Par+cle Filtering. CSE 473: Ar+ficial Intelligence Par+cle Filters. Par+cle Filtering: Elapse Time. Representa+on: Par+cles

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1 CSE 473: Ar+ficil Inelligence Pr+cle Filers Dieer Fo Universiy of Wshingon [Mos slides were creed y Dn Klein nd Pieer Aeel for CS88 Inro o AI UC Berkeley. All CS88 merils re ville ho://i.erkeley.ed.] Filering: roime sol+on Pr+cle Filering Some+mes X is oo ig o se ec inference X my e oo ig o even sore BX E.g. X is con+nos X 2 my e oo ig o do des Sol+on: roime inference Trck smles of X, no ll vles Smles re clled r+cles Time er se is liner in he nmer of smles B: nmer needed my e lrge In memory: lis of r+cles, no ses This is how roo locliz+on works in rc+ce Reresen+on: Pr+cles Pr+cle Filering: Else Time Or reresen+on of PX is now lis of N r+cles smles Generlly, N << X Soring m from X o cons wold defe he oin P roimed y nmer of r+cles wih vle So, mny my hve P = 0! More r+cles, more ccrcy For now, ll r+cles hve weigh of Pr+cles:,2 Ech r+cle is moved y smling is ne osi+on from he rnsi+on model This is like rior smling smles freqencies reflec he rnsi+on roili+es Here, mos smles move clockwise, some move in noher direc+on or sy in lce This cres he ssge of +me If enogh smles, close o ec vles efore nd jer consisen Pr+cles:,2 Pr+cles: 3,,3 2,2 Pr+cle Filering: Oserve Pr+cle Filering: Resmle Slighly rickier: Don smle oserv+on, fi i Similr o likelihood weigh+ng, downweigh smles sed on he evidence Pr+cles: 3,,3 2,2 Rher hn rcking weighed smles, we resmle N +mes, we choose from or weighed smle disri+on i.e. drw wih relcemen Pr+cles: w=.9 w=.2 w=.9 3, w=.4 w=.4 w=.9,3 w=. w=.2 w=.9 2,2 w=.4 As efore, he roili+es don sm o one, since ll hve een downweighed in fc hey now sm o N +mes n roim+on of Pe Pr+cles: w=.9 w=.2 w=.9 3, w=.4 w=.4 w=.9,3 w=. w=.2 w=.9 2,2 w=.4 This is eqivlen o renormlizing he disri+on Now he de is comlee for his +me se, con+ne wih he ne one New Pr+cles: 2,2,3

2 Rec: Pr+cle Filering Pr+cles: rck smles of ses rher hn n elici disri+on Video of Demo Modere Nmer of Pr+cles Else Weigh Resmle Pr+cles:,2 Pr+cles: 3,,3 2,2 Pr+cles: w=.9 w=.2 w=.9 3, w=.4 w=.4 w=.9,3 w=. w=.2 w=.9 2,2 w=.4 New Pr+cles: 2,2,3 [Demos: ghossers r+cle filering L5D3,4,5] Video of Demo One Pr+cle Video of Demo Hge Nmer of Pr+cles Dynmic Byes Nes Dynmic Byes Nes DBNs We wn o rck ml+le vriles over +me, sing ml+le sorces of evidence Ide: Ree fied Byes ne srcre ech +me Vriles from +me cn condi+on on hose from - = =2 =3 G G 2 G 3 G G 2 G 3 E E E 2 E 2 E 3 E 3 Dynmic Byes nes re generliz+on of HMMs [Demo: cmn sonr ghos DBN model L5D6] 2

3 Video of Demo Pcmn Sonr Ghos DBN Model Ec Inference in DBNs Vrile elimin+on lies o dynmic Byes nes Procedre: nroll he nework for T +me ses, hen elimine vriles n+l PX T e :T is comed = =2 =3 G G 2 G 3 G G 2 G 3 E E E 2 E 2 E 3 E 3 Online elief des: Elimine ll vriles from he revios +me se; sore fcors for crren +me only DBN Pr+cle Filers A r+cle is comlee smle for +me se Ini,lize: Genere rior smles for he = Byes ne Emle r+cle: G = G = 5,3 Else,me: Smle sccessor for ech r+cle Emle sccessor: G 2 = G 2 = 6,3 Some More Thoghs on Pricle Filers nd Smling Oserve: Weigh ech en're smle y he likelihood of he evidence condi+oned on he smle Likelihood: PE G * PE G Resmle: Selec rior smles les of vles in roor+on o heir likelihood Roo Locliz+on In roo locliz+on: We know he m, no he roo s osi+on Oserv+ons my e vecors of rnge finder redings Se sce nd redings re yiclly con+nos works siclly like very fine grid nd so we cnno sore BX Pr+cle filering is min echniqe Piecewise Consn ief CSE-57 - Proilisic Rooics 5/5/5 8 3

4 Piecewise Consn Reresenion Proimiy Sensor Model =<, y, θ > Lser sensor Sonr sensor CSE-57 - Proilisic Rooics 5/5/5 9 Proilisic Kinemics Roo moves from, y,θ o ', y',. θ ' Odomery informion = δ. ro, δ ro2, δrns Proilisic Kinemics Odomery informion is inherenly noisy. δ rns = 2 2 ' + y' y δ = n2 y' y, ' θ δ ro = θ θ δ ro2 ' ro, y,θ δ δ rns ro ', y', θ ' δ ro2, Sonrs nd Occncy Grid M Lser-sed Loclizion CSE-57 - Proilisic Rooics 5/5/5 23 CSE-57 - Proilisic Rooics 5/5/5 24 4

5 Smle-Bsed Densiy Aroimion Pricle ses cn e sed o roime densiies The more ricles fll ino n inervl, he higher he roiliy of h inervl Imornce Smling Princile We cn se differen disriion g o genere smles from f By inrodcing n imornce weigh w, we cn ccon for he differences eween g nd f w = f / g f is ofen clled rge g is ofen clled roosl How o drw smles form fncion/disriion? Pricle Filers Sensor Informion: Imornce Smling α z α z w = α z Roo Moion, ' ' d ' Sensor Informion: Imornce Smling α z α z w = α z 5

6 6 Roo Moion ' d ' ', drw i - from - drw i from i -, - Imornce fcor for i :,, disriion roosl rge disriion i z z w = = η, = d z η Pricle Filer Algorihm Sr Smled Moion Model

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9 49 50 Recovery from Filre 5 Pr+cle Filer Locliz+on Sonr Loclizion for AIBO roos [Video: glol- floor.gif] 9

10 Hyrid Model for Peole Trcking WiFi Sensor Model Men Vrince Trcking Emle Adive Smling KLD-Smling Sonr KLD-Smling Lser Ad nmer of ricles on he fly sed on sisicl roimion mesre 0

11 Roo Ming Pr+cle Filer SLAM Video 2 SLAM: Simlneos Locliz+on And Ming We do no know he m or or loc+on Se consiss of osi+on AND m! Min echniqes: Klmn filering Gssin HMMs nd r+cle mehods DP- SLAM, Ron Prr [Demo: PARTICLES- SLAM- ming- new.vi] [Demo: PARTICLES- SLAM- fsslm.vi]