HAL Id: inria-00072605
https://hal.inria.fr/inria-00072605
Submitted on 24 May 2006
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub-
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non,
Tracking Multiple Objects with Particle Filtering
Carine Hue, Jean-Pierre Le Cadre, Patrick Pérez
To cite this version:
Carine Hue, Jean-Pierre Le Cadre, Patrick Pérez. Tracking Multiple Objects with Particle Filtering.
[Research Report] RR-4033, INRIA. 2000. �inria-00072605�
ISRN INRIA/RR--4033--FR+ENG
a p p o r t
d e r e c h e r c h e
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE
Tracking Multiple Objects with Particle Filtering
Carine Hue , Jean-Pierre Le Cadre , Patrick Pérez
N˚4033
Octobre 2000
THÈME 3
132547698:<;=:?>A@!BC:D2C8EF*6G:D474H:?IJ:?1325K47:ML@NFO25PQ4H69RTSUFWVD4H:DXMY
Z0[]\/^3_`bacedDfg_Hhjilkfjmonldp[]nl^q^3_/r9^isk%[tmod]_lu
mv^ixwl_HyHuAz]nsd]d]{H_HyHu]knld]dtixm|yjygisdtk_7y
}!hjnx~_/f Wm|yf%i
Jis]Cnshgf z]_*hg_7k%[]_/h%k%[]_dbs ls`l`Makfjns]hj_*xsl*asqtixwl_Hy
pH/T]ss _pisz]z]hg_7ygyfj[]_]hjns]v_/^nx0^b]ofgmofjishgwl_f*fgh%isk%Amvd]w_/dtk/ns]dDfj_/hj_HzMmod^ixdAMygmofgr
ixfgmvnsdtyOmvdMygmowldtixnshOmo^ixwl_b]hjnk_7ygygmodtwt _3knldty m|z_Hhy fgnk%[tilyfjmvkz]Dd5ix^3mvkqygAy fg_H^yOz_/fg_7kfg_7z<A
nltyg_/hj¡Qixfgmvnsd¢thgnk_7ygyg_HyHZ0[]_*zm¤£¢k/]¤fpomv_Hy0nldpfj[]_¥iskf0fj[tiTf0fg[t_*_Hy fgmv^3ixfgmvnsdnx¦fj[]_y fjiTfj_Hy+d]_H_Hz]y
fjnOAd]nT§¨fg[]_ isyjygmowldtiTfjmonldnx5fg[]_0ns5y _Hhg¡TiTfjmonldty©fjnfg[]_0^bt¤fjmo]v_+fjishgwl_fjyH _0]hjnsCnlyg_ªixd«_¬Afg_Hdtygmonld
ns0fg[]_k|isyjy m|k/isNtixhgfgm|kv_®tofg_Hhb§ []_Hhg_fj[]_py fgnk%[tilyfjmvk¡l_HkfgnshbnxJisyjy mvwsd5iTfgmvnsdm|y_Hy fgmv^iTfj_HzAi
¯ mv]tyWygis^qto_HhH!Z0[]m|yJisowlnshjm¤fj[]^mvyJty _7zfgn3_Hy fgmv^iTfg_°fj[]_°fgh%iT~_7kfjnshjmo_7yªns^«]ofgmv]o_fjixhjws_/fjyª±hjns^
fj[]_/mvhd]nsm|y C_Hixhjmvd]wlyHutfj[AtyOyg[]nT§ mvd]w¢mofjyix]mvvm¤ffgny nlo¡l_*fg[]_3z]ixfji¢ilygygnkm|iTfgmvnsd]hjnsto_H^²³nshj_r
nT¡l_/h´fg[]m|y0ixvwsnshjmofg[]^µk/isdp_Hily mvvqC__¬Afg_Hdtz_Hz¢fgn«^b]ofgmvhg_7k_Hmo¡l_/h+nstyg_/hj¡TiTfgmvnsd5y!§ []_Hhg_Wfg[]_hg_7k_Hmo¡l_/h%y
kHixd]hjnAz]tk_°^3_Hily ]hj_/^3_Hdlf%y+nx¡Qishgmvns5yªd5iTfgthg_°§ mofg[³zmo¶C_Hhg_HdlfJC_/hjmvnAz]mvk/m¤fjmo_7y/
·³¸D¹»ºj¼b½
T¾s
²³t¤fjm¤f%ixhjws_f3fjhjilk%Dmvd]w5u!tixhgfgm|kv_®tofg_/h7u ¿0iQs_Hygm|ixd¨_7yfjmo^iTfjmonldu
¯
mo]5y¢ygis^3]o_HhHu
^«]ofgmvhg_7k_/mv¡s_HhHuAC_Hishgmvd]wly rÀnsd]v3fgh%isk%Amvd]wt
Á|©ÃgÄÀÅHÆ0à ÇÈvÄÀÉ9ÊË
Ì!ͱΦͥÏHÐ?ѻҦÓQÔÕÖ×GØGÔÙ9ÚNÛ7Ö!ΦÖÓQÓQÖØ´ÜÝxÞ©ß%×GÔàÓ7Öáâ¦ãQÖgäÔà×GÔàØ9ß7áåv×
æ
ͱΦͥÏHÐ?Ñ©Þ©çÎÏsÝ7èàÖégß%Û7×GÖgäÔà×¥ÔàØÀß7áåo×
êNë
Ôàé ×¥ìØ9ì%å¤ÙΦÖØGÖgß%×¥éÀíbÞ»ÖÓ/ÙGÖ× ÝxÞß%îªïQ×¥ÔàÛQðÖÝTñQñxÖ×GÖògäî Ôàé×GìØGì%åoÙ áéìî
Unité de recherche INRIA Rennes
nltyªfgh%ixmofgnldtyªztixdty0k_h%ix]Cnshgfªv_Othgnl]o\H^3_Ozy tmo¡Am©z_]o5y mv_/]h%yªns~_/fjy0y nl]¡s_HdDf
hj_/d5knsdDfjhg{!_Hdfjhjism¤fj_/^3_/dDfz]«ygmowldtixD_f_/d«mo^ixwl_/hjmo_l nltyknsd5y m|z{/hjnsd5y¦z_7yygyfj\/^3_HyzAdtis^qmD]_Hy
z]{fg_7kfj{Hytish¢z_Hy¢]hgnk/_Hyjy tyznlty _Hhg¡TixfgmvnsdtyH¦i]hjmvdtkmvtixv_<zmo£¢k]ofg{³hj_/Cnlyg_<y tho_³¥ism¤fD]_
_Hy fgmv^3ixfgmvnsd z_Hyq{f%iTf%y«dt{Hk_7ygygmofg_z_k/nsd]d5i|fghj_v_Hy3isyjygnAk/mvixfgmvnsdty«z_Hyqnlty _Hhg¡Tixfgmvnsdtyqix¬ nl~_f%y/
nsty]hgnl5nDy nldtymvk/m!]d]_p_¬Afg_Hdty mvnsdz®tofghj_tish fjmvk/]vismohj_k|isyjy mD]_z]ixd5y°o_ lt_/!v_¢¡s_7kfj_/]hz_
thgnltix]mvvm¤fj{z_7yisyjy nk/mvixfgmvnsdty«_Hy f_Hy fgmv^q{tish3]d.{7k%[tixdDfjmovonld]_/thqz_ ¯ mv]tyH!"isowlnshjm¤fj[]^3__7yf
]fgmvom|y {5nl]hq_Hy fgmv^q_Hhbv_Hybfgh%iT~_7kfgnlmohj_Hybz_p]vtygmo_H]h%ybnl~_f%y]d]mD]_/^3_Hdlfqwsh$#sk/_%³v_/]h%yb^3_7y ]hj_Hy
zisd]wsv_Hy_f*]hjnst¡s_«yjik/ix5iskmofg{&%hg{7y nltzhj_bv_3]hgnl]v\/^3_qzilygygnkm|iTfgmvnsd¦('W_3]vtyHuisowlnshjm¤fj[]^3_
C_/]f*)fghj_3{fj_/dtzixk/ily°z+nltyg_/hj¡Qixfgmvnsdtym|ygygty*z_kHixfj_/]h%y°zm¤¶»{/hj_/dDf%y°5nl]¡TixdDf*]hgnztmohj_3o_H]hjy
^3_7y ]hj_Hy0iQ¡l_Hk°z_Hy0C{/hjmvnAz]mvk/m¤fj{Hy yg_/^btvis]o_7y0nszmo¶C{Hhg_Hdlfj_HyH
, ½ 7 º .- / ]mv¡Am^b]ofgmor9nl~_f%y/ux®t¤fjhjisws_+tixhgfgm|ktvismohj_suQ_Hy fgmv^iTfjmonldq¿0iQs{7y mv_/dtd]_suQ{Hk%[5ixdDfgmvovnsdtd]_/]h
z]_ ¯ mv]tyHu]^«]¤fjmohj{Hk/_/fj_/]h7u]m|yf%ixwl_5ixh ^3_Hyg]hj_°zisd]wsv_HyH
1 2
«¦ ´
²<]¤fjm¤f%ixhjws_/fªfjhjilk%Dmvd]w43566870z_7ix|yª§ mofg[³y fjixfg__Hy fgmv^3ixfgmvnsdnxisdtd]Ad]nT§ dpdA]^«5_Hh nx93¥^qnT¡Amvd]w7
f%ixhjws_/fjyH9:¡Qismo|ixto_^3_7isyg]hg_H^3_/dDfjy0^iQ[tiQ¡s_°nshjmvwsmvdtiTfj_Hz±hgnl^$fj[]_f%ixhjws_f%y0m¤Nfj[]_/ixhj_z_/fg_Hkfg_7z
nlh0nxiqyg5_7km|ix»^3nAz]_/k/isov_Hz<;k/o]f fg_Hh=;x/>ªofgfg_Hh mvy+ws_Hd]_/h%ixvv¢knsd5y m|z_/hj_Hzpisy0iq^qnz_Hz_Hyjkhjmv]modtw
¥isvyg_°ix|ixhj^3yHcÀfjy'3¥ygtixfgmvnxr9fg_/^3Cnsh%ix7!y fjixfgm|yfjmvkHix©]hjnsC_/hgfgmv_Hy+ixhj_ D]mofg_*zmo¶»_/hj_/dDf0±hgnl^µfjixhjws_/f+nld]_Hy
§ [tmvk%[^ixs_7y+5nDygygmoto_fg[t_y _Htixh%iTfjmonldpnxfjishgwl_f0fgh%isk%y+nsdfg[]_*nld]_°[tixd5zisdtzk/o]f fg_HhJ^3nz_/©nld
fj[]_°y _7knsd5z©NZ¦n«5_Hh ±nlhg^µ^bt¤fjm¤f%ixhjws_fªfgh%isk%Amvd]wfj[]_Onltyg_/hj¡s_/h´[tisy+iTf0m¤f%y0zmvygCnlyjix»i[A]ws_ix^3nstdlf
ns»ztiTfjitusCnlyjy mv]v«k/nsvo_7kfg_7zbnld3^b]ofgmv]v_Jhg_7k_Hmo¡l_/h%y/@?!o_H^3_/dDfjishg^3_7isyg]hg_H^3_/dDfjy!ishg_0hj_Hk/_/mv¡s_/hnlf r
tfjyHu]_swtvuC_Hixhjmvd]wlyHuAhjisd]ws_7y/uDfgmv^3_rez_/|iQy/u 'Onst]o_HhjyHu_f%kx
¿+ffg[]_+^ixmvdbzmo£¢k]ofknl^q_7y©±hjns^ fg[t_+ilygygmowld]^3_/dDf¦ns5i wsmv¡s_Hd^3_Hily ]hj_/^3_Hdlf¦fgnOiJfjishgwl_f^3nz_HG
AtnshWk/hgmofgm|k/isy mofg5iTfgmvnsd5y/ufj[]_Hyg_bilygygmowld]^3_/dDfjy ishg_°]dtDdtnT§ dutisyWixhj_Ofj[]_*fjhg]_°f%ixhjws_/fJ^qnz_HvyHªZ0[tmvy
m|y+id]_7iTf+z]_/tish fj]hg_J±hgnl^µk/vilygygm|k/ixt_Hy fgmv^3ixfgmvnsd¢thgnl]o_H^y/Z0[Aty/uDf§+nbzm|yfjmod5kf0]hgnl]v_/^y![tiQ¡l_ fgn
C_ygnsv¡s_HzB "CD EFHG!z]ixfji3isyjygnAk/mvixfgmvnsdixdtz_Hy fgmv^iTfgmvnsd¦
Z0[t_y mv^3]o_HhJix]thgnDisk%[mvy0]hjns5ix]vfg[t_
_7ixhj_Hy f
_/mvws[ACnshJixt]hgnDisk%[(IOy mvd]wnsdtofj[]_nlty _Hhg¡Tixr
fjmonldfj[]_+k/onDy _7yffgnOfg[]_+]hj_Hzm|kfj_Hz«yf%iTfg_luQfg[]_0ixvwsnlhgmofg[t^ m|yd]nxfhgnl]ty f_Hd]ns]wl[mvdb^ixdA*y mofg5iTfgmvnsd5y/
²<nshj_J_/|ixCnsh%iTfj_Hz©ulfg[]_KJlnsmvdlfª}"':LAM3ONPDQ!7uA_¬Afg_Hdtygmonld¢nx©fj[]_O}´hgnltix]mvvmvy fgm|k 'iTfjiR:WyjygnAk/mvixfgmvnsdAmv¤r
fj_/h±nlhN^b]ofgmv]v_ ns~_7kfjy,3SNT"Q7us_7yfjmo^iTfj_Hyfj[]_Jyf%iTfj_HyAbi°y t^ nT¡s_HhisoAfj[]_JisyjygnAk/mvixfgmvnsdty§+_/mvws[Dfg_7z
Apfg[]_thgnltix]mvvm¤fjmo_7y+fg[tixfOi3^3_Hisyg]hj_/^3_/dDfJm|yJisyjygnAk/mvixfg_7z¢fjnpiqfjishgwl_fH Od]v¢fg[t_bisyjy nk/mvixfgmvnsdty0iTf
nld]_«fgmv^q_3C_/hjmonzixhj_bfj[]_/hj_3knsd5y m|z_/hj_Hz«Z0[]_3²³]ofgmv]v_UJA5nsfg[]_7y m|y°Z¦h%isk%l_/hhg_7k]h%ygmo¡l_/vt]mo|z]y
fj[]_isyjy nk/mvixfgmvnsd?[AACnxfg[t_Hygmvy*isdtzMilygyg]^3_HyOfj[tiTf*_Hilk%[M^3_7isyg]hg_H^3_/dDf°kHixd5_3m|ygyg]_7z<±hjns^ id]_H§
ygnsthjk/_s¦¿+_HkHixtyg_Nfj[]_Hyg_´f§+nOisowlnshjm¤fj[]^y¦ilygyg]^3_Nfg[5iTfnsd]_´fjixhjws_/f]hjnztk/_Hynsd]v°nsd]_ª^q_7isyg]hj_su7fg[]_
yg_fnx´ilygygnkm|iTfgmvnsd5y0fgn5_«_/dA]^3_/h%iTfj_Hz³wlhgnT§Jy _/¬5nld]_/dDfgm|ixvvisdtz³C_Hknl^3_Hy ltmvk%AvmvdDfgh%iskf%ix]v_s
Znknl5_°§ mofg[fg[]m|y ]hjnsto_H^uthg]dtmod]wisdtzpwDiTfjmod]wq_/vmv^qmvdtixfg_°fg[t_*o_7ygy0vmol_/v¢[AA5nsfg[]_7y _7yªtfWk/isd
fjnAnq_Homv^3mod5iTfg_*wlnAnAzkv]_7y/
Z0[tmvyb]hgnl]v_/^ m|ydtn<^3nshj_ }NrÀ[tixh%z isyby nAnsd ily*fg[t_pisyjy nk/mvixfgmvnsdty°¡Tixhjm|ix]v_Hyishg_¢k/nsdtygm|z_/hj_Hzisy
y fgnk%[tilyfjmvk3¡Tishgm|ix]v_Hybixdtz^3nshj_/nT¡l_/hy fjixfgm|yfjmvkHixvomod5z_/C_/dtz]_/dDf«vmol_¢mvdfg[]_}!hgnltixtmovmvy fgm|k¢²VUOZ
3¥}´²VUOZ7=A]nsh¦_¬]ix^3]v_!mvdWNs=QlnlhXNZY=Q9uHfg[t_ªixvwsnlhgmofg[t^)mvy¦]hj_Hyg_/dDfg_7zily¦isdmvdtk/ns^3]v_fg_ªz]iTf%i ]hjns]v_/^
ygnsv¡s_7zApixd?´² ixvwsnshjmofg[]^NZ0[]_hg_7y ]ofjy ishg_Wfg[]_HdyjiTfjmvy ¥iskfgnlhg3§ []_Hdpfj[]_°^q_7isyg]hj_/^3_/dDf0_DtiTr
fjmonldmvy0vmodt_HixhJisdtz§ []_/dfj[]_°fgh%iT~_7kfgnlhgmv_Hy0ishg_*z_/fg_/hj^3modtmvy fgm|kx!ced<NàT-Q¦fg[]_isowlnshjm¤fj[]^$m|y _¬Afg_Hdtz_7z
fjnfj[]_Wfjhjilk%Amod]wbnx^ixd]_H]¡s_Hhgmvd]w*f%ixhjws_/fjy!§ mofg[ixd[]mvztz_/dH[^3nz_/orey § mofjk%[]\J]hjnk_7ygyªknsdDfjhgnlov_Hz3A
i²?ixhjsnT¡]hjnstis]mvomofy fghjtkfj]hj_s9: kns^3tishgm|ygnsdnxfg[]_}ª²VUWZ § mofg[³fj[]_^Js} ':LA m|yJz_Hyjkhjmv5_7z
mvdpi*thjilkfgm|k/isf§+nxr9fjixhjws_/f´ygk/_/dtishgmvn*mvdVNT7=QÀus±nk5y mvd]wnldfg[]_O^3_Hixd]rÀy Dtixhj_0_Hy fgmv^3ixfgmvnsd¢_Hhghjnsh%yNixd5z
fj[]_C_/h%k_Hdlf%ixwl_*nx!vnly f fgh%isk%y/,UWnT§ª_H¡s_/h7ufj[]_Hyg_bixvwsnlhgmofg[t^3yWzn¢d]nsfOknl5_§ mofg[?d]nsd³vmodt_HixhOyf%iTfg_
nlh0^q_7isyg]hj_/^3_/dDf ^3nAz]_/|yJixdtzd]nld ¯ istygygm|ixdyf%iTfg_°nlh ^q_7isyg]hj_/^3_/dDf d]nsm|yg_HyH
IWdtz_Hh¢y tk%[ isyjy t^q]fgmvnsdty_3¥y fgnk%[tilyfjmvky fjiTfj__DtiTfjmonld.isdtz dtnsd vmvd]_Hish3y fjixfg_nsh3^3_Hily thg_H^q_HdDf
_ DtiTfjmonlduTd]nsd ¯ ixtyjy m|ixdbd]nsm|y _7y7uQfg[]_0tish fjmvk/o_´®tofg_/h7uxix|ygnWdtis^q_7zCnAnxfjy fgh%ix®t¤fj_/h7uxm|y¦tish fjmvk/]|ixhjo
ilz]ix]fg_HzWcÀfO^ismod]v³knldty m|y fjyJmvd<]hjns5ixwlixfgmvd]w¢i¢§+_/mvws[Dfj_Hz³yg_fOns!tixhgfgm|kv_HyW§ []m|k%[?ix]thgnQ¬mv^3ixfg_7y
fj[]_+]hgnltixtmovm¤f*z_Hdtygm¤f*ns]fg[]_0y fjiTfj_+k/nsdtz]m¤fjmonldtixvofjnWfj[]_0nstyg_/hj¡TiTfgmvnsd5y/cÀfNk/isdbC_+is]]vmo_7z]d5z_/h
¡l_/hj3§ª_7ix[AA5nsfg[]_7y _7y+isdtz¢m|y+¡s_Hhg_7isyg3fgnqmo^3]v_/^3_/dDf7Ncedtish fjmvk/]|ixh7usfj[]_°^q_7isyg]hj_/^3_/dDf0_DtiTr
fjmonld³k/ixdC_*d]nsdvmodt_HixhJisdtzfg[]_«zAdtix^3m|k*ixdtzns5y _Hhg¡TiTfjmonldpd]nlmvyg_Hy kHixdC_d]nsd
¯
istygygm|ixd / 5k%[
®5¤fj_/h%y[tiQ¡s_+5_H_/dqtyg_Hzqmodq¡s_Hhg*¡Tishgmvnstyishg_7isy¦±nsh!¿0iQs_7y m|ixd*®5¤fj_/hjmod]w5ux]dtz]_/h!zmo¶C_Hhg_HdDf!dtix^3_Hy`Gfg[]_
CnAnxf%yfjhjis®tofg_Hh±nlhfjixhjws_/ffjhjilk%Amod]wOmod4NaDQÀuTfg[]_L>ªnldtz_/d5ygixfgmvnsdbisowlnshjm¤fj[]^mod3knl^3]fg_Hh¡Dm|ygmonld+NbTcT-Q
ishg_bf§ªnp_¬]ix^3]v_Hy°ix^3nld]w¢nxfj[]_/h%yHK:+ffg[t_«C_/wlmod]dtmod]wDyWns´tish fjmvk/o_b®t¤fj_/hjmodtwtuCfg[]_3ixvwsnlhgmofg[t^ §0isy
nld]v3k/ns^3Cnlyg_Hznsf§ªn«5_Hhgmvnz]y Gfg[]_tixhgfgm|kv_Hyª§+_/hj_W]hj_Hzm|kfj_Hzisk/k/nsh%zmvd]w*fgn«fg[t_y fjixfg__DtiTfjmonld
z]]hgmvd]w°fj[]_W]hj_Hz]mvkfgmvnsd¢y fg_/sfj[]_/dfj[]_/mvh´§+_/mvws[Df%yN§ª_Hhg_JkHix|k]|iTfj_Hz3§ mofg[3fj[]_Wvmol_/vmo[tnDnzqnx»fj[]_Wd]_H§
nltyg_/hj¡Qixfgmvnsd<k/ns^btmod]_7z³§ mofg[³fj[]_b±nlhg^3_HhO§+_/mvws[DfjyH : hg_7ygis^3]omvd]wyfj_/<[tilyWh%ixtmvzv5_H_/dMilz]z_7z
fjn«zm|yg^qm|yjy!fj[]_Wtish fjmvk/o_7y!§ mofg[onT§+_/h!§+_/mvws[Df%y´ixd5z¢iQ¡snlmvzqfj[]_Oz_Hws_Hd]_/h%isk/bnx©fj[]_tixhgfgm|kv_Wyg_fª§ mofg[
ip]d]mD]_«5ixhgfgm|kv_bnx![tmowl[?§+_/mvws[Df 3ONaDQ!7*²<isdA§0iQyJ[tiQ¡l_bC_/_HdMz_H¡s_/vnsC_Hz³fgnilk/k/ns^3]vmvyg[³fg[tmvy
hj_Hyjix^3]vmvd]wW§ []nDy _ª®tdtiswsnDixAmvyfjn_Hd±nsh%k_+tish fjmvk/o_7ymvd3ixhj_HisynxC[]mvws[qomvs_Homv[]nAnz©Z0[]_0C_/hjmonzm|kmof
nsfj[]m|y hg_7ygis^3]omvd]wq[tisyWix|y nq5_H_/d<y fgtz]mo_7z©´²³nlhg_HnT¡s_/hªfg[t_*ty _*nsl_/hjd]_/|y+®tofg_/h%y^3SNT7=Q7+[5isy C_/_Hd
mvdDfghjnztk_7zfjn°hg_Hws]|ixhjmH_!fj[]_Jy t^ nx+'Wmvh%isk0z_/d5y mofgmv_Hyhj_/]hj_Hyg_/dDfj_HzA*fj[]_ tish fjmvk/o_7y§ [t_/dqfg[]_ zDr
d5ix^3mvkªd]nlmvyg_0nxtfj[]_ yf%iTfj_ª_ l5iTfgmvnsdq§0isy¦fgnAn°onT§M3Gy _H_cNbT=Y Q!7 : fj_/h´isoDfj[]_Hyg_ yfjtzmv_HyHuxm¤f!yg_/_H^3y D]mofg_
fj_/^3fjmod]wfgnyfjtzfg[t_«Cnlyjy mv]v__¬Afj_/dtygmonldtyOnxNfg[t_«tish fjmvk/o_®t¤fj_/hfgn^b]ofgmv]v_bnl~_HkfWfgh%isk%Amvd]wt
ced¨k/ns^3]fj_/h¡Am|y mvnsd¨ithgnltix]mvvmvy fgm|k3_¬]kvtygmonld ]hjmodtk/moto_¢[5isy*C_/_Hd¨z_/¡l_/vnsC_Hzmvd NT P=Q´fjn³fgh%isk%
^«]ofgmv]o_«ns~_7kf%yW]]fWfg[t_«ixvwsnlhgmofg[t^ m|yW¡l_/hjz]_/C_/dtz_HdDfOnxNfj[]_bnltyg_/hj¡Qixfgmvnsd³^3nz_/ixd5z³mvyWnsd]v
is]]vmo_7z±nlhªf§+nbnl~_HkfjyH _°]hjnsCnlyg_W[]_Hhg_°i ltm¤fj_Owl_/d]_HhjisCisowlnshjm¤fj[]^ ±nsh0^b]ofgmofjishgwl_f+fgh%isk%Amvd]w
mvdfg[]_*5isyjy mv¡s_°y nldtixh k/nsdDfg_/¬Df7
Z0[tmvy*§+nshj<m|ynlhgwDixd]m/_7zMily°±nsvonT§JyHpced yg_Hkfgmvnsd c cu§ª_¢z]_HyjkhjmoC_3fg[]_ptisygmvk35ixhgfgm|kv_3®t¤fj_/h§ mofg[
f§+n¡s_Hhjygmvnsdty0±nlhJfj[]_hj_Hyjix^3]vmod]w¢y fg_H<§ []m|k%[<k/isd³5_qy y fg_/^ixfgm|k°nshOilz]ix]fgmv¡s_s Z0[]_«y ]C_/hjmvnshjm¤f
ns´isz]isfgmv¡s_bhg_7ygis^qtomvd]w3fgnT§0ixh%z]yJygyfj_/^iTfjmvkhg_7ygis^qtomvd]w¢m|yOk/o_7ixhjoz_H^qnldty fgh%iTfg_7zmodMitisyjygmo¡l_
ygnsd5ixh3ix]]vm|k/iTfjmonld mvd yg_Hkfgmvnsd.c c c / _Hkfjmonld.ce«ufg[]_³k/_/dDfgh%ix0tish f3nxOfg[]m|yq§ªnlhg»u´z_7ix|yq§ m¤fj[ isd
_/¬Afg_/d5y mvnsdns©fg[]_Otisygmvk ®t¤fj_/h´fgnb^«]ofgmv]o_Ons~_7kf%y/Z0[]_Wdt_/§)ixvwsnlhgmofg[t^ knl^b]mvd]_7yNfg[t_Jf§+n^iT~nsh
y fg_Hty+nx¦thg_7zmvkfgmvnsdixdtzp§ª_Hmowl[lfjmodtwbnx¦fg[]_*k|isyjygmvkHixCtixhgfgm|kv_J®tofg_Hh § m¤fj[ ¯ mv]ty yjix^3]v_/h0knl^qtf r
mvd]w¢isd³_Hy fgmv^3ixfgmvnsdnxfj[]_¡s_7kfjnshJnsfj[]_bilygygmowld]^3_/dDfJ]hjnstis]mvomofgmv_HyH _mvdlfjhgnz5k_*f§+n¢zmo¶C_Hhg_Hdlf
¡l_/h%y mvnsd5yJnxªfg[]m|y ¯ motty*ygis^3]o_Hh°§ []mvk%[?fjiss_qmodDfgniskHknl]dDfWfg[t_q5isy fmvd±nshj^iTfjmonld?mvdizmo¶C_Hhg_Hdlf
§0iQs :Jdix]]vm|k/iTfjmonldfgn«5_7ixhjmodtwly r9nld]oq²<Z Z _/d5ix]v_Hyªty´fgn«k/ns^3tishg_ fj[]_Whj_Hyg]ofjyªnsf%ixmvd]_Hz3§ mofg[
fj[]_Hyg_3f§+n¡l_/h%y mvnsdtyH3ced_Hisk%[k/ily _lu©fg[t_¢z]iTf%iilygygnkm|iTfjmonld?]hjns]v_/^ mvy*nT¡l_/h%knl^q_7z?isdtz<fj[]_3®th%yf
¡l_/h%y mvnsdMmvybkv_Hixhjv<y ]C_/hjmvnsh7:Jd_¬Afg_Hdtygmonld?fjn³^b]ofgmor9hj_Hk/_/mv¡s_Hh°ztiTfjimvdfg[]_¢k/nsdDfg_/¬Dfnsª^«]¤fjmoto_
f%ixhjws_/fjyO_/dtz]yfj[]m|y*y _7kfgmvnsdixdtz?[]mvws[]vmowl[DfjyOfg[]_3wlnDnz?¡s_/h%yjiTfgmvvm¤fnx+ns]h*is]]hjnlisk%[¦^:Wy°knldtk_Hhgdty
fj[]_*d]nsfjiTfjmonldtixk/nsdA¡s_HdDfgmvnsdtyHuA§ª_*ixv§0iQAy+tyg_fg[]_*mvdtz_/¬´fgn3hg_/±_/h0fjnnsd]_*ix^3nld]wqfg[]_fgh%isk%s_7z
nl~_HkfjyHZ0[t_Wmvdtz_¬«z_Hygmvwsdtixfg_Hy´nsd]_Wnx©fg[t_ nltyg_/hj¡Qixfgmvnsdty!nsf%ixmvd]_Hzixfªmvdtyf%ixdDf!NZ0[]_Omodtz]_¬
"
m|y hg_7y _Hhg¡l_Hzp±nsh0fj[]_# tixhgfgm|kv_HyWz_/d]nsfg_7zA%$s`Amodtisov'&m|y tyg_Hz±nshWmodtz]_¬modtw3fg[]_mofg_Hhjixfgmvnsdty
mvdfg[]_ ¯ mv]ty / ix^3]v_/hJixd5z(«mvyJty _7z¢±nlh0fg[]_z]m¤¶»_/hj_/dDfJhj_Hk_Hmo¡l_/h%y/
)
&" * + %0
AtnshOfg[]_3yjixs_«nxªk/ns^3]v_fj_/d]_7ygyHuCfg[]_qtisygm|ktish fjmvk/o_«®tofg_/hm|yOdtnT§]hgmv_+*5³hg_H¡Dmv_/§+_HzZ0[]_qws_Hd]_/h%ix
thgmvdtkmv]v_Wns¦ygis^qtomvd]wmof+hj_/vmv_Hy!nld¢§ mvo»C_Wtyg_Hz3fj[]hjns]wl[]nsfªfg[]_OtixC_/h7 _knldty m|z_Hhªibz]Dd5ix^3mvk
ygyfj_/^$hj_/thg_7y _Hdlfj_HzpD3fj[]_y fgnk%[tisy fgm|kO]hgnk/_Hyjy,.-/1032 4657§ []nDy _Ofg_H^35nlhjis©_/¡snlo]fgmvnsdpm|y0wsmv¡s_Hd
Afj[]_y fjiTfj_°_DtiTfjmonld G
-/98;:<=,>-/@?BADCFEGH0=I 3OT 7
_§+isdlffgn _Hy fgmv^iTfj_?fj[]_y fjixfg_¡s_7kfgnlhJ,.-/10ixfzm|yjkhj_fg_?fgmv^3_Hy§ mofg[)fj[]_[]_/v ns«ygAy fg_H^ y
nltyg_/hj¡Qixfgmvnsdtyb§ []m|k%[ ixhj_phj_HisomHixfgmvnsdtybnxJfj[]_y fgnk%[tilyfjmvkp]hjnAk/_Hyjy',LK 02M4 5DN wsnT¡l_/hjd]_HzAfg[]_
^3_7isyg]hg_H^3_/dDf+_ DtiTfjmonld G
K 8 =,>-/=C H0=I 3Gc7
Z0[t_*f§ªnp]hgnk/_Hyjy _7y,LE 02J4 5 ixdtz , 02 4 5 ishg_*nld]vyg]]Cnlyg_Hzfjn¢5_«mod5z_/C_/dtz]_/dDfO§ []mofg_
dtnsm|y _7y/N²³nlhg_HnT¡s_/h7uDm¤fJm|y+fgn3C_*d]nxfj_Hzfg[tixfJd]n3omvd]_7ixhjm¤f¢[AACnxfg[t_Hygmvy0nld :<ªisdtz ªmvy z]nsd]_l
_¢§ mvo+z_/dtnxfg_AJKWfj[]_pyg_D]_/d5k_nx0fj[]_¢h%ixdtznl^ ¡Tixhjmvis]v_Hy ,LK C I I I CKH0*ixd5zD Onsd]_
hj_HisomHixfgmvnsdnx¦fj[]m|yJy _ D]_/dtk/_s
Oth*]hgnl]v_/^ k/nsdtygmvy fjy°mvd¨knl^3]fgmvd]w³iTf_7isk%[Mfgmv^3_ !Wfj[]_¢knldtzmofgmvnsdtis!z_/d5y mofWnx+fg[t_¢yf%iTfg_
-/wsmv¡s_Hdpixv5fg[]_Onstyg_/hj¡TiTfgmvnsd5y´iskHk]^«]|iTfg_7z]fjn!uAm9_lou 98 ,>-/K8 C I I IBCFKG 810ªixd5z
isvygnmvd<_Hy fgmv^iTfgmvd]wixdAp±tdtkfjmonldtixnxNfg[t_«y fjiTfj_B,>-/H0 Afg[]_«_¬5_7kf%iTfgmvnsd, ,.-/ 0K10OZ0[]_
J_Hkthjygmo¡l_«¿0iQs_7y m|ixd®5¤fj_/h7uix|y ndtix^3_Hz Ofjmo^ix(Amv¤fj_/h7u©hg_7y nlo¡l_HyJ_/¬]iskfjofj[]m|yOthgnl]o_H^ modMf§+n
y fg_Hty iTfJ_7isk%[pfgmv^q_!
/
]]Cnlyg_§+_*Ad]nT§@?BAQ!Z0[t_ D %" %CD $# ?mvy znld]_*iskHknsh%zmvd]w«fgnqfg[]_°±nlovnT§ mvd]w3_DtiTfjmonld G
<,.- 98K @? A38 @?BA 0 8"!#%$
7
<,.-/68-/@? A38 0& @? A ,' 0&()I 3¥`7
IOy mvd]w ,&* 0u]§+_*k/isdkHix|k]|iTfj_+ ,>-/68G-/@?BA38 0-G
<,.- 8 - @? A 8 0 8 !# $
<,>- 8 - @?BA 8CE 8, 0- ,LE 8,%- @?BA 8 0.(, 3± 7
8 ! # $
0/
,G21 :=,'C., 00<, E 8, 0.(, 33c7
§ [t_/hj_
/
,' 0 z]_/d]nsfg_Hy+fj[]_*'Omoh%isk°zm|yfjhgmv]fjmonld
Z0[t_/du]mvdfg[]_+#CD-" %CDV$-0»ufg[t_¿+iQl_Hyy+hj]v__Hdtixto_7y0ty+fgn¢k/ns^3]fj_4 G
=,'G 0 8
<,.K68D- 98H0-<,.-/98GK@?BA8 @? A+0
<,.K 8 K @?BA 8 @? A 0 I 3%P7
_k/isdhj_/§ hjmofg_5<,LKG98D-/68GH0+§ m¤fj[fg[]_*^3_Hily thg_H^q_HdDf0_ DtiTfjmonldJ,60-G
,.K98D -/ 80 8"!
# $
7/
,018 ,'G=C:900<,3 890.(9I 3 Y7
²<nshj_/nT¡s_HhHulfg[t_d]nshj^ixvmHmodtw3z]_/d]nl^qmvdtixfgnsh; ,.K
8
K
@?BA 8
@?BA
00m|y wsmv¡s_HdA¢fj[]_*±nlovnT§ modtw
mvdDfg_Hwsh%ixG
<,.K 8 K @?BA 8 @? A 0 8 ! #<$
7 ,.K 8 - 8 0-<,.- 8=K @?BA 8 @? A 0.(<I 3¥7
Z0[t_Hyg_!_Dtixfgmvnsdtyk/ixd*C_ªis]]vmo_7zisy¦§ hgmof fj_/dmo]§+_´isyjy t^q_´hg_7yfjhgm|kfjmo¡l_![ADCnxfj[]_Hygm|y¦ygtk%[isy0>*ixv^3isd
Amv¤fj_/h yªnsdt_HyHZ0[t_J±]dtkfgmvnsdty :<!ixdtz@? !ixhj_ fg[t_/dyg]]Cnlyg_Hz¢fgn«5_omvd]_7ixh0ixdtz3fj[]_d]nsm|y _7y EG!ixd5z
Ofgn³C_ ¯ ixtyjygmvisdIJd±nlh fj]dtixfg_/vMfg[]m|y*^3nz_/vmodtw³mvy*dtnxf«is]]hjns]hjmvixfg_qmod ^isdD?]hgnl]v_/^y*mvd
ygmvwsdtisisdtz<mv^ixws_q]hjnk_Hyjygmod]w5u5§ [tmvk%[Mhg_Hdtz_/h%yOfg[]_3k/isvk/]|iTfgmvnsd5yWns!fg[]_3mvdDfg_/wlhjisvyOmvd ,A 0ixdtz ,'B 0
mvd±_7isygmo]v_W3±d]n¢k/onDy _7zAr9±nshj^W7
Z0[t_+5ixhgfgm|kv_ª®5¤fj_/h7usdtis^q_7z«isvygnB>ªnsdtz]_/dtyjiTfjmonld«ixvwsnlhgmofg[t^ nsh
/
is^qtomvd]w*ce^35nlh f%ixdtk/_ _Hyjix^3]vmodtw
3/
cL7+ixvwsnlhgmofg[t^uD]hjnsCnlyg_Hy!fgn3ix]]hjnQ¬mo^ixfg_Jfj[]_°z_/dtygmofgmv_Hy ,'10H!Ai®tdtm¤fj_§+_/mvws[Dfj_Hz¢yg]^nx #
'Omvhjilkz]_/dtygm¤fjmo_7y k_Hdlfj_/hj_Hznsd_/v_/^3_Hdlf%y0nx64 5 7
udtis^3_Hztixhgfgm|kv_HyH
Z0[t_°is]]vmvkHiTfjmonldnsfj[]_*tixhgfgm|kv_®tofg_/h hj_D]mvhj_Hyªfg[tixfJnsd]_°Ad]nT§Jy0[]nT§'G
fgn¢yjix^3]v_±hgnl^$modtm¤fjmvis]hjmonlh+^ishgwlmodtis <,>- 0=
fgn¢yjix^3]v_±hgnl^ <, E 0ª±nlhJixvB!=
fgn¢k/ns^3]fj_+ ,.K 8 - 8 0ª±nshJixvB!ªfg[]hjns]wl[iqAd]nT§ d±]dtkfgmvnsd ygtk%[fg[tixf
,. 0 ,.K 8 - 8 00§ [t_/hj_^3m|ygygmvd]w3d]nshj^ixvm7iTfgmvnsd^bty f d]nxfWz]_/C_/dtznsd ¦
Z0[t_®th%yfOtixhgfgm|kv_byg_f
m|yOk/hg_7iTfg_7zAz]hjiQ§ mvd]w #-mvdtz_H5_Hdtz_/dDfhg_7ixvm7iTfgmvnsd5y0±hgnl^ <,>-
0Jixd5z
ilygygmvwsd]mvd]w]d]mo±nshj^ §ª_Hmowl[Df * +# fgn_Hisk%[³nsNfg[]_H^Z0[]_Hdu©y t]5nDy _«§ª_«zmvygCnlyg_«iTfOfgmv^3_ !;1*bns
fj[]_*tish fjmvk/o_°y _/f @?BA 8 ,L$ 5
@?BA C 5
@?BA
0
5
A § []_Hhg_
5 A 5
@?BA
8 *sN}nly fg_Hhgmvnshjm5^ishgwlmodtis% @?BA
m|y+fg[t_/d_Hy fgmv^iTfg_7zD¢fg[]_*]hjns5ix]mvomofpz_Hdtygm¤f 8
5 A 5
@?BA
/"!
$
Z0[t_LD %" %C $-0Mk/nsdtygm|yf%y0mod]hjnstiswlixfgmvd]wb_7isk%[tixhgfgm|kv_°nx# @?BAJfg[5ixd]y0fjn«fj[]_*_Dtixfgmvnsd
_H¡snlofjmonld ,.* 0
Z0[t_ª§+_/mvws[Dfnxt_7isk%[b5ixhgfgm|kv_ªm|y]CztiTfg_7z«z]]hgmvd]wOfg[]_^#CD-" %CDW$-0» IWbfjn°iknldty fjixdDf7uT_DtiTfjmonld
,%$ 0pkns^3_7yznT§ d)fgn iszQ~ty fpfj[]_§ª_Hmowl[lfnxbthg_7zmvkfgmvnsdtypAU^b]ofgmv]vDmvd]w.m¤fA fg[]_Momvs_Homv[]nAnz
, 0!Z0[]_*ixvwsnshjmofg[]^$m|y z_7ygk/hgmv5_7zpmvd:Jvwsnlhgmofg[]^ T*5_HonT§*
-&
½
'¥)(+*
¿0isygmvkOtixhgfgm|kv_®tofg_/h
}!hj_Hzm|kfjmonld
, ½ " 8 *C I I IBCF# ¾ ½
¯ _/d]_Hhjixfg_*iqhjisdtzns^$yjix^3]v_, 5
±hjns^ ,LEG 0=
>ªns^3]fj_$ 5 8 :<+,L$ 5
@? A C., 5
0
¸.- ¾/,½
>ªnshjhj_Hkfjmonld
, ½ " 8 *C I I IBCF# ¾ ½
>ªns^3]fj_ 5
8 0
132465
! $ 78
$
9;:
$)<
0
=132465
!$ 78
$
>
¸.- ¾/,½
?´y fgmv^iTfgmvnsd
?´y fgmv^iTfg_7<B, 0+A@?; ,' 0 8A
5
A 5 B,L$ 5
B@?BA 0
¿+3knsd5yfjhgtkfgmvnsdusfg[]_Otixhgfgm|kv_Hy´ixhj_ modtz]_/C_/dtz_HdDfH!Z0[]_J§+_His«k/nsdA¡s_Hhgwl_/dtk/_ªns©fg[]_Jthgnltix]mvvm¤f
z]_/dtygm¤f fgnT§0ixh%z]y § []_/d'#DCFE § mofg[¢h%iTfj_ * G # k/isd¢5_O]hjnT¡s_Hz UWnT§ª_H¡s_/h7uTfj[]_O_Hhghjnsh´mvy
dtnxfªtd]m¤±nlhg^3v5nl]dtz_7z¢mvd¢fjmo^3_s!Z0[t_Oz_Hdty mof H!m|y´nsfg_/d^b]ofgmorÀ^qnz]is©isy+y _H¡s_/h%ix5[ADCnxfj[]_Hyg_Hy
is5nlffg[]_+5nDy mofgmvnsdbnx]fj[]_ªnl~_HkfkHixdC_0^isz_+iTfnsd]_´fgmv^q_lcÀfNm|y±nlhmodty fjisdtk_´fg[]_0k/ily _ª§ []_/d«nsd]_
nl~_Hkfm|yOfgh%isk%l_Hz³§ mofg[ixdMmo^3CnshgfjixdDf*kvf fj_/h7 / _H¡s_/h%ix[AA5nsfg[]_7y _7yis5nlffg[]_3ns]~_Hkf°Cnlygm¤fjmonld
kHixdfj[]_/d³C_bl_/fWmoNfg[t_by _/fOns5ixhgfgm|kv_HyJyg]vm¤f%yWmvdDfgnpyg_/¡l_/h%ixyg]tyg_fjyHZ0[tmvyWmvyW§ []_/hj_*fg[t_wshj_Hixf
y fghj_/dtwxfg[nxfg[]m|y0®tofg_HhJvmo_7y/
Z0[t_«tish fjmvk/o_qy _/fjyO_/dtis]v_HyWfgn_Hy fgmv^3ixfg_qixdA±]dtkfjmonld]dtisns-/ modMtixhgfgm|ktvishJfg[t_bf§+n¢®th%y f^3nxr
^3_Hdlf%y*§ mofg[8B, 0 8 ixd5z B, 0 8 hg_7y C_Hkfgmv¡s_HolpZ0[]_^3_HisdkHixdC_ty _7zMfgn³_Hy fgmv^iTfj_fg[]_
Cnlygmofgmvnsdnxnld]_Jnl~_Hkfª]f+m¤f0k/isd5_°i*tilz3_Hy fgmv^3ixfgnlh´mo©fg[]_OviQ§ m|y´[]mvws[toq^b]ofgmv^3nz]ix9cedpy 5k%[
kHisyg_Hy!fg[]_Omvz_7ixC§ªnl]|z35_Ofgnqk/ix|ktvixfg_ fj[]_O^3_7ixdnsdto3nT¡s_HhNfg[t_Otish fjmvk/o_7yNfj[tiTf0knsdDfjhgmv]fj_Jfgnbfg[]_
thgmvdtkmvtis©^qnz_°]]fOy 5k%[isd_7yfjmo^iTfjnsh [tily0d]nxf C_/_Hdz]_/¡s_Honl5_7z¢±nlh0fg[]_*^3nl^q_HdDfH
ced thjilkfgm|k_lu¦fj[]_p5ixhgfgm|kv_py _/fbm|y*®td]mofg_ixdtzfj[]_p^ix~nshbzh%iQ§ tilk%<nx0fg[tmvy«ixvwsnshjmofg[]^mvybfg[]_z_r
wl_/d]_Hhjilkns¦fg[t_*tixhgfgm|kv_y _/f'G!nsd]v±_H§ tish fjmvk/o_7y0s_H_/[]mowl[§+_/mvws[Df%y ixdtzfg[t_*nxfg[t_/h%y0[tiQ¡s_¡s_Hhg
yg^ixvnsd]_7y/qZ0[]_b®5hjy fk/ixhjhjfj[]_3mod]±nshj^3ixfgmvnsdM]f°fg[]_yg_Hk/nsdtzMixhj_«tyg_/v_HyjyHbZ0[]_3hg_7ygis^3]omvd]wmvy
i?wsnAnz¨§0iQfgnhg_H^q_7zfg[]m|yzh%iQ§ tisk%C_Hk/istyg_pmofkHixdtk/_/|yfj[]_tixhgfgm|kv_Hy«nxy ^ixvv_Hy fq§+_/mvws[DfH
Z0[t_JyfjnAk%[5isy fgm|kªhj_Hyjix^3]vmvd]w*knsd5y m|yf%ymodyjix^3]vmodtw # tish fjmvk/o_7yN§ mofg[3hg_H]|isk_H^3_/dDfNmodqfg[t_Jtixhgfgm|kv_Hy
yg_f§ mofg[fj[]_¢]hjnstis]mvomof 5Mfgn<zh%iQ§ $ 5©pZ0[]_dt_/§ tixhgfgm|kv_Hy°[tiQ¡l_3]d]mo±nshj^ §+_/mvws[Dfjy°_ l5ixfgn
* =# +Z0[]_hj_Hyjix^3]vmodtw3kHixdC_mo^3]v_/^3_Hdlfj_Hz³§ mofg[<ik/ns^3]v_¬mofpmvd/,.# 0Jmod³i§0iQpz_/fjixmvv_Hzmvd
is]C_/dtzmo¬43P]àc7Z0[t_ hg_7ygis^qtomvd]w*yfj_/¢znA_7yNd]nxfª^qnzmo±«fg[]_0fj[]_/nlhg_/fgm|k/ix5knsdA¡l_/hjws_/d5k_0isyfj[]_ f§+n
5ixhgfgm|kv_°yg_f%y+±nsvonT§ isygA^q]fgnxfjmvkHixvo3fj[]_yjix^3_*z_/dtygmofs
:)®th%yf0y nlofjmonlduAisznlfg_7z3mod Na=QC±nsh+_¬]is^qto_luDk/nsdtygmvy fjy´modix]]vAmodtwfg[t_Whj_Hyjix^3]vmod]w«yfj_/pixfª_Hilk%[
fjmo^3_¢C_/hjmvnAzZ0[]_pk/nshjhg_7y Cnsd5zmodtwisowlnshjm¤fj[]^ ns+tish fjmvk/o_3®5¤fj_/hb§ mofg[¨ygyfj_/^iTfjmvk3hj_Hyjix^3]vmvd]wmvy
z]_HyjkhjmoC_Hzmod:Wowlnshjm¤fj[]^
Z¦n«^q_7isyg]hj_ fg[]_z_/wl_/d]_Hhjilk«nxfj[]_Oisowlnshjm¤fj[]^usfj[]_W_/¶C_7kfgmv¡s_ygis^3]o_y m/_#b[tisyªC_/_/dpmodDfghjnxr
z]tk_7zmod NbT7 QÀu NTH DQmvdfg[]_b^qnlhg_*wl_/d]_Hhjis¦knldDfg_¬AfJnsmv^35nlh f%ixdtk/_hj_Hyjix^3]vmod]w5 _«kHixd_Hy fgmv^iTfg_
fj[]m|y l5ixdDfgmofA #8? * #
5
A
, 5
0§ []m|k%[^q_7isyg]hj_Hy´fg[]_°dA]^bC_/h ns¦^3_Hisd]modtwx±]©tish fjmvk/o_7y/
Z0[t_*hg_7ygis^qtomvd]wqmvy0fj[]_/d³znld]_*nsdto¢mo@?# # !
0
NcÀfW_/dtis]v_Hy+fg[t_*tixhgfgm|kv_*y _/f fgnC_f fj_/h
v_Hishgd<fg[]_q]hjnAk/_HyjyWisdtz³fjnl_/_/?m¤f%yO^3_H^qnlhg³zthgmvd]w¢fj[]_qmodDfg_Hhg¡Tis§ [t_/hj_bd]nhg_7ygis^qtomvd]wpnkHk]h%y/
-&
½
'¥)(
}Nixhgfgm|kv_O®5¤fj_/h § mofg[³y y fg_H^3ixfgm|khg_7ygis^qtomvd]w
}!hj_Hzm|kfjmonld
, ½ " 8 *C I I IBCF# ¾ ½
¯ _/d]_Hhjixfg_*iqhjisdtzns^$yjix^3]v_, 5
±hjns^ ,LEG 0=
>ªns^3]fj_$ 5
B@? A
8;:<+,L$ 5
@?BA C., 5
0
¸.- ¾/,½
>ªnshjhj_Hkfjmonld
, ½ " 8 *C I I IBCF# ¾ ½
>ªns^3]fj_ 5 8 0 132465
! $
78
$
9;:
$)<
0
=132465
!$ >
78
$
¸.- ¾/,½
?´y fgmv^iTfgmvnsd
?´y fgmv^iTfg_7<B, 0+A ;? ,'G 0 8
5
A 5 B,L$ 5 B@?BA
0
_7ygis^qtomvd]w
, ½ " 8 *C I I IBCF# ¾ ½
'Wh%iQ§M$ 5 ±hjns^
/
!
/ _f 5 8 * +#
¸.- ¾/,½
'O_f%ixmvvyOk/isd³5_*±nl]dtz³mvd NbT7 QÀu@NbT/ Qnlh^N=Q9:W]5_Hdtzmo¬ 3%P]àc7 ]hg_7y _HdDfjy0fj[]_b]h%iskfgm|k/is§+iQtyg_Hzfgn
hj_Hyjix^3]v_Ofg[]_*tish fjmvk/o_*yg_f7
-& ½ '¥)( }Nixhgfgm|kv_O®5¤fj_/h § mofg[³isz]isfgmv¡s_°hj_Hyjix^3]vmodtw
}!hj_Hzm|kfjmonld
, ½ " 8 *C I I IBCF#
¾ ½
¯ _/d]_Hhjixfg_*iqhjisdtzns^$yjix^3]v_,
5
±hjns^ ,LEG 0=
>ªns^3]fj_$
5
B@? A 8;:<+,L$
5@?BA C.,
5 0
¸.- ¾/,½
>ªnshjhj_Hkfjmonld
, ½ " 8 *C I I IBCF# ¾ ½
>ªns^3]fj_ 5
8 0
132465
! $
78
$
9 :
$)<
0 132 5!$
>
78
$
¸.- ¾/,½
?´y fgmv^iTfgmvnsd
?´y fgmv^iTfg_7<B, 0+A ;? ,' 0 8
5 A 5
B,L$ 5
B@?BA 0
?N¶»_Hkfgmv¡s_ygmH__7yfjmo^ixfgmvnsd
>+ix|ktvixfg_ #8?
A
9 :
$)<
18 $ 7
_7ygis^qtomvd]w
', #? # !
0
)( ¸-
,½ " 8 *C I I IBC # ¾ ½
'OhjiQ§ $ 5 ±hjns^
/
! >
/ _/f 5
8 * =#
¸- ¾/,½
¸ -¥ ¸
,½ " 8 *C I I IBC # ¾ ½
$ 5 8M$ 5
B@? A
¸- ¾/,½
¸.- ¾/'%,
+° b * b" * "
ZnJmvovty fgh%iTfj_fg[]_ª]hg_H¡Amonltyixvwsnlhgmofg[t^3yHu/§+_N®th%y fz_Hisx§ mofg[bk/vilygygmvkHixxC_Hishgmvd]wDyrÀnsd]vJ]hjnsto_H^3yH¦Z0[]_
nl~_HkfOm|yJfj[]_/diR[ Cnsmvdlfgr9nl~_HkfO\mvd<fg[t_ 1³]visd]_sced<fj[]_«k/nsdDfg_/¬Afns´ipygonT§ v^3isd]_/t¡s_/hjmvd]w
f%ixhjws_/fHux§+_ [tiQ¡s_ k%[]nDy _Hdqid]_7ixhjoDreknldtyf%ixdDf rÀ¡s_Honk/m¤f°^3nz_/ 3Gy _H_cNbTH`=Qt±nsh´i°hj_/¡Amv_/§ ns5fj[]_ ]hjmod5kmvtix
z]Dd5ix^3mvkHix©^3nz_/|y0tyg_Hzmvdpfj[]mvyWzns^ixmvdE7
Z0[t_°y fjixfg_°¡s_7kfjnsh -/!hg_H]hj_Hyg_/dDfjyªfg[t_knAnsh%zmvdtiTfj_Hy+ixdtzpfg[]_*¡l_/vnkmofgmv_Hy0mvdpfj[]_ 1 ¢tvisd]_HG9- 98
,'G=C:DC., GC., DH0´Z0[t_°z]mvyjkhj_fjmH_Hzyf%iTfg_*_ DtiTfjmonldilygygnkm|iTfg_7z¢§ mofg[fgmv^3_*5_Hhgmvnz !+mvy G
-/668
( ! (
! ( "
-/$#%
6 (
! ( "
EGC 3%a7
§ [t_/hj_
( m|yfg[]_3m|z_/dDfjm¤f³^iTfjhgmo¬?mvdz]mo^3_/d5y mvnsd86pisdtzJEGJm|y*i ¯ istyjy m|ixd /_/hjnxrÀ^3_Hisd<¡s_7kfgnlhOns
k/nT¡Tixhjmvisdtk_¢^ixfghjm¤¬'&( 8*),+ - !
! +
2/.
_f ?-/*5_fg[t__7yfjmo^ixfgmvnsd¨ns-/bknl^qtfg_7z¨Afg[]_
5ixhgfgm|kv_O®5¤fj_/h%y0§ m¤fj[@B, 08utm9_lu© -/68?
5 A 5 $ 5
B@?BA
Z0[t_nltyg_/hj¡Qixfgmvnsdty0ishg_*iQ¡Tixmvvis]v_ixf z]mvyjkhj_fj_Ofjmo^3_7yJiskHknsh%zmvd]w«fgn G
K 810325465037,
1
98
!
01
:8
!
0# =C 3STH7
§ [t_/hj_ +mvyOi//_Hhgnsr9^3_Hisd ¯ istyjy m|ixdd]nlmvyg_*nxNknT¡Tixhjm|ixdtk/_
+ ;
mvdtz_H5_Hdtz_HdlfOnxE %598
!
ixdtz 98
!
ishg_Ofg[t_ >+ixhgfg_Hygm|ixdk/nAnsh%zmod5iTfg_7y0nxfg[]_*nlty _Hhg¡l_/h7ul§ [tmvk%[³ixhj_DdtnT§ d
=< >?@BACEDF@GIHKJMLONPDFQR$TSUVDPNW@X'QVDPY@[Z@[DB\]L^DFQRTLO_C`LaLOJDFQVbcdNF@eLagf
JUQ:_hiNW@eJjRkDFQEbcVZ
Z0[t_mvd]mofgm|ixCnlygmofgmvnsdnxfg[]_°f%ixhjws_fJisdtzpnsfj[]_°nstyg_/hj¡s_Hh ixhj_
- 8mln
no 6 !p! ^
*rq ![! ^
* I! ^y
? A
1 ! Isqb^y
?BA tvu
u
w -
98
!
8mln
no 6 !p! ^ 1x ![!p! ^
*I6«^y
? A
# ! Isq^y
?BA tvu
u
w I
Z0[t_*nstyg_/hj¡s_Hh mvy0±nlovnT§ mvd]w¢i3o_HwApv_/w3fgh%iT~_7kfjnshjs´cÀf%y ¡s_Honk/m¤f¡s_Hkfgnlh mvyOknsd5yf%ixdDf nsd³_Hilk%[v_/w
isdtz^qnzmo®t_7zixf fg[]_±nlovnT§ modtwqmvdty fjisdlf%y"G
,
98
!
:
,) 98
!
" 8 1 ! I$
! Ix " , 98
!
y
, :8
!
y
:
" 8 6 I!
! Ix "
,) :8
!
z
,) 98
!
z
" 8 1 ! I$
! Ix "
, 98
!
:
,) 98
!
" 8 6 I!
! Ix "
,) :8
!
, :8
!
:
" 8 1 ! I$
! Ix " I
Z0[t_py _ D]_/dtk/_¢nxJ_7yfjmo^ixfg_Hzf%ixhjws_/fb5_7ixhjmodtwlyishg_]hj_Hyg_/dDfj_Hzmvd ®twsthg_Tl?Z0[]_/ixhj_¢ygmo^«]vixfg_7z
§ mofg[ i ¯ ix5ygygmvisdUd]nsm|yg_<nx¡Tixhjm|ixdtk/_
+ ; 8 ! I!
qh%iszm|ixdty 3¥ixCns]fx z]_/wshj_/_7y7_/¡s_Hhg fgmv^3_MC_r
hjmvnAzu©mG_3_/¡s_Hhg$yg_Hknldtz]yHbZ0[]_zAdtis^qm|kqd]nsm|yg_«m|y°idtnshj^3is<H_/hjnxrÀ^3_Hixd ¯ ixtyjy m|ixdM¡s_7kfgnlhO§ mofg[
+ - 8 + 2 8 ! I!p! */^y
? A _*ty _°fj[]_*ygis^3_°z]Dd5ix^3mvk°dtnsm|y _fgn3]hj_Hz]mvkf fg[]_*tish fjmvk/o_l
Amvhjy fHut§ª_*k/isd³k/ix|ktvixfg_fg[]_b_Hy fgmv^3ixfg_7zpfjhjix~_Hkfgnshj3±nsh nld]_*tish fjmvk/]vish0hg]dnsfj[]_tish fjmvk/o_®tofg_HhH
Z0[t_Jfghj]_ixdtz_7yfjmo^ixfg_Hzfgh%iT~_Hkfgnlhgmv_HyNnlfjismodt_Hz3§ mofg[ * !p![!p! tixhgfgm|kv_Hy+ixhj_J]vnxfgfg_7ztygmod]wqy y fg_H^«r
ixfgm|khg_7ygis^qtomvd]w3mod®twl]hj_*3isdtzisz]isfgmv¡s_°hj_Hyjix^3]vmod]w3mvd®tws]hj_*`]!Z0[]_°fj[]hj_Hyg[]ns|z# !
0 mvy
®t¬A_7zfgn ! I]!Z0[]_iQ¡l_/h%ixwl_J±hj_D]_/d5k¢nshj_Hyjix^3]vmodtw«±nlhJy 5k%[iqfj[]hg_7y [tns|zpm|y ! I* x 6*±nlh 8 * ![!
z]m¤¶»_/hj_/dDf*hgtdty*nxªfg[]_3®5¤fj_/h§ mofg[ isztixfjmo¡l_«hj_Hyjix^3]vmodtwtZ0[]_¡Tixv]_Hy°ns #? ixhj_3]hg_7y _HdDfg_HzMmvd
®5ws]hj_° «±nlhJiqtixhgfgm|k]|ixh0hj]d
Zn³isyjy _7ygyOfj[]_¢iskHk]h%isk/³nx+fg[]_3f§+n®t¤fj_/h%y/u§ª_3[tiQ¡l_kns^3]]fg_HzMfj[]_]m|isy*ixd5zMy fjisdtz]ixh%zz_r
-0.5 0 0.5 1 1.5 2
0 100 200 300 400 500 600 700 800 900 1000
bearings in radians
time in seconds Noisy Bearings Measured
(t,y)
Amvws]hj_RTcGN¿+_Hixhjmvd]wlyª^3_Hisyg]hj_HziTf0_Hisk%[pfgmv^3_*5_Hhgmvnz±nsh0fj[]_*y mvd]wlo_Ofjishgwl_f05_7ixhjmod]wDyrÀnsdto3_¬C_/hjm¤r
^3_Hdlf
¡Am|iTfjmonld³§ m¤fj[ 8 * ![! zm¤¶»_/hj_/dDfhg]d5yJnxN_7isk%[®tofg_HhJ±nshWfg[]_b±ns]hknl^qCnsdt_/dDfjyWnxNfg[t_¡s_7kfgnlh-¨
Zixto_WTk/nsdDfjismodty fg[]_hj_Hyg]ofjyH`:+fO_Hisk%[fgmv^3_!ªfg[]_b]mvily ±nlh fg[]_
k/ns^35nld]_/dDfJns6- m|yWz_/®td]_7z
A
$ 0 8 *
A , ?- 0
1J-/0
0=C 3STcT 7
-2500 -2000 -1500 -1000 -500 0 500 1000 1500
0 1000 2000 3000 4000 5000 6000 7000 8000
y-coordinate in meters
x-coordinate in meters True and estimated trajectories
target trajectory estimated target trajectory
Amvws]hj_G Zhj]_isdtz _Hy fgmv^3ixfg_7z fgh%iT~_7kfjnshjmo_7y nlfjismod]_7z § mofg[ THlss tixhgfgm|kv_Hy ixd5z
ygyfj_/^iTfjmvkhj_Hyjix^3]vmodtw
isdtzpfg[]_y fjisdtz]ixh%zz_/¡Am|iTfgmvnsd G$ !&( 0 8 *
A ?- 0 1 , *
A ?-
00 I 3ST7c7
Zn°iQ¡snsm|zk/ns^35_HdtyjiTfgmvnsd«nxC_/v_/^3_/dDfjishg*tmvily`3¥nxCns]Cnlygm¤fj_+ygmvwsdty#7ux§+_0iQ¡s_/h%ixwl_Nfg[t_0istygnsvfg_+¡Tixv]_Hy
ns¦fj[]_*]m|isy $ 0
!Z0[]_/du§+_z_/®td]_
$ 0 8 *
A $ 0C 3STH`7
isdtz§ª_*iQ¡s_Hhjisws_Wfg[]_y fjisdtz]ixh%zpz]_/¡Amvixfgmvnsdty
$ !&(
0 8 *
A $ !&( 0I 3ST/ 7
Z0[]_¢zmo¶»_/hj_/dtk/_Hy*C_f§+_/_HdMfj[]_]m|isyg_Hyishg_3d]nsf¡s_Hhg?ygmvwsd]mo®5k/isdDfW3Gyfjmov9umofmvyby vmowl[Dfgv?vnT§ª_Hh§ mofg[
ilz]ix]fgmv¡s_bhj_Hyjix^3]vmvd]w7uCtfOfj[]_yf%ixdtztixh%z<z_/¡Am|iTfjmonld<mvy°ygmowld]mo®5k/isdlfjo[]mvws[t_/hmod?fg[]_k/ily _«nxªygyr
fj_/^iTfjmvk0hj_Hyjix^3]vmvd]wtZ0[]_ _Hy fgmv^iTfg_7y]hjnT¡Dm|z_7zbAnld]_ tixhgfgm|ktvishhj]dixhj_+fg[]_Hd3o_7ygyhj_/vmvis]v_+§ mofg[
ygyfj_/^iTfjmvk3hj_Hyjix^3]vmvd]wfg[tisd § m¤fj[¨isz]isfgmv¡s_nld]_s_: z]isfgmv¡s_hj_Hyjix^3]vmodtw³§ mov!fj[D5yC_¢tyg_Hzmvd
-2500 -2000 -1500 -1000 -500 0 500 1000 1500
0 1000 2000 3000 4000 5000 6000 7000 8000
y-coordinate in meters
x-coordinate in meters True and estimated trajectories
target trajectory estimated target trajectory
Amvws]hj_ `G Zhj]_isdtz _Hy fgmv^3ixfg_7z fgh%iT~_7kfjnshjmo_7y nlfjismod]_7z § mofg[ THlss tixhgfgm|kv_Hy ixd5z
ilz]ix]fgmv¡s_hg_7ygis^qtomvd]w
Zixto_4TcG'>ªns^3tixhjm|y nld<5_/f§ª_H_/dMtixhgfgm|kv_b®5¤fj_/hjmod]wC_/hg±nshj^3isdtk_«§ m¤fj[ygyfj_/^iTfjmvkqixd5z?isztixfjmo¡l_
hj_Hyjix^3]vmvd]wtuAmvdfj[]_ygmod]wlo_/r9nl~_Hkf+C_Hishgmvd]wDyrÀnsd]v¢ygDdDfj[]_fjmvk_¬]is^qto_
¿+m|isy
/
f%z
ygAy fg_H^iTfgm|k isz]isfgmv¡s_ ygyfj_/^iTfjmvkTisztixfjmo¡l_ ygyfj_/^iTfjmvk ilz]ix]fgmv¡s_ ygyfj_/^iTfjmvkTilz]ixfjmo¡l_
aTlT x` s`]P)cP Tllca Tlall tZYaca `Y
P Ts) x]x]Y Tls l` ta]Y]T/ t DT7 ]Y
, -
]s]YDa ]s)ca TlDx` ]slcal ]sls`as P
,2 ]YYT`l` ]YT` TH Ts) ]slYY tlss`s àP
fj[]_*hj_Hy f0ns¦fj[]mvyJ§ªnlhg»
cÀfOmvyJfgn¢C_bd]nsfg_7zfg[tixfWmodfj[]_«kHisyg_*nxNhj_Hixz]iTf%i3fg[]_b¡Qishgm|ixd5k_*nxfj[]_«y fjixfg_d]nlmvyg_znA_HyWd]nxfOd]_/_7z
fjnC_WAd]nT§ d]hj_Hk/mvyg_/vGmom¤f+mvyªnT¡s_Hhg_7yfjmo^iTfj_Hz©uxfg[]_Otixhgfgm|kv_Hyªixhj_ ]hg_7zm|kfg_7zmvd¢i|ixhjws_/h!ishg_7i°]f
ishg_Jisvygn^3nshj_J_Homv^3modtixfg_7zmod¢fg[]_Ohg_7ygis^qtomvd]wy fg_/¦}´hjilkfgm|k/isovqm¤f+mvy+i*wshj_Hixfªy fghj_/d]wsfg[nx5ixhgfgm|kv_
®5¤fj_/hjmod]w5
Z0[t_O]thgCnlyg_Ons¦fj[]mvy0yg_Hkfgmvnsdp§0isyªfjn«]hjnT¡Amvz]_Oiqws_Hd]_/h%ixChg_H]hj_Hyg_/dDfjixfgmvnsdnxtixhgfgm|kv_J®5¤fj_/hjmod]w5 _
kHixdd]nT§)fj]hjdfjn3m¤f%y _¬Afg_Hdtygmonldpfjnq^«]ofgmorGf%ixhjws_f0fjhjilk%Dmvd]w5
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
0 100 200 300 400 500 600 700 800 900 1000
effective sample size
time in seconds Effective sample size
Amvws]hj_ GqZ0[]_¢¡Tixv]_7y*nx0fg[t_¢_¶»_Hkfgmv¡s_pyjix^3]v_¢y m/_ #³nlfjismodt_Hz§ m¤fj[? THlslptish fjmvk/o_7yixd5z
ilz]ix]fgmv¡s_hg_7ygis^qtomvd]w
%*+ * + %0"
M aDPL^DFQVc_C@
¦_f 5_0fj[]_JdA]^«5_HhNnx»ns~_7kfjyNfgn°fgh%isk%3¥isyjyg]^3_Hzbfgn*C_JAd]nT§ dqisdtz«®]¬_Hz 7Z0[t_Jyf%iTfg_ ¡l_Hkfgnsh
§+_3[tiQ¡s_«fgn_7yfjmo^iTfj_mvy°^ilz_3DMknsd5k/iTfj_/dtixfgmvd]wfg[]_¢y fjixfg_3¡s_7kfgnlh°nx0_Hisk%[Mns~_7kf7H:+f*fjmo^3_!u
- 8 ,>-
A
C I I I C -
0ª±nsvonT§Jyªfg[t_yf%iTfg_°_ l5iTfgmvnsd ,&* 00z_Hk/ns^3Cnlyg_Hzmod 5ixhgfgm|ix©_Dtixfgmvnsdty G
-
8 :
,.-
@?BA CFE
0 8 * C I I IBCF I 3ST c7
Z0[t_d]nlmvyg_Hy ,LE
0«ixd5z ,LE
0qixhj_pnsdto yg]]Cnlyg_Hz fjnMC_§ []mofg_5nsfg[¨fj_/^3Cnsh%ixvo¨isdtz ygtiTfjmvisovsu
mvdtz_H5_Hdtz_Hdlf ±nlh38 G
Z0[t_³nstyg_/hj¡TiTfgmvnsd ¡s_7kfjnsh¢iTffjmo^3_ !qm|y¢z_/dtnxfg_7z D D8 ,'
A
C I I IBC.
0 AtnsvonT§ mvd]wfg[]_<yg_/^qr
mvdtisOm|z_Hilypns«* / fjhg_Hm¤f³ixdtz Z° ¦]wsmvdA]][]RNàx=QÀuW§+_MmvdDfghjnztk_?fg[]_y fgnk%[tisy fgm|k<¡l_Hkfgnsh 2
*C I I I C
ygtk%[ fg[5iTf 8 °mo mvy«m|ygyg]_Hz ±hgnl^fj[]_
ns]~_Hkf7Mced fg[]m|yqk/isyg_su; m|y«i
hj_HisomHixfgmvnsdnx¦fj[]_y fgnk%[tisy fgm|k]hjnAk/_Hyjy"G
K
8
,>-
C
0+mo
8;I 3ST P7
:Wwlismodu¦fg[]_pd]nsm|y _7y ,3
0ixdtz ,
0*ishg_nld]oy t]5nDy _7zMfgn<C_¢§ []mofg_¢dtnsm|y _7y/umodtz]_/C_/dtz_HdDf±nsh
8 _°isyjy t^q_Ofg[5iTf+fg[]_O±]dtkfgmvnsdty
ixhj_Oygtk%[pfg[tixfªfj[]_/¢kHixdpC_°isyjy nkm|iTfj_Hz3fjnb±tdtkfjmonldtix
±nlhg^y
z]_®td]_7zD
,. 0# ,.K
8
8 C -
8 0
