Adaptive Stream Resource Management Using Kalman Filters Ankur Jain
Edward Y. Chang
Yuan-Fang Wang
Computer Science University of California Santa Barbara, CA 93106
Electrical & Computer Engineering University of California Santa Barbara, CA 93106
Computer Science University of California Santa Barbara, CA 93106
[email protected]
[email protected]
ABSTRACT
!"# $ %%&'&()+*,&- ./.0&1&23.54)6378.$.!94,7*:43;!?3/ .@ A./! /)6B$C&>;Q .R/-=S+.0- . % UT. 4# )$ V .R#@.)6/ W$6C4)6&>&-/ XK# Y?S.!2C4 " &2C&F7Z:F . % [+*,-36, [(? .%./B %%3C .&>$!A >&-+\C&F7Z:]? .%._^A ..3 $`6, a . % -..$ %/$G "6D/0!V&((= $/b4C4+6AM^J.D 4,*a6/&Fi? _+ .6/3 %JC4r.b? .%6 6=N . D@ Y]C4F _}%.+{/-8}.[{U $ _=k {z{=-z,}QSg.S}.S+{/i/a{[|A~K~"}.[{ SD`S }.3.==}F)%/.>{z=Br=z%.D".%=.M ¡z}M¢ .£ {z ¢] }.9,_}. {/==3{/z >¤J¥j¦ >{z,
2.z,} {).8o=,3
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. SIGMOD 2004, June 13-18, 2004, Paris, France. Copyright 2004 ACM 1-58113-859-8/04/06 ... § 5.00.
[email protected]
+¨j/¨3r¨=©/V.)=%(-}. Q}.". `}.-{/-=z,}b {/} { 7SD. }.#}.U%.D+ªyA}.U%.DY+{zu{/z_¢ K«,.7 ¢]o}.Sz[%)o¬ .S%7z"=z_}% {/Sz}.3}.%Q-}. `z} z{} {/} {-FzS+{/}.SzpyMz g}.%-}. N{+D )z%+¢]z#5}.SD-C`. SzKz}M¢J/.£,0{z ¢] }.=z3 %-3}.S=zp}..
"{/7%[z%.Sz(}.`_}./ {F{/z .,%_ Sz(S={ Q{/}]}.g%.D+ ® >{+¯_/F%%}.-SzN/h}.(°3S_}.SzK%73}.S=zi+¢J=+ SQ}.{/}b}.
K{:.2/C}.z{ ,=9{b°37{Sz 7zE :p{z {+D )zYS=S
Y{SS+{/}.Sz )z z}+V±b-zo¬ %=S3}.7zK{/
,}b)z DS=) CA>{/z{Sz[_}%.+{².%=3.ayMzN}.S {/)+3¢JA}%.+{/}8_}%.+{/³.%=3.A>{z{=-z,}8{hz {/-z } {So
U{F¬S}..7z>.=SN ® zY5}.SD`_}%.+{(¬S}..7z>{S=/ .o}.´% ¬o}.b=3}g{(>{:°S2³{/-=z,}8 {/} {>{Q7z {h}.A.S%S=zY=z_}% {Sz,}.b{:.A-}]{/}]}.A%.D+ µehSz,}%. ]=3]¶g3m2= &(-nV 0 F%·]¸ ¹,j{:.o}.}.. {`{Yz {J{/z { {/}.SD(%73}.S=ze}."}.-_}%.+{(.%. >{z{-z,}].SN µa{ D,+{/}.A}.`%Aj}.Aºa{/S>{z »iSo}.(%¸V¹3ao+¼:i/A_}%.+{/(¬o}..Sz%Sz[¸ ¹[{/Q)zN¢JS _}. S {z ¢] o
A{/SS }.]>{z,
{:} {J¬o}..Sz]{/z %-,}.3 Sz8.S-j~)o¬{So
,¢ Sz/.) {:}.J}.Wºa{S>{z2»iSS}. {J}.b{%SgS SzFS,£-/j{`_}%.{³>{z{-z,} _
3_}. /Q}.bS7+¢]Sz-}0¢JF.+{/%=z½ { S}.Sz{W-}. b{ Y.$ {/} {-}.{/}a{%So
) ¾ p =-(_} {/S[:DA}.7-[JS2z%%o} {:}.`¿.+«,z,}`{/z °3)z%SDg_
3z3.=zSÀ+{:}.S=zY)}M¢JzYSSz,}.8{z %.D. }..==t.}% {/z%-S%%S=zp³ÁbY-}. bzu}./}. {z A{ N¬S}.U{/ {/-}..N}.{/}Kz{7¡6&F$ {z = _0g_
_}.3. S}.S=zUzU}.a%.DQ¢]S}.=3} S7z}.ÂSz,}..Dz,}.S=z9 ¢]SSj)`CSo
K°37{/7z Sze~}.S=z¨3 ,9}.2ºa{/S>{z ¾ ® Q »i7o}.r+{zA)j+{/%SS
g_}.-7À }.h{/z Sj{/%
3Szh_}%.+{/ {/ {}..S_}.7D%z%jzS%=D{/z }.S-V{/.7{zV}.8-} }.2.«o.-z,}.Q%)o¬ 7zB FJ2.{-`¬o}..Sz C {-¢J.£+{z#)>{ {/}. }.U{ .%F{Y¢] >{/.S}0
p_}%.+{ª.%=3.b>{/z{-z,}V.=S-,.: Sz`{ zo¬ {/ { S=Ã}.{:}87])/}.Y)+¢J%Cr{z D..{:}.7S= yMz}.Sa{)+ (}.N}.-%{/>7S-o} {/}.Szk¢J-C,2=z %+¢]Sz"}.(%(J}.Y¸V¹N}.Yz%.DFz}0¢J.£U{z ¢] }. {z zk}.k_}./ {= {z .,%%Sz].%=.k{/}9}.j%.= rK3%}.F-{%SÀ-}.>z }.K=z%.D[z}0¢J/.£e{/z ¢] }.9kS}Fa=z% F{Y}M
3S+{/V¢]o.S%F%z%F-=zS}./.Sz _
3_}.NqyMzO{SS+{/}.S=z%O{-/Sz/=¯_}K}% {/£Sz3 ¢J{/}.a-=zo}./.7zp{z "%3.DSS¿{/zp}.F)+¢J S_ %S{:}.7z[ {:}.Q/p{A¢]o.S%h%z%%z 87 {z>S%%8p.S>{/%
Central Server (Running KFs ) Send update received from remote source YES
Update the central server with new value YES
Is update available from remote source ?
User
Remote Source (Running KFm )
NO
Is prediction of central server outside given query precision ?
NO
Send prediction from the server KFs
Streaming Source
Drop the data tuple
e·]¸ ¹ =z.zpBy0}({F)zB_} {7S% ¼h¨=:]}.{:}(}.">{:¯M% o}0
Nj)+¢ 7%%S{/}.S=zU,3.Q¢]zY}% {z%-o}%}.7z-o}.8/= ¢]o.S%az}M¢ .£5z/}g¢]zU3.,%%Sz[}.NgJ2 {:}.S"/ z./
"%)z}J7z[%z Sz`=zgo}h:DJz}0¢J.£J}.a}.{:}h%)z,} Sz>°33}.Sza=zQSz_}%.}.S=z-SJ)}0¢JzY©g}.2 ©=©a=z>={:% S-{:.S}.}.." 3J! +eJj¬S}..7z {/} {U{:}(%z%. Sh)z¬¿{/)z/}h=zS
F]=z%.3Sz2{z ¢] }.p}J{S%2C =z%.3Sz`)+¢ +V~3Sz]}.h=-} {:}.7z{/_}JSz3%. ,
¸V¹KS`Sz%7zo¬{z,}`7z>{z,
U {/}.S+{V%z%SzN%z{/.S=h¸V¹ SA{/z{:}%}% {}.SD2=3}.7z{b}.`¬S}..7z"%S}.S=zb.%=3. =z%.={:}.7zp »iS.N S}.g}.F.=S-]a3.=)=% ·]¸ ¹N- j7z {F}0
3S+{p|a~K~"{/. o}.}.3.= ® %F$zY}.aSC}%{z % / }.`¬=.+8S%%a{[«,%
Y}.[}.2%.=g¢]o}.U%=-F3.o %Sz[=z_}% {/Sz}.WJ]%.D {}.S{/}.V{-¸ ¹ z}. {/b¸V#¹ " {/z {/}A}.2.{-F}.S-=5}.F} {/.}a%z%/`{}.S{/}.`{[-S%./ ¸V¹N¢]o}.}.2.{-({/ {-}.. z/}. {/[¸V#¹ $2>J { ¬o}..2¸V#¹ "g{/z ¸V¹ $ . S}]}.3. {:} {F={/SJÁbzo
>¢]z }.A¬o}.A{:}Q}.A.-}.a%=3.=k¸V¹ $`{SSb}.>. S}QC}.3. {/} {"¢]o}.7z}.2.S%S=z=z_}% {Sz,}>{z }.(¸V¹ "2+{/zz/} 3.:3 ]{z-{/ {:}.]. 7}.7z-{/}W}. %.Dr}.{:}j}.h%z% %z a {/}.g}.e¸ ¹ ":N~S=zo¬+{z,}a{/z ¢] }.z%.{/}.Sz {zE)Y{/SD og{N.S7{SN{z {3 {/}. {:} {3. S}.S=z -{zS% Sj-7+
, 9µeJ3.=)=%J}.g¸ ¹g{j% ({8-3 {/zS%I/`S}.A%S-7So}0
,r(Sz
,r{z 3./{SF=3}.S>{So}M
z h${/S.o
Y=z {p=z o}.S=z
1.1 What is Kalman Filter?
Jbºa{/7>{/z[»i7o}.J7J{`_}., {/_}.7..%SD {/} {g¬o}..Sz /{ S=.o}.NVy}]{/8)z"¢] S
[% SzY3. S}.SzF{F_
3_}.NÂ Sz,}..z{J_} {:}.Y{/% =z#}."%.{/}.S=zE/Qo}.2°}..z{/J) {+3S/+E»(_}%.+{P>{z{/=-z}2{/SS+{:}.7zJ{_}%.+{/ S - S {/F{Nz {:}.SD>.,%"{Y_}%.+{/-7zK- ¿gz }%.S7 ,
e}."_}%.+{NÂ (Sz,}..z{]{: {-}..Y$_} {/}.:V¢]S D=SDK:D>}.S-= JK_} {:}.U>{+
B/">{
Bz/}[) o.}.o
%.{S=i{/z z=9{/g}.")(Sz3%. ,
K=%.7z"}. _
3_}.NÂ 9°}..z{/D){:S+iJj=%.D A {/} {h_}%.+{/ %.= {/Q}.2°}..z{p=%.={:}.7zK}.{/}QSg% }.[_}.7>{:}.A}.aSz }..z{3_} {/}.h/)}.J_}%.{NÂ j=z {/}.SDh3.,%WJh_} {:}.h_ }.S>{:}.7z(.,%V) {/}. %Szb.3.%7=h_}.W53. S}.S=z $3.={D{:}.SzK}.>Sz,}..z{/ _} {/}.[]}.[_
3_}.[A{/z /%. }.Szt¬z}.zSz"}.-. S}.S=ze¢]o}.E°}..z{/ %.{/}.S=z o©3r¼3¨D: ® =z.}.]°{-7hSj}.].S 5_}.7>{:}.Szg}.h_} {:}. /p{b-:3SzgD77jJ]_
3_}. _} {/}.]-.S%k}.h3%.z,} S,+{:}.S=zU{z D7,S}0
[i}.gD77{/z 7h.3.%z,}. ,
[{ =}.& %&'{/}W{ S%.}.W}.7-V_}. (5jJ _
3_}. D=SDr/=
}.S- >}.}. .7=+Â ({S {/}.Szt{z 3 {£Sz{}.Sz {z .={ C.S}.S=z"k{a {z =N*)bz=,}.8}.S-Q==S}.S=z" }.b_
_}.NÂ ]_} {:}.A7]/=.z ,
[}.g+«,{:}.S=z
%&',+.-0/213%4'6587:93' _: @A ;CB*D @ IH @JA ; @ HMLCN= / 5 9 O 5 > ; ' © F E ;KF F H E ;CB*DGF ¢].P> ' Si.,%kz7%D>{/}%.SQ1 {z 71.¿{:}.V}. _} {/}. {/}&g ( }.8}.{/}k{/}Q([ 5 =R9SzC.>{/}.SzE}.{:%.7=Y{:}F}.>)_}F_}.S>{/}. V}.`_
3_}.x_} {:}.F:Dg}.S-=AJY¸V¹"¢ S=a{/Sj{:{S7{S SzC.>{/}.SzN,
[} {/£7zFSz,}.(z% {:}.S=zY}.Az=S%ASzY°3}.% z{/r-+{/%.-z}8{/z }.az%} {Sz,}M
[SzK_} {/}.a.{/D{/}.Szp Y.F%)o¬+{/SS
,pS}AA{%%-2}.{:}b}.F_} {/}.2.{={/}.S=z z%} {/7z,}0Y
>Z'[Sh¢]o}. X {%%7{/zN¢]S}.N{(:={:.¿{/zA>{:}%.o° [ WJA-+{/%.-z,} z=S% V ; S]¢]o}. X {%%7{/zY¢]o}.K{F/ {/.7{z->{/}%.o] ° \Ui{z S}`S`z}`/%.7{/}. ¢]o}.}.-z7% SzU_} {/}.`.={={/}.S=z9gJ`C.F7{/}.S=zUj}.[¸V¹Y{/S=.o}. .: ]J¢]S}."}.bC=SS:¢]Sz"_} {:}.7_}.S+{/r3.=)%}.S½ =hJA°3)}. {Sg/i}.F¸ ¹-_}.S>{/}.AS]+«,{/)}.F}. °3)}. ={/S(/ }.F_} {/}.=(J{/}aSJB{/}.Ak}.A_} {/}.A¢]SSi+«,{/9}.g}%.A_} {/}.]ÁQ]}. ¸ ¹-S8{zNz37{% _}.S>{/}.+ ]ÁQ {/SWSSz{/A_}.S>{:}.7z{/S=.o}.-9}.>¸ ¹N{/S=.o}. -7zS-7ÀV}.Q{/.7{z8r}.Q.«,{/.89}.8_}.S>{/}.S=z %.+[J{/}`S]B{:}.S=zB%.+ÁQ(}.¸V¹S(}. 7Sz+{/F_}.S>{/}.`}.{:}`+{z S7=2}.>-=_}`=z%S_}.z,} _}.S>{/}.S=zY.%o}. ¤ =z,}.SzSz ¢]S}.O=°{/-SeF}% { £3Szt{DSSE{Uo} :DjSz[{b}M¢J/ S-z%Sz{%{=,}.]DSS8-S}V)8{7 }.a.: ] { {/}. po}. )%S}.Sz[}.A}.]z}% {/)%.D {`o}`-/=-$= Sko]o}`7a+«,7) ¢]o}.#{ X ¥ ~)%o}.7zSz _
3_}.[ ® z"Sz.z,}]7S-o} {/}.SzNS]}.{/}]}.b°{}8=¯_}87/ +{:}.7zE+{zz}2)[ {:}. z,}.7z=%o
-}.N}.[SS-o}.
{z ¢] }.K{/z {/}%}.%
[)+¢Jb/k}.g.-/}. SJJ {/3.:°3S>{/}.{/z_¢J.Y}.#}.«,.S"a}.UDSS=Â Y)=%o }.Sze{/.({} {S= ® .-S%7zY%73}.S=zSg}.">{Sz,} {Sz{ 3.S%S=zE)=z ¢] }. N{/}2}.(.-/}.-%=3.Y{/z {:}. }.U%.D[¢]zD[}.N}%.U={/7 7{/}.[-.N}.{z zo}.]C.=´}.A%.DQ={/7`{8.=)% Sze ¨3p:hµea% {ºa{S>{/zF»iSo}.V{.D{/2}.g{=-7S%F}.Sh$_
_}. «{/}.S=z8{/. S%%% Sz } {S97zK~3}.Sz , ® D{/7z9 S}((%"}.[% >{:}.7 7{/ { SzB»iS=3."}. °7{SzpA~3)=%2{[%A«,%
N-Q¢]o}.{>.S%S=zz _}% {/Sz} 3]ÁbQ_
_}.´¢]SSj{}.7{/}.`{(ºa{/7>{/zU»iSS}.(¸ W¹ "`{:} }.Az,}% {9%.Db{/z o}.]-o%.8ºa{S>{/zN»iSo}.F¸V¹ $ {/}]}. .-}.Y%o}.=¡JY.-}.Y%.Y£DF}% { £#g}.Y%.= 3. S}.Sz {:}F}.S->_}.8 (¡$z/}.[}.{/}`}.S ,Fz}F.«o. {/z,
Y°}% {F--%
>°33}]8}.A%{/p>{:}%.7Q/k}.-¸V¹ {/z ¬o}..g}Q}. {/} {U ,gz/}g/%¢h{/ o}b}.>}.`z,}% { %.D(oA}.K. S}.S=zt{:}>}.Kz,}% {/Q%.= 7{/}.[,
S%(}.{z {>{:.=Sz / E±b/}.7Y}.{:}K¸ #¹ "/J{:C}.-.S3Sz }.F¬._}aC¢ª-+{%3.-z,}.bC. }.F.-/}.(%=3.=p¢J= {+Dh_} {S7% {g=, _}.7>{:}.h5}.h_} {:}.hD}./b A ; E ; {% =z-}.{:}+,}.8%.D +{z>-3}.]}.h {/}.b/r {/zQ/ }. {/z S,+{/}.Sz8%Sz-W«Y={z ¢ = .«o.b¢ {:}.gC.x}.`.-}.2%=.= ¦ {/}.A{/.(z zo
¢]zN% zK{S {/}.S=zU/b3 {£Sz-{/}.S=z8Sz a{(7{/. %.V7z2}.h_} {/}.]_}.S>{:}.=D/V¢]z(zS%8/ { {So
(%.3}. }.b_} {:}.b. S}.S=z>}.2%"{ /.Q}.{/}]{A.C.%"Shz_ .{:%
,-»/A}% { £7zY{/z ..+{:}.7zK{"=SS=Â AS,+{/}.Szi}. %.D ,Az}az }.". {/z,
U7z3/.>{/}.S=z}.A}.{z }. {z , Sz{/}."g}.KDSSU{/z }.Nºa{S>{z »iSo}.Q>{/}%.S
1.2 Contribution Summary
0y z({ o}.S=z(}.b).SSza{z /.F¿{:}.Szg_}%.+{/ .%=3. >{/z{/=-z,}p{9z {/-z,} {So
g{ ¬o}..Sz].SN:{/z .)=_ SzF%Sz2}.Qºa{S>{z[»iSo}.8{]{`=z {9{/z { {/}.SDg%S }.Szp}.g%)o¬A=z,}%.S3}.7z]r}.S]{)b{:.a{hS7+¢]½ Jµe .%z,}V{b-{: {/}.SDh{/z{o
3%SV/)=3W- D.% }.>°3S_}.SzK}. z¿«,`{z # S%% o5.z,}2{SS+{/ }.S=zF¢]."}.[ºa{S>{zB»iSo}.>{/()zB%%_7o
Sz/.) {:}. ~3}.7zK ,Jµe".%z}F}.Y>{:}.>{:}.S>C.27{/}.S=z Q}."¬o}. {z 7%%>+¢´}.Y¬o}.-/.F7{:}.7z¡+{/z¡)N+{/%7o
_}.=-SÀ C]{A7{/.b{/.S}M
(9.S .27{/}.Sz SzN_}%.+{/³>{z{/=-z}+J~3}.SzK¨D ¨JµeU3.=)=%=3 {bºa{S>{zu»iSo}.N- F$Sz ~ }.S=zK¨S:h{z Y S%%]+¢ =z_}% {Sz,}.`«,%
>.7%Sz {z %-,}.Sz(${/}.. ].: ,
>}.A%b{/.a% }.eSz_} {/Sb{/z %}"SzS}.7{/b{: {-}..(>}.Nºa{S>{z »iSo}..
3]J.(°{-7k{z
-S.S+{/_}. S]$Sz-~}.S=z { z =8¢JU%+¢}.{/}"-7+
3Sze}.Kºa{S>{zu»iSo}. +{/zF${/S7o} {:}.g{z %)%} S5.z,} «,%
`%z{:.S=jyMz }..-j5{z ¢] }.2=z%.={:}.S=zp=}.hºa{S>{/z-»iSS}. S {/}rS+{_}i{r, {/p}% { o}.S=z{/{.D{//oz}r)}%}.+ Y.S-)%} {z,}+Qo}.N=z {So}M
{/z { {3}.7o}M
%+¢ .-S%{/K{BS SzE7, £CK_}%.+{/ {/SS+{:}.7z }.{:}8=z.z"C%S=zU{/z 7z,}./ {/}.S=z9
,hyMzN~3}.7zK2¢ 2{ {zA{F%}8/j.=-S%Sz2°}.z%Sz }.(S )z"}.7h¢ .£)
2. RELATED WORK
® S.o}.-kSz {/} {b_}%.+{/-j{+D .SD Sz.+{% {/}%}.z3 }.S=z-:DW}.]{_} }0¢Jg
,{/. ® -.z%SDh%3.D
25}. S%%WSz {:} {b_}%.+{/-WSW.%z}. SzN /VN{+¯_V.%+{:. o.}.7zgSzS `z%.Sz>-} {:}.S=z{/k{z =-2zo +{:}.7zN.%=3.2S5/¨/)=3}.S>{9_}. {F{/S=.o}.-)_}%.+{ -SzSzt ¨/a«,%
=3}.7-SÀ. :a{/z «,%
%=SD.S : |A{:} {B_}%.+{/-N{+D{S% )zu}%.+{/}. {"}.7-%.S`{/z +{/FC. z}%.J}./%
e¢J.Y)%.+¢ C(}.".)=% W{/3.:°3S>{/}.Szo=k{z -SzSzY ¨=: 8%=3.J>{z{-z,}kSz {/} {Q_}%.{-jSk)3.7-V=z.z J}.g}.oVz)=z =z,}.Sz,{/z }.S-{/%
3Sz {/} {: {/%.S{3{/ {/}..S_}.SW»%}..-.--%
a{/z =-2zo +{:}.7z.%=.b/.x)/}%}.7z £bSz{>_}%.{x>{/z{/=-z,} _
3_}.NÂ b)%C.>{/z2{8}.
U{:.F{:5}. { D.%S
N
"}. {):DY_} {/}. .=)%}.7[/ {:} {_}%.+{/-tJ.K{/-)z {"=z% {7>{/-=z}g .%+{/. ¢J/.£KSz}. o.}.S=z --/%
->{z{=-z,}VC8.,%%7z {/} {2_}%.{³«,.7A ¨ /¢].Q}.Q3¯M}.SDgS }.2{z_¢J]{a=SDzY«,%
(%SzF{ -SzSF³{-z,}8W--/%
"z ]}.a=SDzK=z_}% {/Sz}b .S%7zE2{/ {}..SÀ[}.---%
U.+«,S.-z,}.g2}. «,%
, 8%+{/. ¡¢J/.£¡.)=% Sz ¨:>~ Q ® 3./¯M} +C .: j{/z2Sz%7,}j7z,}.8}. 7_}%.S}. 0%. {:} {Q_}%.+{/( Sz[.S¢].({ {/}.SDa¬o}..A{:.FSz_} {/7S {/}g+{ . -}.W%=3.J {/}.SzQ{]z,}% {/3%.D+kJ D{Si}.Q{ SD >{/°3SFI.S%7z SDze}.>z_}% {/7z,}F8z}0¢J/.£e{/z ¢] }.9AJ2%.Db+{ Q}.`7{/}._} {/} {-.7= C.=²}. %z%[z,}.S]{z¢´={/SNS(.7= ¡JN+{/Sze- $ }.-5}.SD==S z/}V{ {/}.SDh}.g}.] {: {}..S_}.SV5}. Sz}g_}%.{I{:}%}%.S}.`{SA»A°{/-S=)oJ{>_}%.{-Sz {/}%}%.S}.e{S#%+¢]{ =z,}.Sz=U{%z Sz %z Sz SSz+{:8}%.z :Db{`%{/zNi}.S-=}.7]- )¢J= =z {/}. {US=Ez2)`Q {:}.#JS(SF)+{/%"z¢³3.S%S=z )=z Q{:.az}Q{ ¯__}. { {3}.SDo
${% zY}.S-={:%
37z {/ {/}..S_}.S W{ (}.7-J{g_}%.+{-Szg{/}%}%.S3}.8{Sh=- =3}W)o}.k? .%./N@.)6/D}..
`Sz.+{%Szg}.h.{S7o}0
r}.3.g {/}.kµg.)=%a{F*,5 %k{z v]%\@7g- Sz#¢]S#}."%.=F¢ = . S}F}.[C}.3.[{SF{% =z[}.Q%.z,}J}%.z Sz"}.QSz3}h{S=V~2op}.b_}%.{-Sz {S °3So}]{`7Sz+{/h}%.z ,}.bºa{S>{/zY»iSo}.+{/C}.8{`¢ {/}.¢ = . 7}]={/7h{/% z"}.b%S=)A/r}.b7Sz3 +{:].Dkµeb {: {}..7Àg}.g_}%.+{/-SzF- )%SzF_} {/}. +«,{:}.S=zVSz- }.a.{+DQ-/.]{z ¢] }.-,
2. S}.Szao}. ){:S+ JA3.=7Ãk. SzFz}M¢J/.£-}% {/-A+{/zK{S%-)b.{o SÀ SzA}..-r/rS+D6b_4%6D6/*/¢]. {:} {]}.Sr{/. .=) C. }.>_
_}.q¢]ze}.>SD{ }.} { D=S--/ {/} {=aSz3 .+{/%J}.2{z>°}.z,} }.{/}Jo}h{zz} )b.,%% =-7}.o
, JS(3.=7 {/()zE_}. S Sz ¨©/` ® ¦ 8Á ® .:¯_} oCuJYSD{ {/}>+{/O@.+\ Sz }.Yz}M¢J/.£E7->{/Sz} {/Sz {z 6 _?U? _ g{:.8Sz_} {SS S)}.]7={ .+{/V{b}..%3 = ³JSD{ S". ,
¡{o}..SzE}..{-7SzE}.3 z7«,i {z=Sz"}.(.{/-SSzY {:}.-2- oC
3Sz"%S}.SS}0
.o}..S=z9¡µe"z/}.Y}.{:}US+D6_4%6D6,*ES>z/}(}.N%S}.S=z }.F5}.SDQ.%=.g>{z{=-z,}+3{ho} ." z£V {/} { C. }.(Sz}a_}%.+{/ Sz )z z,}Ah}.(_}%.+{ {/} {N{:% .S={/J {/ {/}..S_}.SBJ[.S }.{/}`}.S(_
3_}. %=SD S o5.z,}h¿.=Ã.%7zgo}h}%.SJ}.F_}%.{Ã>{:°S2ª {:}.(/[{7=z z}M¢ .£#SD{ ¢].+{>-%73}.S=zt{/7- }.[_}%.+{²-SzSF³ {:}.b%>}.{:}g3.S%S=z=z_}% {Sz,}AS .{/}.S_¬ {/}Q{/79}.S- ® z}.`{.D{//2. SzN=-2z7{/}.S=z:D.{
{/z{-z,}g_ Sz
3z{/-7h.{/-SSzA {/}.J{/% =zUS. *D" {/ }.S=3)=z `z/}J {/z=]¢]o}.>7z3} {: {}..S_ }.S]k}.b_}%.+{ ¥ {/%}.7{5«,%
F3.,%%Sz`Sz(}.h¢]o.S%Jz}M¢ .£2}. .=z,}Nzz%.{/%
{/} { )7zBC%¢J{/ $SD{ % SzD |g,Uz}U%e{z,
{.+°37>{:}.S=zO/ +{ Sz(%-
0, M
¥ . S}.S=z`{S.o}. +{za)j% . V( FzS+{/}.Sz²:D.+{ Dz³3%}.+=z37Sz {:} {e%-,}.Sz#S>}.#.: «,%
{/z _¢J.8Dz"/8z=S_
{:} { ¥ . S}.S=z2-{z7% Si{/% z2Sz}r{/% {}..7_}.S}.}jS8 C${:}.S=z[-3 {/zS%1}.`. S} }.Q{S /p}.8}.S-8%.Sh{+{ 9}.S-= Áb3(¢J/.£ o5.-SzB.=)%Sze{=z {]3. S}.S=zEC {/- ¢ .£"{z {zY{ {/}.SDA%73}.S=zp¢]S YSA$ 3 " C5
3.
THE KALMAN FILTER
Jjºa{S>{za»iSo}.r¢J{p7z,}%. Sz(C==©h,
`]+ºa{/S>{z o ¼/k{/8{2.3.%7=g%=S}.SzN}.2}. S%.}. {/} {FSSz+{:]¬o}.% Sz3.=SN#~3Sz[}.zpWo}({FC=z {S7{/}.S=z-7z#}. ¬ a]3.,%az}%.bo /kFS}.o%z% {:} {"%7z¡ ¨=¨: -/}.S=z}% {/£Sze ¨=:jz}0¢J/.£}.S-(£DSz ¼:W{z z3 { Sz3.>{:}.S=zN3.,%%SzK ¨ /}.Fz{-b{2¢AVJg}% { o}.S=z{ ºa{/S>{z>»iSo}.JSV{g7Sz+{/J{S=/.S}.1}.{/}W_}.S>{/}.W}.hSz,}.% z{9_} {/}.A/W{F_
3_}.³{/% zY}M¢ (- {zS%-A ¨=:½
¾$# .%6$/%&J.$&-$$ JSV_}.-S % }.a.={={/}.]}.hSz,}..z{/_} {/}.]5}. _
3_}.N ® } }.S-Q_}. (5}.8¬o}.h3. S}.V}.8={/7b/ }.b7z,}..z{9_} {/}.AD}.Q{/}]}.gz°}h}.S-g_}.: ( 5t ¾('
.%$ JSg_}.Sb.%)z%SS`b¬z}.zSz-}.23. S}.S=z _}.z b}.(Sz !z2/h°}..z{j=%.={:}.S=z ® } }.S-& (5Fk¢]z`{/za{}.{,-+{/%.-z,}5Sk{+{S7{S=:}. ¬o}.W/%.}.Wo}.%op{% =zF}.J. S}.S=z-%./+jJS /%.}.S=zNS zg,
--Sz7-SÀSz2}.Q%.8:{/.7{z= ºa{/7>{/zO»iSo}.U-.S%K{E%}K/(>{:}.>{:}.7U+«,{/ J }.SzA}.{:}a.: -{"..%SD(%73}.S=z}.Y}.(S+{_}%.«,{:.
-}. iµgz+¢uSz,}%. b}.Q>{/}.>{/}.Sbz} {/}.Sz]=( -=z[}.F}.A|b7%.}.aºa{S>{zY»i7o}.2o+©:JJa_
3_}.³- Sh..%z}. Sz"}.gC.³/i}.gC=SS:¢]Sz[«{/}.S=z½ % 'R+P- /*) ' % ' 5O> ' ¨D
+ ' /-, ' % ' 5/. '
¢].
,
% ' / 1032P+5476 9698;:8 E 69=?< E 8>4"4 )='/ 13 0 2D0pE476 9F6C8G6H=R904IJ6HIJIJM=K8"N9F69IJ0O %4' 6H4"4;LP8>N0IQ4R8 + ' / 1LS2 :L8 9 4T =K8RLA8R06U:8 E 6H4 L / 0ZT L^]8R=?{ {3}.SDo
Y3. S}]}.A={/7Q{/}]}.A>{/7z %.Dj¢]o}.F-SzS>{SzC.>{:}.7z( {/}.i¿.= }.h{}.{. -/}.a%=.=Qµ¡zU{U.$C( 2¢]o}.{-.7%Sz =z_}% {/Sz} 7>3.%z,}. }.}.N%.=[=z¡%.K3¯M} 4 _r{[ºa{/7>{/z»iSo}.>¸V¹ " SASz_} {/7S {/}A}.2>{/7z%.D+ ® -o%./Y¸V¹]¸ ¹ $ jSF{}.S{/}. {/}`}.-.-/}.>%=.=j¢]S %S27{/}.g}.F) {/}.S=zg¸V¹ " F»A}.F.{/£D( %S-SSo}M
, ¢ [{%%--}.{/} :/ Q{z }.{/}a¢J Kz}2{+D>«,.S ¢]o}.N:D.¿{/7z(%=3.
T
4 !" ¸V¹
¸V¹ $ ¸V¹ # : ; : $ ; : $ ; D
IJO0ZIQ@ I E 9 0 E 8
u : ;
r} {/rz2)h/k%=3. r} {/i«,.7 ~}%.+{/-SzF%.a3¯M}5IQ1I*/O 6. %
N1 I /O T5 ¥ .S%7zN¢] }.N/ [1 I/O T) ¥ .S%7zN¢] }.K{:; } 4 1 I*/O 6. ¸ ¹[~-,}.Sz2${/}.2$=3}.S=z{/¿8{:}Q%.?4 ¸ ¹>{:}Qz,}% {9%.D8. S}.Sz-{:}%}%.S}. ={/Sa{/G } 4 Yo%.2¸ ¹>{/G } 4 j%727{/}.SzY¸ ¹ " ¸ ¹>{:; } 4 j% / {/} {F%-,/}.Sz"$=}.Sz{¿ ® }.{9={/Sg/j_}%.+{-SzF{/}%}%.S3}.a{/G } 4 {/} }.S-gSz_} {z,6 } ( ¥ . S}.S=zK/j{/}%}%.S3}.A={/SA{:; } 4 kC. ¸ ¹ " {/}]}.S-gSz_} {/z}6( yMzz:={:}.S=zY%«zbC. ¸V¹ " {:; } 4
"
YL] {/}.(.%o}. /¨3D=+{/}p}.W>{SzA%.D+/{/ ¸V¹Q3./ p}.S-={:%
37z _}.S>{/}. {SY`}.U_}%.+{/ {:}%}%.7}.{/}N{BS+¢J =-2zS+{:}.S=z[=_}+ J|g>}.!°37S7o}0
E{z z {/SS}0
Bb}."¬S}.(¢J"+{z - o5.z,}J3.,%%A$=z>z=z37Sz+{/h- S { {:}.o
,{o
37zb}.].{/-JC {-¢J.£2}. o5.z,}V{3 SS+{/}.S=z
!
¨3
7=9fW5;C* %/Y=z,}%.==zF}.h7D/ {:} {b%-,}.3 7 zY{/z }.Q=z,}%.=j:DQ}.>.$.7{/}.SDo
%7-SN}.#{zN}.K_} {:}.«{/}.S=z
3z{-S+{So
,{h}.
Y{:.A{: {-}..h}.F}.g_
3_}.N
3.2 Why Kalman Filter?
y0z¡+{/_}.7zE_}%.+{ .%=3.>{z{/=-z}>Sz,}.E{¬o}..Sz 3.=7N />-.Y%)o¬+{/7o
{ºa{/S>{zE¬o}..Sz.SN o}`S2z%.{:%
}.K°{/-SzF}.-{SS+{7So}M
h}.(ºa{S>{z »iSo}.Uz U{E¢] e={:.S}M
t/()%%7S#.=S C.F7{/ }.Sz2J2ºa{S>{z»iSo}.aSA{[_}., {/_}.S=p..%SD2_}.S>{/ }./+¢] o
>% Sz[_}.S>{/}.Sza}.8Sz}..z{)_} {:}.b/k{a_
_}. {% z}.K%.{/}.SztA}.K_
3_}.NÂ -°}..z{Q){+, S/+NyMz%%z=i¢]{/}F{Yºa{S>{z»iSS}. ,2SA}.N>{/7z,} {/7z {/z {:}.b}.A)_}8_}.S>{:}.Ai}.A7z,}..z{9_} {/}.a,
>. .S
K¢ S=7zK{z =2SzSz"{SW{+={/S¿{/S {/} {U$_} {/}.F3.S {/z °}..z{i-+{/%.-z}. }.>/.x{/z {/}. =%gy} {/-SS%k}.SiC+{/}W,
a.{={/}.SzQ}.J_} {:}.J_}.S>{/}. C% ¢J{/ 7zU}.S-"{-? %.6/$Y.,% pSz/.) {:}.7zN°}..z{ -{%.-z,}.]¢]zD]}.
Y{/.`>{ a{+={/77{/S`}.- {:}. }.V_} {:}.V_}.7>{:}.]{`.
.%$/g.,% {z .)+{/}.Sz]}.% _}.p..%SDo
g{z z,}.7z=%o
b/=p}.S-=iÁQ9}.jºa{S>{z »iSo}.A) {/}.A{-. 7}.7z/%.}.S=z- {zS%²Cg_} {:}. _}.7>{:}.S=zN{% zY}. J{
,%7{zN3.SzSS= N{/z,
u={:.¿{:}.S=zN{/.)%%SSeSz C.27{/}.Sz {#.%=3. >{/z{/=-z,}h3.=7³z h}.bF3.S7{2k}.b? %.6/$; .
.%$/ {: { 7N µt{:}[7"z¿«,U{)=3}"}.Kºa{S>{z »iSo}.+{J¢ b¢]S79SS7_}% {/}.A)S+¢A7J}.{/}h}.bºa{S>{/zY»iSo}. {z)F_}.-7À }.[/.I¢J.£{S(%=S}.SzA/Y}.% C.27{/}.S=zBJ"{ {} {:}.S=zB7zDSDF)/}.E%7-SS¬+{/}.Sz $ 3Sh_} {/}.SYºa{/S>{z »i7o}.>/(.3.%SDYS+{/_}>.«{/. 2{z z {SSÀ+{/}.S=zE$= 37°}.z ºa{/S>{zN»iSo}. V{/.7{:}.7zNSzN.S C.27{/}.S=z]+{zN=-b¿.=q_:V}. _} {:}.=¢]}.Qo}87 o.}.o
"=%.={/SaQz/}+i=J}.A_} {:}. 3.={D{:}.S=z¡+«,{/}.S=z9J¢]}.-o}>S-S7z+{/[/>z}+b¨D2}. °3}..z{p-+{%3.-z,}h+«,{/}.S=z9¢]}.8o}878SSz+{:b/bz}+ Dj}.8°3}..z{-+{%3.-z,}+=¢]}.Vo}J-j¢]S}.[{Az ¬ z{SUz}+a{/z ¬z{/SS
"}.z=S%e3.,%% ¢]}.2}.
e{:.>_} {/}.S=z{/%
e/Fz}+"µe-¢]S7 S%%a}.% ¬Dg_
3_}. %S=zN{/ {-}..]7z".+{:}. } {/79)S+¢A Ja%)7{k+{/%2SzN¢]7 N}.A_} {:}.2S o.}.o
Y=%.={/S ${%>a{):D: ,Qz}8)=%`{z,
".SN JSQS]}.A+{/% ¢]zu}.U.%=3.}.B)>{/z{ 7 o.}.o
u-+{/% {S $ 3S ¤J¥W¦ `--/%
K.{/=:>y0z}.SA+{/%=i}. , >{/}%.o° }.{/}8.7{/}.Q}.aSz}..z{p_} {/}.a}.(}.a°}..z{i-+{/%.-z} SY{z¡ z}.o}0
>{:}%.S°5OyMz¡/}."+{%Q}.ºa{/S>{zt»iSo}. C.27{/}.S=zN{S7Qz {z= JA_} {z {/ ºa{S>{zY»iSS}.b{/%%-h}.{/}])}.[}.g_} {:}. 3.={D{:}.S=ze+«,{/}.S=z{z }.F°}..z{/W-{%.-z,}b+«,{/ }.SzK{/.ASSz+{:` /©/ JS]7h}.g+{%AC]}.b¬._}]°{-7b7z F°3).S-z,}."~}.S=z 37+V¢].>}.[)=%o}.S=zB{z = S,o}0
/]{Y-=S7F7{/}%C. -:7zYSze{"7{z-{/.(}% {/£D JYSz,}..z{/J_} {/}."SzB}.72+{%"=-3.S%F}.[3%.z,}(_}.o >{:}. )%o}.7zU{z DS,o}0
Y/k}.g¿{:}%/.N){z }.g°}.% z{3-+{%3.-z,}.k{:.J}.J%.D )=%o}.S=zV/)}.J7{/}%/. }.3.== +{ .£DzSz3 X ¥ ~)=%o}.S=z7zj/F%z%` { £-µtzo}.a}.(_} {/}.>.{/D{/}.Sze+«,{:}.7zea}. °3}..z{]-+{/%.-z}F+«,{:}.7zS-zzSSz+{:U$+{%"{z ¨ D k}.%>+«,{/}.S=zF{:.>¬._}FSSz{/.SÀ Sz}.>-_}`.z,} D »]°{/-S=oi}.b-/Sz`7{:}%.³{zN{/S%F.} {:}.a{)=3}
_}.S>{/}./¢]Sa.%o}.iSza}.W°}.z ºa{S>{z`»iSo}.h 5¸ ¹3 /.F¿{:}.S=zppµtSS9¸V¹QS%r>{/z
QzSW>{/}.>{/}.S+{/3.=3 %}.SVz¯M:
D ,
F}.h_} {/z {/ ºa{S>{z(»i7o}.g$= S.:{S z3=.=z:2 /©/ro}bz=z}.7%gSgD%
K%$p{_
K}.[7( S-z}+{/z -Sz,}Q{/}].z[}.7- ® (}.Nºa{S>{/zt»iSS}."S-.+{/7o
{ J{
,%7{/zt_}.S>{/}.[Sz S%S%>S+R :o}.8{%SA=) {/}.S=zKSJ}.(3.=).o
>¢JSU{S {+={/S¿{/S {/} {-}."{:%.SD({:}a{[)_}g_} {/}.2_}.S>{/}.=`J {/} { +{/z`) {/}p}.7-r/%.=) {:}.Szb/kz !S}.Sz{z }.Vºa{/S>{z »iSo}. )z 2=zE}."=z3¬ z"-+{%3.Y{/%%,7{/}. ¢]o}. }. {:} {}.3.+{£e}.Y}.SNogz%.{:%
,t~ {=z3¬ z -+{/%.=]Sz J{
,%¿{/z}..-SzS=
,]S>}.N%.":={:.¿{/z >{/}%.o°b}. {:} {h-+{%3.-z,}.pJjºa{S>{za»iSo}.p¢JS= o5.z}`-+{/%.-z}.b%SzN}.(Sz3=.%-h}.-:={:.¿{/z >{/}%.o°$$ =S}.b¿{:.=8}.b%.+}.g%>{/7S]}.g¢JS=,} ~3o}.{/}.S=z [{:.7%2¢]zU% U{>=z3¬ za-+{/%.`>{+
z/})E{:{S7{S ${% ,P»/Sz_} {/z2SzO}.#z}0¢J/.£ -=zo}..Sz[°{-7a% SzU=3g°3).S-z,}.2~3}.Sz, ¨D }.`z}M¢J/.£Y}% {/( {:} {"{:.F-+{/%. °{/}.o
,gyMz{>-=7S .=)/}.Sb{/7S+{:}.S=zp{zYo}% {%z %z%/8-7,}J.}..z[}. S_} {/zb}.2{2z+{/.,
-_} {/S=¢]o}.=}J7z S+{:}.7zF:¢ {/3 {/}.J}.J-+{/%.hS ¦ z j%F{bz o}.S=z9,zS%W{z({/o}.% z{:}.SD`¢J{
K+{zU)az }."{%%Sz{--+{/zSz/r=z3¬ z $`%./b-+{%3.=r}. {/} {N{:.(}%.+{/}. {`{%=S}.S
/% .}F$a{/Q}.2/.=z }%.}.)]µtS7`}.a_} {z {: ºa{/S>{z »iSo}.>.27{/}.Sz¡S[_}.SSQ{S7{S=]>{/Sz} {/SzSz#{/z {:}.SzY}.(:={:.7{z[>{:}%.Sa>{£DA7o}%}.S-%z%= ® g}. -+{/%.-z,}.-{:.N}%.+{/}. {[{%=S}.K¢]o}.¡À.e={:.7{z= }.
=-Sz{:}.F}.F z(%Sze.,% t~,} {/}.-_}.S>{: }.S=z(}.zF+{/z-)h%+¢]zF}.g. J}.g{g7{_}%.«,{/.V/+,-. =z {/7o
,Q{¢ S=,}. S+{_}%.«,{:.>¬}%}.Sze3.=7NJ¢]. }.2_
3_}.x_} {:}.FSA=%zU}.[)_}A°37{/7zU}.2°}..z{/k=3 %.{/}.S=z9(y0zU}.{/}a%z%=p7{_}a.«,{:.A+{z)Fz% . { %)7{/r+{/%`/kºa{S>{/z"¬o}..Sz »iSz{/7o
B/>+{% ¢]}.-}."z=S%K3.,%%"{/.N_} {: }.S=z{/%
B{/5}.(}.[.z,}.S-[)%.>{/zBµ¡z#}."z7% .,%%8{/.g_} {:}.S=z{:%
, 3S¢]z"}.b)=%o}.S=z"j{`-=7S 7{:}%.qSA.)%}. ,
{ X ¥ ~_
3_}. {/}a.7{/`Sz,}..z{/S ¢]o}.E{"¬°3 .7%Szpk}.-3.={D{:}.S=z#]%.2:={:.¿{/z )-A-S}.o
. S} {7>JSaS`)+{%- {:}.Sz %./-:={:.7{zYSzD=SD2=zS
}.>:={:.7{z(8}.[_} {/}. .{/D{/}.Szt{z °}..z{h-+{/%.-z}F.,%%]z/}(}. {}.{]%z%>.+{ Sz(}.-%SDJS-.,%>+{/zB}.z )g)%C.- )SSz=.%o}.7zFSz"}. 8S+{/}.5+«,{/}.S=z /©/ yMz">{z,
-.+{/S¢ . {SS+{/}.Sz}.g%.8:{/.7{zAS]z} _} {/}.Sz{/%
,3= 37{z[o}% {/%=z " S_} {zb.+{ SzFSJ2 >7% { {:}.2oj}.a%=z ¢J{:=`Sb{S- {/}b{(¢h{/7r=S7«,o
,. %o}.Sz`Sz>7o}%}.Sgz.
()=z {/£2}.a}.Q.SD+jyMz(}.S +{/%= }.":{/.7{zY {:}."{2}.)[+{/%.S =3}-SzE.{o }.S-= ).&F&( SZ/!2C4N .%tC42 NNC4Ym`= &-EnV$o; 0 a a .% % 4UCgC4hC4a/&>VfW 0 C*b^ _&> V %R". @ A3.&27Z:%6->D6=6 ..AC4b.$$b&>$).6>D@.0G(y0z}.2S7+¢]SzU%}.7zp¢JF¢]SS S_ %[>/.F¿{:}.S=z¢]o}..%)}>}.}.N}.3.NS-)%} {/z} _
3_}. %7z{/ {-}..½K¢]}.-}.Y.=S /.F7{: }.S=zSgS7z+{/($SVz/}+9{zU°}.z ºa{/7>{/z»i7o}.g%= ) % 8¢]}.Y}.°3}..z{b-+{%3.-z,}.[{/.e{/%%,7{/}.
o}.%oMVo}(S2}.zez%.{/%
#}.KSz.)/ {/}."}.>DSS=Â 2.o z,} {/}.SzU{z {/z7{/bDS,o}M
KSzN}.`_} {:}. %.S}.Szp8J =%.D )=%o}.S=zu{/z /.Sz,} {/}.S=z¡/g}.YDSSN¢]SS8}.z )z =z"}.A_} {/}.AD}.8SzN{Fz=z30SSz{/8>{zz+
¢]o}.2{z`%.i={/7b$oz}+={]7{_}k.«,{:.i/W{]¢ S=,}. 7{_} .«,{/.bC.27{/}.S=zU%= )`-S+
, ){z ¢]}.b}. z=S%g3.,%%8{/.b_} {/}.S=z{/%
$orz}+}.Q:={:.¿{/zb>{/}%.o° S8=-}. {z {/}. Sz".+{/o}.S-:
4.
=¯_}[7zE}.[}M¢ S-z%7z{/8%{½N}.F}.YS,+{/}.Sz¡ }.`=¯_}A+{/z)A.3.%z,}. ,
K{-)=Sz,}(1M ; CY ; 8{/}b}.S- Sz_} {/zS } ()e~Sz-}.>3¯M}-S({/S7+¢ }.-:D-zo
#{/S=z _}% {S}8SSz¢JA{:=b8_} {/}.a{/.7{7½ ¾ M ; }. N,/ Sz{:}.
MODELING KALMAN FILTER FOR DATA STREAMING APPLICATIONS
¾ Y
;
}.
, 7z{/}.
¾Y# ;a {:}.Aj {/z=A/i}. ¾M
µ(z+¢ %.S)-+¢ }.Y>{/{ {/} {[_}%.+{ 3.=SI}. A3.=)% ·8¸V¹"- $g|gA}.[}.2%{`S7-o} {:}.7zb¢ 3.%z,}Q°3).S-z,} {5.%o}.]}.-7SS_}% {:}.2zo
Y{F¢ { {z3 } {/=k-z}.Sz Sz(~}.S=z2¨3rµeV}._}. k3.=)% - z}.3. o5.z,} {:} {[%}.g}. -=z_}% {/}.2}.F{ {z,} { e-z}.Sz Szt~3}.S=z¡¨S=ur_}.7z¢h{/ =zYz)}. _
3z,}.}.7b{z .+{/ {/} {%}.Wµg{/7%F%+¢ +¢t}.Fz_}%.} }.A_} {/}.g}% {/z%o}.S=zN>{:}%.7h o5.z}]%z{:.7
;
{:}.Aj {z=A/i}. Y, 7z{/}.
,/ Sz{:}. JA_} {:}.g}% {z%S}.SzN+«,{:}.7zY}.zY)-½
M ; / M ; Y ; / Y; M ; / M ; #Y ;0/ WY ;
& \D&b?)72 _D R/,*Y%+¢]F}.")%C.>{/z"8}.>ºa{S>{z »iSo}.U¢]zu}.e_}%.{-Sz{/}%}%.S3}.{S ,Kz/} {+DWS2z=S%h{z =z,}.Szk{A$ .6A7z2{/%.S{ {/ {/ }..S_}.S ChS=z= ).S J/5}.7-j»iS=.Q¨a%+¢]V}. _
3z,}.}.S+{/7o
2=z {/}. - {/} {jJh°).7-z}jSzD7= }% { £Sz2}.g)=%o}.S=z$Sz"}M¢ 7-z%S=z k{/zY3¯M} -:7z2z"SSz{/8S7zg%-z,}.J o5.z,}h%S=)jµ -=z_}% {:}.b}.g¬._}8{z }.bC=3%}.K{ ={/z} {/=]-z3 }.S=z SzE~3}.7z#¨3S>}..}.Sa°{-7"µ>{S% %+¢1}.{/}`SSz+{:N¸V¹- W)%/.-2)}%}.2}.{z}. .S%7zN+{/7zF- j /¨/Wy0p¢Jg ,%a{2S%8{ {/}.2- }.`=z_} {z,}-¸ ¹"- ¿J}.2)%/.>{z S]+«,S={/Sz,}h}.F}.{:}]] ¨: & \D&b?)7 / ,* 8{z`/k}.aºa{S>{/zK»iSS}.QC -S°[- S -z_}% {:}.7z2}.g%z { {z,} { Sz-~}.S=z-¨S=jJ {/} {/%}V{/}%}%.S3}.J{SJ% Sz`}.S °{-S %+¢]W{Q%Sz% {}%.z :Dr}.7-Q$%h»iS=3. DQµe`.%z}Q°3).S-z,} {p.%o}.QCASSz{/a{/b¢JS {[%Sz%= {(¸V¹B- S"Sz}.S"°{/-S=OµK%+¢ D{/Sz(SzE)%/.>{zYo8¢J[%N{K/%.}-- $V{z {S%}.{/}2}.Y)%.>{/z ,(z} { N2 #o ¢J8%8{AS%J{/3 {/}.8- p}.]=z_} {z,}Q¸ ¹`- ¿ & \D&b?)7 a$ V .RC C*,G ¾ W JS8°3).S-z,} {9%}%}.Sz-S8%CpCQ-=zS}./.SzF}. )gh ¥ }% {:-])}M¢ z>{/z-.D{/zSÀ+{:}.7z[{z }.h=3}.% ¢J/. ¨3[J7a°3).S-z,}b7a% }."°3-SoC
K}. }.o {z }.>=3%}.B{ {z,} {/=(/b%SzB·8¸V¹EJ °3).S-z,} { {:} {%}r%+¢]za7za»iS.4 ,rz} S} {z,
KS%{/SS
z,}.o¬){/S2}%.z M )b.a¢J2S7S_}% {/}.F}. %W}. {/} {h%-,}.7zJ+{:}..V}.Wºa{S>{za»iSo}.+ µea{/S%-%+¢O+¢ }.g%b+{/zNz}%.9}.A%z%o}.So}M
Sz}.(¬z{/ «,%
{/z_¢ F%SzN}.F%-,}.SzN${}. F
!
y0z(-=_}V5}.8-:Sz/03¯M}j}% { £Sza_
3_}.-=}.]C}.3. S,+{:}.S=z-}.J3¯M}jSj- S {j{8S7z+{/jCz}.7zF/}.S-= J}.g}% {+¯_}.%
Yj}.g-:Sz(3¯M}QSb{(SSzA%-z,} Sz[}.g%{}.S- =>{Sz9kµeb._}%.S}]}.g-:D-z,}Vi}.
¢]. >6 7]}.Q}.7-b7z,}..{5)}0¢Jz (Y{/z ( u JK-{%.-z,}FC. }.N%z%.U [SzU -=_}>{%$= S %Sze{ X ¥ ~F7(}.YU S,+{:}.7z / {z }.F}. -+{/%.-z,}h>{:}%.o° 7 U U
JQ.{-Qºa{S>{z"»iSS}.h.27{/}.SzY+{/z")Q+{%So
Yz% { SSÀ j%S-So¬ }.Q%o}k>{/z
o5.z,}i_
3_}.O- Sk{/z °}..z{J%.{/}.S=zW=S7zK}.>_
3_}. }%.-z =v!°3o SSo}M
#SzE- 7Sz o5.z,}(){+3S/.#»/-°{-7jS8¢J °3)}8}.g}% {+¯_}..Sb}.-)h¯M.£,
,}.zN-.A_} {:}.2{/ {( }..9¢]S £D}% {/£K/JSz.+{%Szo
7%/ a){+ S.9+{/zK)2% Q»/gSS°{-S=¢J`+{/zK{+D`{-_} {/}.F=}. 8}.-C.' . S {/z {N}% {z%o}.S=zB+«,S7 {:}.S=zE8}. /.! ; /" ; D 5 ; D "6=5 D ; D "6 L 5 # D ; D >6%$ y0a{ U DU 7,S}0
%{:C}-z -SF% Vo}(S()=%L %S7"}.} U {/7zEU }.> SzC.>{/}.SzY}.(z3.7 Y}.g-+{%3.-z,}]{/` µe`+{/z{/7%Y- r}.Sg.,%g¢]S}.>¯__}($ VY_} {/}.2={:.o {Si¢].F¢J Nz/}a>{Sz,} {Sz}.F {/}.-/h {z=-/J}. {/z ,/ Sz{:}. ® o}.E}.SF¢J )N{U7%-{ +«,{:}.N- ]}.>{E}.N_
3_}.NV¢JK%:¢²Sz-.%o}. }.{:}ho}h)%C.-]{/}J7{_}8{J¢ S9{J}.Q=zDz}.Sz{){ Sz -}. =+ ¦ %Sz{=z_} {z,}>_} {/}.N}% {/z%o}.S=z - h¢J {+D
M ; / M ; D Y ; /-Y ; D `
µe`+{/zz+¢ .%z,}b}.`>{/}%.SbSzD=SD SzK}.`z_}%. }.S=z }.Fºa{/7>{/z»iSo}.a/A}.SA.SN2JF_} {/}.-{/z :{/.7{zF>{:}%.7A{/.2W}.`.{- S-z%7zp5}b}. o -z%7z{/7o}0
)z [z¡}.
3z{-SK=-)zz,}.>Sz¡}. _
3_}.N»F%7-S7S}0
e¢J[£DE}. [ {z \ >{:}%.7({/ 7{/==z{V>{/}%.Sg¢]o}.{S-© ` ©DN{/z S-z%S=z ^2 {z n 2,).%)}.SDS
,gJ`_} {/}.2D}./ % ' Sb.3.%z,}. {
'
M ;
(
Y ;
&'
% ' /
µ(z+¢ %.S)-+¢ }.N¸V¹K+«,{/}.Sza+{z)(C {/- C { Nk}.g°{-7h%+¢]zK{):D
4.1 Tracking a Moving Object
D D "6"655$Y M ; ; D D D D
)* *
M ; Y;
+
`
_+¨=
JA_} {:}.g}% {z%S}.SzK>{/}%.o°-/g{FSSz{/8- 9S ) W` © ©` © &'
) ' / (
'
©` © ©` ©
"6 K ` © ©` © ©` ©
©` ©
©` ©
)*
©` ©
"6 K ` © +
©` © W` ©
*
©` ©
`
'
S
_ D
~S-77{:.S
F}.]_} {/}.8}% {z%o}.S=z>>{:}%.S°2/]{A=z_} {z,}J- S
@ W ` ©
)=' /
©` ©
©` © K` ©
©` ©
©` © K` ©
F `
_+=
Jh_} {/}.h-+{/%.-z}i>{/}%.o°?, '`Sk..%z,}. {/jC=SS+¢]½
, ' /
@ K ` © ©` ©
©` ©
©` ©
©` © F `
_D
µJ{/%%-V}.{/} ) ' .>{Szr=z_} {z,}k.= ® S}.==2{8-/. .{SS_}.7F={/7a)='>¢J >{£DA}.`- i-/.2{/3 {/}.= ¢ %{E=z_} {z,}N{SCK%S-So¬{/}.S=z9A{z %+¢I}. z {So}M
N/i}.b- 5¢JA3.=)=% µg{/%%-y , ' }.F)b=z_} {z,}J}.F>{/Sz} {/SzY%S-SSo}M
, ® 3 z,}Q¿.=´}.a+«,{:}.7z]}.a=¯_}gSb°)}. }.-S7+¢ o}.N }% {+¯_}.%
uSzt}.{%z2{z,
¡C.SzBCz}.7zp Jj¢]zF}..]{/.hzg-+{%3.-z,}./}. ¬S}.V3. S}.Sz ¢ = )({/% =z}.F7{/}._}`}%.z _S ?/]}.{/}A}.F3¯M} {])z"=SS+¢]Sz
4.2 Monitoring Average Zonal Electric Load
y0z}.7A°{/-S2¢ --+{%3.F}.FS}%.S-)+¢J`SD{ h{ {/%}.S¿{:WÀ=z=D {/}. =%
`=3] =: ® S=%]S,=£2{/}k}. {/} {/%}N»iS=3.[DA7z S+{:}.2}.{/}`}.--+{/%.-z,}.AS7+¢ {e%Sz% {8}%.z h¢].K}.NSD{ .{ [o}.")+{/£ {S .SzN}.-¢J.£SzU=.F{z # .= .SzN}.>zS=,}F{z {/.o
B-.zSz=. ® }F}.S-"7z_} {z,3 } ()Job}.Y%Sz% { =-)=zz,}FS 4RIJ0j [645=j}.ze}.72.,%(+{zB)[)_} - S ,
[%SzF}M¢ (_} {/}.A{/.7{S M ; {z 4 ; {/]C=SS+¢]½
¢].=
M ;0/rM ; D5 E }. " ) * , * .+{ Sz#{:}>}.Y.-/}.N%=3.U{z : ; S[o}.>+{/ / . S}. ={/7=r}.(%./% - ; 7 : ;"'&)(+* u : ;" *., * >yJ}. }.} {/Jz2)ah.+{ SzF>{ -,
}.(.-}.>%z%F7? 0k }.ze{/}%.o°5
&
5.1 Example 1: Moving Object Environment
µeb%727{/}. {F-:Sz3¯M}]}% {:¯M}./%
Y/]}.A3.)=% j}.7]°3).S-z,}+JV{/K-:SzF3¯M}b{ }M¢J>{:}%}%.S}. z{/-o
S+ /$E$SzY}..-J/ q{z , 7z{/}. ]{z {/zz+UJa}.>=¯_}( {z3 -o
-{z=go}.J%) {z +{ Sz{/z }.z>z}.Szh=z }.{:}(SSz+{:-{:}.e/>{N {z =-o
ez {/}. Sz/}.E8}.7- JQ>{/°3SFª%) /p}.b3¯M}J¢J{hSS-S}. }.F©©`zo}. ¢].+{b}.2%S)F {/.o}% {:.7o
U {/z=2,
K{z,
N{-=z,}+ µeV=z_}%.}. { {/} {/%}k%:¢]z2SzF»iS=3.h¨3%SzQ}. {):D - z} {/SzSz =©=©=© {:} {g)=Sz,}. {:}J{g.{/-SSzg {:}.Q/k+©=© - µeV}._}. }.J)%/.>{zJ)}.Jºa{S>{/z(»iSo}.V{3.D{/ =z"}M¢J o5.z,}]_} {/}.A- SA½ ¾ ¤ =z_} {/z,}2¸V¹-- J[_
_}. S2- S %e}.{/}`}.>7{/}._}F {:}.
{SQ7V}.8)_}h. S}.S=z>/h}.]}.3.=WJSJ- SYz}.{/SS
%S-77{:Y}.e}.K{ {/.+°3S>{/}.S=z {SN- A /tJN-+{/%.-z}F=z%S_}.[/J¯__} }.W)=%o}.S=z2}.W=¯_}jSzA}.W}M¢ 7-z%S=z{,%{/= $ =S ,/ Sz{:}.2{/z ,/ Sz{:}.=
&
¾ pSz+{/`¸ ¹-- ¦ z j}.7j- ¢ ]} {/£DJ}.J {:}.]9{z=h5}.h) %o}.S=z`7z,}.]z% {:}.S=za¢]za. S}.Sz]3}..j={/S JA_} {:}.A+«,{:}.7zh¢J. %.S) 7zK~3}.Sz S=
.9{/z {Si}.3.a- Sb%+¢ -{/ {/S`)%/.>{z= µeF{S%N%.D2}.{/}b}.Y·]¸V¹Y)%C.-a{/}aS+{/_}`{g¢ S {/ }.a+{/Sz>%-aDzKSzU{(¢J/._}%+{%2%z{:.S$z_} {/z} ¸ ¹F- ¿Q )b+¢ D+3oi%-gSz/.>{/}.S=zY{)}h}.Q_}%.+{ {/%.S{k {: {}..S_}.SgSA{+{S7{7"$S7z+{/F¸ ¹[- ¿)o}b+{z .: A{2),=_}8}.F}.g)%.>{/zA/i}.A_
3_}.N
X " K ,/,*"! P t O w
t w
¸ ¹
»iS=3.ee%+¢]Y}.U=-{/ {/}.SDU.%S}.[/K{+D {/=% .g={/7aJF3.Db°So}. ,
N}.`z_} {z,}-·]¸V¹Y{/z }.[+{/7z% -"{:.Y%S-S7{/ J+¢JD+V}.[)%.>{/z }.FSSz{/[·]¸ ¹NSA%SS=,}.o
¢ .%(/`7+¢ª.S%7ze{S 3}F)}%}.FC-7(.S%S=zB=z#JY%./.-{/.[-+{: %. {/(%PQ%..F7zB)}.#}. '{z ,/ Sz{:}. JVS M ; S }.]%.hSz-}. ², 7z{/}.b{z Y ; S }. %./(Sz , Sz{/}.Y{/}`}.S-[Sz_} {z,Z } ()k}.-}.} {/h%.FS ?M ; 5 Y ; FJb¢J(%.=2}.{:}ADz{:C}.a.{+Sz %S=zS¬+{z,}8-FzS+{/}.S=z":D.{ 9·]¸ ¹ ,]z/} / { }.b)%/.>{zAk}.b_
_}.´{ =.%o
,
(
( (
(
: { & Q4 ! +! > " t ? w
»iS. Q%+¢]i-{: {/}.SDV.%o}.i}.j}M¢ Qºa{/7>{/z`»i7o }.]- S]{={Sz_}]}.b+{/ {/.+°3S>{/}.S=z[% -=jY+{/ %3.-z,}.j{/.h} {/£DzFSzF}.J/. 5)=%o}.S=z (1M9Y X SDzF{ 3.S%S=z>z_}% {Sz,} 3D)=Sz,} (1M9Yi7W {/}. }.g}.h%.= or%.hSz[o}. / ={/SbSJ/.+{/}.h}.{z jyMz>)}.-}. ¸V¹N- 7p=zo
)%o}.7zeSg./ p}..(SAz"-+{%3. -z}Jk}.Q {/}.Ai{zAk, Sz{/}.a={/S ® 83 z,} ¿.=´»iS=3. 3}.Q).z,} {/=g/k {/}.J%SzF{ SzF{z =z_} {/z,}K¸ ¹- 72}.>.{-=eJS(S(){%>}.[z _} {/z,}J- S %S-S7{/ }.g}.]+{ Sza% -D¢].h}.] {:}. /b {/zY8{S(SFz/}F} {/£DzESz}.Uz% {/}.S=z9O )b+¢h D+Do¢ h%J}.JS7z+{/Q¸ ¹A- $¢ ]%J}.{:}j}.SS7À{/}.S=z-/ }.2=-FzS+{:}.7zU%=.2¢h{/g3} +¢]zU,
U{.+°37>{:}.o
{:}]{2- {/}.8.S%7z"¢] }.[i¨2zo}. ® V}.b3.o %SzF¢] }.`7z.+{/%D}.V=-2z7{/}.S=za.%=3.h}.SSSÀ+{/}.Sz
, AQ
t % w
5.2 Example 2: Monitoring Power Load
JS {:} {%}F=z%7_}.28S}%.S[.o
e)+¢JFSD{ C.= {eÀzK/K{e-=z,}.{z =z,} {SzY¼¨3 {:} {e)=Sz,}. J {:} {%}YS"%:¢]zuSzu»iS=3. ® S=%N7,£¡{:}Y}. {/} { %+¢]A{(%Sz% {i}%.z b~7za% K_}%.+{{/ {/}..S_}.S +{/zN=zS
[) {/¿}.]}.g_}%.+{/³{/8)zN{/z{o
3À
}.8_
3_}.N{/z"{/3 {/}.b- >{
Fz}J{o¢h{
3J)Q{+={/77{/S=
: { & Q4 ! +! > " t % w )Qz=¢Ja}._}Q}.
{:} {%}AzN}M¢ ¸V¹"- S)=z`}.{/}g{_ %- %Sz% {)=-)=zz,}.J{/z }.8}.J}.{/} ¢ .£ z[{ %S-72S7z+{/>¸V¹N- ¦ %7z"z} {:}.7zg¿.=q~}.S=z ¢ "% }.(C=SS+¢]7z{/ {-}..2Sze}.[%Sz% { - $½ /¼WNW /¡{/z (]/ ¨=©©3[µe(}._}. }.-%Sz% { - j=z o5.z,}a{: {-}..r}az"%S=zo¬+{z,} / { {/ }.SzBSz#)%C.>{/z-¢h{/F%.D W{z SzE{S-=_}({SJ+{/% }.>%7z%= {/A¸ ¹U- V=3}.)%/.- }.>+{/7zU- $ }.V°37o}.7zb}.h._}.z%WW·]¸ ¹j»iS.M b%+¢] ( {/ {:}.7=(.%o}.A/2}.F}M¢ e¸ ¹K- S`% C[·]¸ ¹"»/ %e{N=-7° {/} {K{/%.S{V{/ {}..S_}.7V%SzU{N/%.} ¸V¹-- 9=SD8)%.>{/zA),_}8W{S-_}A+© »iS.[¼N%+¢]a}.>{+D {/=>%.2{SYy0}`Sa%ze}.{:} )%.>{/z>SA.7{/}.SDo
=-{/ {S(2S+¢h03.S%S=z#{o & )b+¢JD+/b7]3.S%S=zQ+{/Sz2}.g- 9SD %SS=,}.o
E)}%}.`.%S}. ® }F7F.7%SzB¢] }.2}."{+, {=>%./.2Sz.+{%>/Y·]¸V¹K- Si}`)%C.>{z-=z =-FzS+{:}.7z".%.A=z%.={:}.7zNS-.:D
J 8 , 8 t
zo}. ® 3 z,}V¿.=ûiS.0g}. {/} {a%+¢]JSo}%}.7Q7%S7 }%.z {/z {)+{/.ASS£D({[=SS}.SzeVz7_
-+{/%.-z}. yMz% %o}.{:}.7z[o}YS>¿}.zu{} {/SK}.e.: U«,%
.%S}.F{% z -:Sz{+D {Y{S )b+¢J=(-:Sz {+D {/= az} =SS+¢t}.]}%.z Sz-}.8.S7z{ {:} {`7%o
, jDz[{A%.Shp%S£D {/¿}.]{A¢t_}.{
(-+{%3.-z,}.W¢]SS z/}2{o}.F}.--:3SzN{+D {/=[={/7-%S=zo¬+{z,}.o
,KJa_ SzA}.SV-}. ( , z} .: WfW5;C* %/Nz,}%.=):DW}. «,%
a3.S%S=z9h¸ ¹A3./ r}.Si¬z {/7z2=z,}%.{% =z {]{/ {/-}. B{%% }.8}.k¬o}.j{/7z]¢]o}.2/}.r7zo}.¿{/S7À{/ }.S=zK{/ {-}..8Ja{Sa SQ}.A:={:.¿{/z2{%%- SzN}.a.,%b- $]J`{ ={/z,} {=a/V%SzU¸ ¹>SQ}.{/}8o} ,Vz}W.+«,o.8{z,
F°3}% {g--%
,:
,}W.: j¢]o}.>{b}%. =zS7zA%=S}.Szp
!
!
" , * R O¸V¹ * G " A , ,
>d q EHW¶ d 7G ' +^Gi )*,&>h_^Q¶`)~{/z |gS=3 ¤ ® ¦ ~ ® 4=za/©=©=¨ + ® ® {/%p Q J{/), £5~5 J{/p|A{/} {:+º(3y0}.3 `Y}0¢h{/z$)y3±Q7%SÀ+{¢h{3 ¦ ~.S{_} {+={|2J=>{/ ` V{/.>{3{/z 43µt N~ Q ® ½JA_} {zC _}%.+{ {/} {F>{/z{+)9d &\&[&t¶`/ &J*) ,* ]37$½S pN{/. U©©=¨3 ¨: ® ® {/%p Q J{/), £5~5 J{/p 4Y ® SS_}.+{z 4µ¡ =N ¤ {: {}..SÀSz---%
-.+«,S.-z,}. / «.S]:D]z}.Sz {:} {2_}%.+{/-y0z # %+ .%6* _^gC4 ' >d q #HV¶a; >d q ' k; >d q Q /&b?3.& # ) ?)7A_^b¶`/D@. /.0&F.){/=Q ¨= N{ S%zpµ¡y ¦ ~ ® 4=z`©©D / Q {), £)5~5 J{/p|A{/} {:+ a)Y/}M¢J{z${z |FJ=>{/)Áb) {:}.8% SSzFSz {/} {F_}%.{ _
_}.-pzS+{/p.)/%}+)~,} {zC Y¦ zSD.%o}0
, ¤ ® ¦ ~ ® Áb}.=)Q/©=©¨3 + Q {), £)5~5 J{/p|A{/} {:+ a)Y/}M¢J{z${z 4µ¡ =NY SQ{z S%%]Sz {/} {F_}%.+{/³_
3_}.- yMz # %+ .%6,*FM^AC4 ' >d q EHW¶a; >d q ' k; >d q Q /&b?3.&² # ) ?)7 _^Q¶`D@. .0&F.{a 3)N{ S%zpµ¡y ¦ ~ ® 4=za©©D : Q {), £)5|A{/} {:+){z aY}M¢J{z p={ % Sz`b{.={/}.S=z«,.78:D {/} {2_}%.+{-yMz ¶ &td 7G ' ^+GkY¶` # _+.%6,*2_^gC4gd ' 5 &h,*5. * =_}.zp5 ® ¦ ~ ® N{/. ©=© +2~5 J{p ¦ ~.S{_} {+={{/z 4µ¡ =Nj°37o}.7z £z_}% {/7z,}.J}.F. A--%
-:D.+{ Sz =z,}.Sz=]«,.S]:D {:} {2_}%.+{/-pzS+{/ .)%}+~} {/z/ Y¦ zSD%o}M
, ¤ ® ¦ ~ ® 3±Q/=F)]©=©¨3 ¼: ® S}..{)W{S{:}.S=zN/jºa{S>{z[¬o}..SzFC8z}M¢J/.£ }.7-b£D7zyMz # _+.%6,*`_^ # ' & 9d &[&\&ud 7G ' +^+Gk # { >}.3.:3 ".%S}.F%7-S7{/-}. }.=%g/i-:Sz2{:= {hoi¬zQ/ {z7{/.o}0
"Shz} %o {S=
6.
CONCLUSIONS AND FUTURE WORK
µ j{+Dk.)=% {Jz/==%73}.S=za{/% =z`{ {ºa{S>{z »iSo}.J{3.D{/(}.A.{+D]-FzS+{/}.S=z`.%=3.V7z>{g2o}.o S {/} {(_}%.+{/-]z3o.z-z,}+ JgC {/-¢J/.£YS8.%z,}. {/[{=z {Q- $V¢]S+{z )K% 7z{7{/.K={:.7}M
/ {:} {/_}%.+{-Sz-{SS+{/}.S=zJk°3).S-z,} {).%S}.h.=+{ }.{/}2}.U¸ ¹{.D{/#SDFS-3./= )%C.>{z[7z#.{+, Sz-FzS+{/}.Sze.%=3.#JY_
3_}. SF%+¢]zE}.U) ._}+½Ao}2)%.-g¢ SVDzU¢]z}.-{/SS+{:}.7ze+{/zz/} )8- 7 {/3 {/}.o
,j»/ C}..]¢J/.£F¢J8¢J 7S£D]}.aSz =_}.SD{/}.h}. 7S+¢]SzaS%%V{z Sz.) {:}.h}.oW%=S}.Sz Sz,}.(8°3S_}.7z(- ½ | =S=Szt{z z }./z _
3_}.Na{+Sz¡{ =z { ¾ g C {/-¢J/.£[Cb{SS+{/}.S=z"}.(_}%.+{-Sz(_
3_}.- ¾ yMzD_}.7={/}.Sz {/}.SzE}._} {/}.}% {/z%o}.S=z >{:}%.7 =zS7za{]}.g_}%.{-Sz {/} {a}%.z {z ¾ |g=S=Sz(- SJCQz=z37Sz+{/8_
3_}.-
&
: a» =S%D%}+ Q)YS7S+ ` ¥ =Àº( 8-Sz/}.=zp 4 )bS£SSzp ¤ 5YS+){/z Y¥ 3µep 4 ® ® ½ ® ¯%{+{ >{/}%.o°[{/£{= o©/ a X V.+¢]zp5d $ %+6/$$ h)6D/& 7*) 8= . 6(m2 &-"nV$ 0 ,*µtSS
,3±b¢ V.£)3± 2 ¦ ~ ® ¼=¨ o ® 73}8{z ® º(~3Szp~µ ® b½ )bS {/. S+{/r_}%.+{/ %->{:.SÀ+{/}.S=z"SzY7{/.Az}0¢J.£yMz # _+.%6,*`_^gC4 d ' ¶ &¡d 7G ' +^GiN¶` &h,*5. *{/= ¨=©¨ ,¨3 3 J{zD{/7/.=)y0z 7{)N{:.U/©=©¨3 o+:2~5 ¤ {/z {%£{/ {/zprS {/ ¤ ½ ¤ =z,}.Sz {:} >{ !:¢ 3.,%%Sz-/Q{zNz%} {/Sz"¢J/. y0z # %+ ..6/*2_^gC4 ' d%¶ ' /+^+GkNd ]_^Q¶`/{=b 3=p~3{zN|gS ¤ ® ¦ ~ ® 4=za/©=©=¨ o a ¤ 7{/.£== 43µ#{ 7z}.zp{z 4±2µ#{/77{/=5J {SS+{/}.SzKkºa{/7>{/z"¬S}..7z(}.2}.A7={ /.%%. z}%.p/jD{/o¬. )7S.yMzK9d &\& ' S+&² m Q &("nV$ 0 ]d $ %+6$/! ?D?) $ /$A)6 n9$ .A¶`d q EHV¶ d 7G ' ^+Gk )*,&>h_^Q¶`{/=bR R ,¨3+© ¥ S7{ 77{3 ¥ ® ¦ ~ ® 4=z( R!3 o¼/ ahºa{/S>{zp ® z¢ {.={ Y}.(SSz+{:8¬o}..Sz>{z . S}.S=zN3.=7-V %=$2_^gC4 & )=kM^ 8.; &J*). ,*)¼=3~3.7 |a½ ¨D D9N{:.C =©3 oC /ay r{/À+{/. 7Q{z ~))Y3.}% { ¤ {3}..Sz %z%%=z {/}. }.7-b%.Sh¢]S}.N«{So}M
"={/ {z,}.% yMz # _+ %6C*2_^gC4gd ' 5 ¶ &td 7G ' ^+GkN¶` &J*) ,*{/= ,, ,© J{/zD{/S.=)y0z ¿{)N{:. ,¼>©©=¨3 /©/ ¥ )~))N{
3) £) + 4.$ +6D ! &J.$&-$$! )6 ' $ %= D=S-2= ® +{ -S ¥ .%±Q¢ /.£)± F ¦ ~ ® 5 !R , a)Y/}M¢h{/z$ 43µt =N ® ® {/%p Q {), £) ~5 J{/p|A{/} {:+ X )N{z£9 ¤ )ÁbS_}.=zp 4 Q%z_}.Sz9{/z a {:.>{3 %
>3.,%%Sz3 .%.a>{z{-z,}+3{z {.+°3S>{/}.S=zNSzY{ {:} { _}%.+{/³>{z{/=-z}]_
3_}.N3y0z # %+ ..6/*`_^AC4 ' d%¶ ' +^Gj/Yd )/]_^Q¶`/{=b/=¨ 3! p~3{zN|gS ¤ ® ¦ ~ ® 4=za/©=©=¨
&
&
&
&
&
/ ¤ )ÁbS_}.=z9 Q p,3){/z 43µt =N ® {/}.SDQ.S%S=z %}%}.SzFCQ+{ {.+°37>{:}.g{SyMz # _+ 6C* _^ ' >d q EHV¶ d 7G ' +^+Gk )+*,&-]M^ ¶`{/=8¨D ,¨==p~{/z} { J{/.{/ { ¤ ® ¦ ~ ® N{
©=©= =+ ¤ )ÁbS_}.=z9 Qb p,{z 4µt =N ® {3}.SD .S%S=zK%}%}.7zF/8+{ {3.+°S>{:}.g={/SyMz ' >d q EHV¶ d 7G ' ^+Gk # _+.%6,*2_^gC4 )*,&>h_^Q¶`{/=8¨D ,¨==p~{/z} { J{/.{/ { ¤ ® ¦ ~ ® N{+
Y/©=©3 : ¤ ¥ .S {5~) X } {3º(±bo
,=$y p{À+{:. S ~5Y./}% {3{z ` X 3} {3Wz.
"-7z} =-2zS+{:}.S=z>8.S7{7So}M
N{z «,{/7o}0
Y{¢J{/.a%z%/ z}0¢J.£r z7{5.)%}+ ¦ zSD.7_}0
> ¤ {/7oC.z7{>{/} y0.SzA{/z >¦ zSD.%S}0
[ ¤ {/7oC.z7{>{/}Q~3{z"|gS=3 ® 3.S ©=©¨3 ! + 2 b{/=z{/}.{zp ¤ ~3 33.=.~5 ¥ {:.£5{z )~,.7{_} {+{3Wz.
Y{¢h{:.g¢]S.7%b-S.=%z% z}0¢J.£)9d &\&[& 7*)= # %+ . C* +*DZC5 ½ D© ©pN{/. U©©D ¼:`b)~72z7{z[¬o}.+yMz ' >d q;q # d 7G ' ^+Gi ' &b?0 qJ _?4`/)6Fd 0 %=${z[¬o}.+yMz ` % d +^ &-/$ # %+ . C* /.0&F A$ %=k/)6 /C4${A+¨¨ D© {/zD+ V.o}.S% ¤ =S27{3 ¤ {z{ {|gF)8©©D ¨D+ F J{/-{z 4 X .£== %
[.,%%Sz(/b%z% z}0¢J.£yMz # _+.%6,*2_^gC4 ' d%¶ ' ^+Gk d )/