Groe Krussraa 2/1
More informationEnhancement of Particle Filter Resampling in Vehicle Tracking via Genetic Algorithm
01 UKSm-AMSS 6h European Modellng Symposum Enhancemen of Parcle Fler Resamplng n Vehcle Trackng va Genec Algorhm We Leong Khong, We Yeang Ko, Y Kong Chn, Me Yeen Choong, Kenneh Tze Kn Teo Modellng, Smulaon
More informationTHE PREDICTION OF COMPETITIVE ENVIRONMENT IN BUSINESS
THE PREICTION OF COMPETITIVE ENVIRONMENT IN BUSINESS INTROUCTION The wo dmensonal paral dfferenal equaons of second order can be used for he smulaon of compeve envronmen n busness The arcle presens he
More informationBayesian Inference of the GARCH model with Rational Errors
0 Inernaonal Conference on Economcs, Busness and Markeng Managemen IPEDR vol.9 (0) (0) IACSIT Press, Sngapore Bayesan Inference of he GARCH model wh Raonal Errors Tesuya Takash + and Tng Tng Chen Hroshma
More informationComb Filters. Comb Filters
The smple flers dscussed so far are characered eher by a sngle passband and/or a sngle sopband There are applcaons where flers wh mulple passbands and sopbands are requred Thecomb fler s an example of
More informationLecture VI Regression
Lecure VI Regresson (Lnear Mehods for Regresson) Conens: Lnear Mehods for Regresson Leas Squares, Gauss Markov heorem Recursve Leas Squares Lecure VI: MLSC - Dr. Sehu Vjayakumar Lnear Regresson Model M
More informationJanuary Examinations 2012
Page of 5 EC79 January Examnaons No. of Pages: 5 No. of Quesons: 8 Subjec ECONOMICS (POSTGRADUATE) Tle of Paper EC79 QUANTITATIVE METHODS FOR BUSINESS AND FINANCE Tme Allowed Two Hours ( hours) Insrucons
More informationComparison of Differences between Power Means 1
In. Journal of Mah. Analyss, Vol. 7, 203, no., 5-55 Comparson of Dfferences beween Power Means Chang-An Tan, Guanghua Sh and Fe Zuo College of Mahemacs and Informaon Scence Henan Normal Unversy, 453007,
More informationImplementation of Quantized State Systems in MATLAB/Simulink
SNE T ECHNICAL N OTE Implemenaon of Quanzed Sae Sysems n MATLAB/Smulnk Parck Grabher, Mahas Rößler 2*, Bernhard Henzl 3 Ins. of Analyss and Scenfc Compung, Venna Unversy of Technology, Wedner Haupsraße
More informationDensity Matrix Description of NMR BCMB/CHEM 8190
Densy Marx Descrpon of NMR BCMBCHEM 89 Operaors n Marx Noaon If we say wh one bass se, properes vary only because of changes n he coeffcens weghng each bass se funcon x = h< Ix > - hs s how we calculae
More informationCS286.2 Lecture 14: Quantum de Finetti Theorems II
CS286.2 Lecure 14: Quanum de Fne Theorems II Scrbe: Mara Okounkova 1 Saemen of he heorem Recall he las saemen of he quanum de Fne heorem from he prevous lecure. Theorem 1 Quanum de Fne). Le ρ Dens C 2
More informationNormal Random Variable and its discriminant functions
Noral Rando Varable and s dscrnan funcons Oulne Noral Rando Varable Properes Dscrnan funcons Why Noral Rando Varables? Analycally racable Works well when observaon coes for a corruped snle prooype 3 The
More informationTSS = SST + SSE An orthogonal partition of the total SS
ANOVA: Topc 4. Orhogonal conrass [ST&D p. 183] H 0 : µ 1 = µ =... = µ H 1 : The mean of a leas one reamen group s dfferen To es hs hypohess, a basc ANOVA allocaes he varaon among reamen means (SST) equally
More informationISSN MIT Publications
MIT Inernaonal Journal of Elecrcal and Insrumenaon Engneerng Vol. 1, No. 2, Aug 2011, pp 93-98 93 ISSN 2230-7656 MIT Publcaons A New Approach for Solvng Economc Load Dspach Problem Ansh Ahmad Dep. of Elecrcal
More informationShort-Term Load Forecasting Using PSO-Based Phase Space Neural Networks
Proceedngs of he 5h WSEAS In. Conf. on SIMULATION, MODELING AND OPTIMIZATION, Corfu, Greece, Augus 7-9, 005 (pp78-83) Shor-Term Load Forecasng Usng PSO-Based Phase Space Neural Neworks Jang Chuanwen, Fang
More informationA Monte Carlo Localization Algorithm for 2-D Indoor Self-Localization Based on Magnetic Field
03 8h Inernaonal Conference on Communcaons and Neworkng n Chna (CHINACOM) A Mone Carlo Localzaon Algorhm for -D Indoor Self-Localzaon Based on Magnec Feld Xaohuan Lu, Yunng Dong College of Communcaon and
More informationChapter 6 DETECTION AND ESTIMATION: Model of digital communication system. Fundamental issues in digital communications are
Chaper 6 DEECIO AD EIMAIO: Fundamenal ssues n dgal communcaons are. Deecon and. Esmaon Deecon heory: I deals wh he desgn and evaluaon of decson makng processor ha observes he receved sgnal and guesses
More informationDensity Matrix Description of NMR BCMB/CHEM 8190
Densy Marx Descrpon of NMR BCMBCHEM 89 Operaors n Marx Noaon Alernae approach o second order specra: ask abou x magnezaon nsead of energes and ranson probables. If we say wh one bass se, properes vary
More information2.1 Constitutive Theory
Secon.. Consuve Theory.. Consuve Equaons Governng Equaons The equaons governng he behavour of maerals are (n he spaal form) dρ v & ρ + ρdv v = + ρ = Conservaon of Mass (..a) d x σ j dv dvσ + b = ρ v& +
More informationMath 128b Project. Jude Yuen
Mah 8b Proec Jude Yuen . Inroducon Le { Z } be a sequence of observed ndependen vecor varables. If he elemens of Z have a on normal dsrbuon hen { Z } has a mean vecor Z and a varancecovarance marx z. Geomercally
More informationHidden Markov Models Following a lecture by Andrew W. Moore Carnegie Mellon University
Hdden Markov Models Followng a lecure by Andrew W. Moore Carnege Mellon Unversy www.cs.cmu.edu/~awm/uorals A Markov Sysem Has N saes, called s, s 2.. s N s 2 There are dscree meseps, 0,, s s 3 N 3 0 Hdden
More informationAdvanced Machine Learning & Perception
Advanced Machne Learnng & Percepon Insrucor: Tony Jebara SVM Feaure & Kernel Selecon SVM Eensons Feaure Selecon (Flerng and Wrappng) SVM Feaure Selecon SVM Kernel Selecon SVM Eensons Classfcaon Feaure/Kernel
More informationReactive Methods to Solve the Berth AllocationProblem with Stochastic Arrival and Handling Times
Reacve Mehods o Solve he Berh AllocaonProblem wh Sochasc Arrval and Handlng Tmes Nsh Umang* Mchel Berlare* * TRANSP-OR, Ecole Polyechnque Fédérale de Lausanne Frs Workshop on Large Scale Opmzaon November
More informationDiscrete Markov Process. Introduction. Example: Balls and Urns. Stochastic Automaton. INTRODUCTION TO Machine Learning 3rd Edition
EHEM ALPAYDI he MI Press, 04 Lecure Sldes for IRODUCIO O Machne Learnng 3rd Edon alpaydn@boun.edu.r hp://www.cmpe.boun.edu.r/~ehem/ml3e Sldes from exboo resource page. Slghly eded and wh addonal examples
More information. The geometric multiplicity is dim[ker( λi. number of linearly independent eigenvectors associated with this eigenvalue.
Lnear Algebra Lecure # Noes We connue wh he dscusson of egenvalues, egenvecors, and dagonalzably of marces We wan o know, n parcular wha condons wll assure ha a marx can be dagonalzed and wha he obsrucons
More informationEfficient Asynchronous Channel Hopping Design for Cognitive Radio Networks
Effcen Asynchronous Channel Hoppng Desgn for Cognve Rado Neworks Chh-Mn Chao, Chen-Yu Hsu, and Yun-ng Lng Absrac In a cognve rado nework (CRN), a necessary condon for nodes o communcae wh each oher s ha
More informationThe Finite Element Method for the Analysis of Non-Linear and Dynamic Systems
Swss Federal Insue of Page 1 The Fne Elemen Mehod for he Analyss of Non-Lnear and Dynamc Sysems Prof. Dr. Mchael Havbro Faber Dr. Nebojsa Mojslovc Swss Federal Insue of ETH Zurch, Swzerland Mehod of Fne
More informationIntroduction to Boosting
Inroducon o Boosng Cynha Rudn PACM, Prnceon Unversy Advsors Ingrd Daubeches and Rober Schapre Say you have a daabase of news arcles, +, +, -, -, +, +, -, -, +, +, -, -, +, +, -, + where arcles are labeled
More information. The geometric multiplicity is dim[ker( λi. A )], i.e. the number of linearly independent eigenvectors associated with this eigenvalue.
Mah E-b Lecure #0 Noes We connue wh he dscusson of egenvalues, egenvecors, and dagonalzably of marces We wan o know, n parcular wha condons wll assure ha a marx can be dagonalzed and wha he obsrucons are
More informationON THE WEAK LIMITS OF SMOOTH MAPS FOR THE DIRICHLET ENERGY BETWEEN MANIFOLDS
ON THE WEA LIMITS OF SMOOTH MAPS FOR THE DIRICHLET ENERGY BETWEEN MANIFOLDS FENGBO HANG Absrac. We denfy all he weak sequenal lms of smooh maps n W (M N). In parcular, hs mples a necessary su cen opologcal
More information