Dec 1, 2009 - Lawrence D. Stone, Thomas L. Corwin, and Carl A. Barlow: Bayesian Multiple Target. Tracking, August 1999 Book Publisher: Artech House, Inc ...
DE
:
1DLGEV6TCEMKPIWPFGT*KIJ%QTTGNCVKQPHQT -CNOCPહï(KNVGT '0$NEDU+XVVDLQDQG=DNL$KPHG 'HSDUWPHQWRI(OHFWURQLF6\VWHPV (VEMHUJ,QVWLWXWHRI7HFKQRORJ\ $DOERUJ8QLYHUVLW\(VEMHUJ'HQPDUN DNEDU#DDXHGN
]DNL#KRWPDLOFRP
$EVWUDFW7KHLQYHVWLJDWLRQSUHVHQWHGKHUHFRPSDUHVWKHDGYDQWDJHRIXVLQJD.DOPDQILOWHU DVRSSRVHGWRDQȽെȾILOWHUIRUPXOWLWDUJHWWUDFNLQJV\VWHPV7KHIRUPHULVRIWHQXVHGWR VSHHGXSWKHFRPSXWDWLRQWLPH+RZHYHULWLVVKRZQKHUHWKDWGXHWRWKHGLIILFXOW\RIGDWD DVVRFLDWLRQ WKH EHQHILWV DUH QRW DV JUHDW DV PLJKW EH H[SHFWHG ZKHQ FRUUHODWLRQ LV KLJK ([WHQVLYHDQDO\VHVDUHSHUIRUPHGE\VHOHFWLQJYDULRXVVFHQDULRVZKHUHWKHFRUUHODWLRQIDFWRU DIIHFWV WKH SHUIRUPDQFH RI Ƚ െ Ⱦ ILOWHU FRPSDUHG ZLWK .DOPDQ ILOWHU 7KH UHVHDUFK DOVR LQYHVWLJDWH D QHZ IUDPHZRUN RI IRUPLQJ D WUHH FOXVWHULQJ VFKHPH WR SUXQH IDOVH WDUJHW PHDVXUHPHQWSDLULQJLQWURGXFHGZKHQPXOWLSOHWDUJHWVDUHLQWKHVDPHYLFLQLW\ .H\ZRUGV)LOWHULQJ.DOPDQȽെȾ)LOWHU7DUJHW7UDFNLQJ6WDWH(VWLPDWLRQ
+PVTQFWEVKQP
'XULQJ WKH SDVW WZR GHFDGHV WKH LPSURYHG WHFKQRORJ\ DYDLODEOH IRU VXUYHLOODQFH V\VWHPV KDV JHQHUDWHG D JUHDW GHDO RI LQWHUHVW LQ DOJRULWKPV FDSDEOH RI WUDFNLQJ ODUJH QXPEHU RI REMHFWV XVLQJ LQIRUPDWLRQ IURP RQH RU PRUH VHQVRUV OLNH UDGDU VRQDU HWF 7\SLFDO VHQVRU V\VWHPV VXFK DV UDGDU REWDLQ GDWD UHWXUQV FRUUXSWHG ZLWK QRLVH IURP WUXH WDUJHWV DQG SRVVLEO\IURPRWKHUREMHFWV,QJHQHUDOWKHWUDFNLQJSUREOHPUHTXLUHVSURFHVVLQJRILQFRPLQJ GDWD WR SURGXFH DFFXUDWH SRVLWLRQ DQG YHORFLW\ HVWLPDWHV >@ 7KHUH DUH WZR W\SHV RI XQFHUWDLQWLHV LQYROYHG ZLWK WKLV LQFRPLQJ GDWD ILUVW WKH SRVLWLRQ LQDFFXUDF\ DV WKH PHDVXUHPHQWVDUHFRUUXSWHGE\QRLVHDQGVHFRQGWKHPHDVXUHPHQWRULJLQVLQFHWKHUHPD\ EH XQFHUWDLQW\ DV WR ZKLFK PHDVXUHPHQW RULJLQDWHV IURP ZKLFK WDUJHW > @ 7KHVH XQFHUWDLQWLHVOHDGWRDGDWDDVVRFLDWLRQSUREOHPDQGWKHWUDFNLQJSHUIRUPDQFHGHSHQGVQRW RQO\RQWKHPHDVXUHPHQWQRLVHEXWDOVRXSRQWKHXQFHUWDLQW\LQWKHPHDVXUHPHQWRULJLQ> @ 7KHUHIRUH LQ D PXOWLWDUJHW HQYLURQPHQW H[WHQVLYH FRPSXWDWLRQ PD\ EH UHTXLUHG WR HVWDEOLVK WKH FRUUHVSRQGHQFH EHWZHHQ PHDVXUHPHQWV DQG WUDFNV DW HDFK UDGDU VFDQ > @ $IWHU WKH GDWD DVVRFLDWLRQ SURFHVV WUDFNV DUH QRUPDOO\ XSGDWHG XVLQJ HLWKHU VWDQGDUG .DOPDQRUȽെȾILOWHU>@$OVRWUDFNVZKRVHVWDWLVWLFVGHYLDWHIURPWKHDVVXPHGPRGHO DQG VKRZQ WR EH IROORZLQJ WKH VDPH WDUJHW DUH QRUPDOO\ HOLPLQDWHG > @ .DOPDQ RU
)
"%# & ' (
Ƚ െ Ⱦ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
2TQDNGO5VCVGOGPV
6JG&CVC#UUQEKCVKQP2TQDNGO ,QDJHQHUDOPXOWLSOHWDUJHWWUDFNLQJVLWXDWLRQDVH[SODLQHGLQWKHLQWURGXFWLRQDQXPEHURI PHDVXUHPHQWV IURP DQ XQNQRZQ QXPEHU RI WDUJHWV DUH UHFHLYHG DW HDFK UDGDU VFDQ 7\SLFDOO\WKHUDGDUVHQVRUPHDVXUHVWDUJHWSRVLWLRQLQSRODUFRRUGLQDWHVWKDWLVLQUDQJHU DQG EHDULQJ Ʌ 0HDVXUHPHQW LQDFFXUDF\ FDQ QRUPDOO\ EH PRGHOHG DV DGGLWLYH ]HURPHDQ XQFRUUHODWHG*DXVVLDQQRLVHRQUDQG Ʌ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
DE
*
+HUH ZH ZLOO EH FRQFHUQHG ZLWK WKH LPSOHPHQWDWLRQ RI D GHWHUPLQLVWLF DSSURDFK WKH 76) DOJRULWKP
)LJ5HFXUVLYH0XOWL7DUJHW7UDFNLQJ6\VWHP
5VCVG'UVKOCVKQP )RUWKHHVWLPDWLRQRIWDUJHWSRVLWLRQDQGYHORFLW\IURPWKHWUDFNGDWDLWLVFRPPRQWRXVHD UHFXUVLYH .DOPDQ ILOWHULQJ DOJRULWKP > @ 7KLV UHTXLUHV D PRGHO IRU WKH PRWLRQ RI WKH WDUJHW EHLQJ WUDFNHG DQG RQH RIWHQ DVVXPHG D FRQVWDQW YHORFLW\ WDUJHW ZLWK UDQGRP DFFHOHUDWLRQGHVFULSWLRQJLYHQE\ DQGWKHFRUUHVSRQGLQJPHDVXUHPHQW]QLVJLYHQE\
+
"%# & ' (
7KHVWDWHYHFWRUWKHVWDWHWUDQVLWLRQPDWUL[WKHH[FLWDWLRQDQGWKHPHDVXUHPHQWPDWUL[DUH UHVSHFWLYHO\ +HUH ο W LVWKHVDPSOLQJLQWHUYDODQGFRUUHVSRQGVWRWKHWLPHLQWHUYDODVVXPHGXQLIRUPDW LV ]HUR PHDQ ZKLFK UDGDU PHDVXUHPHQW GDWD LV UHFHLYHG 7KH DFFHOHUDWLRQ QRLVH *DXVVLDQ DQG LQGHSHQGHQW LQ HDFK &DUWHVLDQ FRRUGLQDWH ZLWK FRYDULDQFH 4Q 7KH LVDVVXPHG*DXVVLDQZLWKFRYDULDQFH5Q7KH&DUWHVLDQFRRUGLQDWHV PHDVXUHPHQWQRLVH RI WKH PHDVXUHPHQWV DUH REWDLQHG IURP WKH SRODU FRRUGLQDWHV U Ʌ UHFHLYHG E\ UDGDU WKURXJKDQRQOLQHDUWUDQVIRUPDWLRQ 7KLV WUDQVIRUPDWLRQ UHVXOWV LQ WKH PHDVXUHPHQW HUURUV RQ WKH &DUWHVLDQ FRRUGLQDWHV EHLQJ QRQ*DXVVLDQ GLVWULEXWHG EXW XQGHU WKH UHDVRQDEOH DVVXPSWLRQ WKDW WKH PHDVXUHPHQW HUURUVRQWKHSRODUFRRUGLQDWHVDUHVPDOOFRPSDUHGZLWKWKHWUXHWDUJHWFRRUGLQDWHVU Ʌ LW FDQ EH VKRZQ WKDW WKH &DUWHVLDQ HUURUV DUH ELYDULDWH *DXVVLDQ UDQGRP YDULDEOHV >@ ZLWK ]HURPHDQDQGFRYDULDQFH5QJLYHQE\ ZKHUH
DE
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Ʒ LV WKH DVVXPHG WDUJHW PRWLRQ PRGHO RI HTQ .Q LV WKH ILOWHU JDLQ LQQRYDWLRQV + LV WKH PHDVXUHPHQW PDWUL[ 3Q LV WKH VWDWH FRYDULDQFH PDWUL[ %Q LV WKH FRYDULDQFH RI WKH LQQRYDWLRQV ƥ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ȽെȾILOWHUV>@7KLVILOWHUFRQILJXUDWLRQVLPSOLILHV WKHFRPSXWDWLRQDOUHTXLUHPHQWVFRQVLGHUDEO\EHFDXVHWKHVWDWHVUHODWLQJWRHDFKRIWKHWZR FRRUGLQDWHVFDQEHHVWLPDWHGLQGHSHQGHQWO\7KHHTXDWLRQVIRUDQȽെȾILOWHUWRHVWLPDWH[ SRVLWLRQDQGYHORFLW\DUH
,
:KHUH
"%# & ' (
DQG DUH WKH SUHGLFWHG SRVLWLRQ DQG YHORFLW\ UHVSHFWLYHO\ WKDW LV IRU WKH IXOO .DOPDQ ILOWHU DQG LV WKH [FRPSRQHQW RI WKH PHDVXUHPHQWYHFWRU 7KH.DOPDQJDLQIRUWKHȽെȾILOWHULV
ZKHUHȽQ DQGȾQ DUHWKHJDLQFRHIILFLHQWV7KHHVWLPDWLRQHUURUFRYDULDQFHFDQEHVKRZQ WREHJLYHQE\ LV WKH YDULDQFH LQ WKH HUURU RI WKH Q W K [SRVLWLRQ PHDVXUHPHQW :KHUH 5HFXUUHQFHUHODWLRQVIRUȽȾ DQGɁ FDQHDVLO\EHREWDLQHGXVLQJHTXDWLRQVWR
6TCEM5RNKVVKPI#NIQTKVJO
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
DE
-
7KH VFKHPH IRU WUDFN LQLWLDOL]DWLRQ LV TXLWH VLPSOH $ PHDVXUHPHQW P LV FRQVLGHUHG WR EH XQXVHG LI LW KDV QRW EHHQ XVHG WR XSGDWH D WUDFN 7KLV PHDVXUHPHQW LV WKHQ VWRUHG IRU SRVVLEOH FRUUHODWLRQ ZLWK DQRWKHU PHDVXUHPHQW Q DUULYLQJ DW D ODWHU VFDQ XVXDOO\ WKH QH[W VFDQ DQG LI WKH DFWXDO GLVWDQFH EHWZHHQ WKHVH WZR PHDVXUHPHQWV P DQG Q LV OHVV WKDQ D GLVWDQFHWKUHVKROGɁGPQ D QHZWUDFNLVLQLWLDOL]HG$PD[LPXPVSHHG9PD[ LVDVVXPHGIRU DWDUJHWWKXVWKHPD[LPXPGLVWDQFHWKDWFDQEHWUDYHOHGLQMWLPHVWHSLV9PD[ M ο W ZKHUH ο W LV WKH WLPH LQWHUYDO EHWZHHQ WZR VFDQV 7KH GLVWDQFH PHDVXUHPHQW QRLVH YDULDQFH
V 7 P N RIPHDVXUHPHQWPDWWLPHNLVREWDLQHGIURPWKHPHDVXUHPHQWQRLVHYDULDQFHVRQ WKH[\ FRRUGLQDWHVDV 7KH GLVWDQFH WKUHVKROG Ɂ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
,.
"%# & ' (
ZKHUH Ƚ Ⱦ DQG Ɂ DUH WKH JDLQ FRHIILFLHQWV >@ )RU D GHFRXSOHG Ƚ െ Ⱦ ILOWHU LW IROORZVWKDWWKHDERYHFRYDULDQFHPDWUL[EHFRPHVWKHEORFNGLDJRQDOPDWUL[
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
LV D VXP RI VTXDUHV RI 0LQGHSHQGHQW ]HUR PHDQ DQG XQLW VWDQGDUG
GHYLDWLRQ*DXVVLDQUDQGRPYDULDEOHV7KXV
ZLOOKDYHD ɖ GLVWULEXWLRQZLWK0GHJUHHV
RI IUHHGRP 7KH PHDVXUHPHQW DFFHSWDQFH FULWHULRQ IRU D WUDFN LV WKXV GHILQHG WKDW LI
LV
DE
,/
OHVVWKDQDWKUHVKROG-ZLWKVRPHNQRZQSUREDELOLW\ WKHQWKDWSDUWLFXODUPHDVXUHPHQWDW VFDQQFDQEHXVHGIRUXSGDWH>@
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
IRU Q VFDQV LV ɖ GLVWULEXWHG ZLWK 1
ɖ GLVWULEXWHG ZLWK 1 GHJUHHV RI IUHHGRP ,I ZH ZLVK WR GHILQH D WKUHVKROG 7 IRU D ɖ GHJUHHV RI IUHHGRP ZKHUH 1 Q ൈ 0 7KHUHIRUH WKH VXSSRUW IXQFWLRQ 6Q LV DOVR
GLVWULEXWLRQVRWKDWWKHSUREDELOLW\RIWKHYDULDEOHH[FHHGLQJWKHWKUHVKROGLV3U7 WKHQZHFDQ HLWKHU XVH ɖ WDEOHV RU LI WKH GHJUHH RI IUHHGRP LVODUJH XVH WKH DSSUR[LPDWH UHODWLRQVKLS >@ ZKLFKUHODWHVWKHHTXLYDOHQWWKUHVKROG7 J IRUD*DXVVLDQGLVWULEXWLRQRIXQLWYDULDQFHWRWKDW RI7IRUWKH ɖGLVWULEXWLRQ)RUH[DPSOHLI1 7 J IRUDWKUHVKROGSUREDELOLW\RI 3U7 HTXDOWRDQGWKHDERYHIRUPXOD\LHOGV7 FRPSDUHGZLWKWKHYDOXH
,0
"%# & ' (
IURP WKH ɖ WDEOH )RU WKH LPSOHPHQWDWLRQ RI WKH VXSSRUW IXQFWLRQ FULWHULRQ DVVXPLQJ WKDW 0 DQGWKXV1 ൈ QWKHQ7·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
DE
,
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
#PCN[UKU $V PHQWLRQHG HDUOLHU ZKHQ WKH WUDFN VSOLWWLQJ ILOWHU DOJRULWKP LV XVHG WKH WUDFNLQJ ILOWHU VSOLWV LQWR EUDQFKHV ZKLFK DUH HTXDO WR WKH QXPEHU RI PHDVXUHPHQWV IRXQG ZLWKLQ WKH SUHGLFWHG DFFHSWDQFH HOOLSVH 7KLV PHDQV WKH VKDSH RI WKH PHDVXUHPHQW HOOLSVH LV YHU\ LPSRUWDQW LQ WKH FDVH RI QHLJKERULQJ RU FURVVLQJ WDUJHWV$ IRXU FURVVLQJ WDUJHW VFHQDULR LV FRQVLGHUHGIRURXULQYHVWLJDWLRQDVVKRZQLQILJXUHIRUORZDQGKLJKFRUUHODWLRQIDFWRUVRI DQG UHVSHFWLYHO\ 7KHVH IRXU WDUJHWV DUH PRYLQJ IURP D IL[HG ORFDWLRQ ZLWK VDPH YHORFLW\DQGWKH\FURVVHDFKRWKHUDIWHUVHFRQGV7KHFRUUHODWLRQIDFWRULVDSSUR[LPDWHO\ NHSWFRQVWDQWWKURXJKRXWWKHUXQ6HFRQGV E\PDLQWDLQLQJWKHUHODWLYHSRVLWLRQVRIWKH WDUJHW DQG WKH SODWIRUP VHQVRU LV RQERDUG D VKLS 7R REWDLQ WKH WZR FRUUHODWLRQ IDFWRUV RQO\ WKH LQLWLDO SRVLWLRQ RI WKH SODWIRUP LV FKDQJHG DQG DOO RWKHU SDUDPHWHUV UHPDLQ WKH VDPH 7KH VFHQDULR ZDV UXQ ZLWK WHQ GLIIHUHQW UDQGRP VHHGV WDEOH JLYHV WKH QXPEHU RI DYHUDJH WUDFNV SUHVHQW IRU WKH WZR ILOWHUV ZLWK ORZ DQG KLJK FRUUHODWLRQ IDFWRUV $V DQWLFLSDWHG EHFDXVH RI WKH LQIHULRU PHDVXUHPHQW SUHGLFWLRQ HOOLSVH Ƚ െ Ⱦ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ȽെȾILOWHULVLQ WKHRUGHURIWRDSSUR[LPDWHO\
,)
)LJ&URVVLQJ7DUJHW6FHQDULR
"%# & ' (
DE
&255(/$7,21
.DOPDQ)LOWHU ȽെȾ)LOWHU 6FDQ1R /RZ +LJK /RZ +LJK
,*
&OXVWHULQJ $ %
7DEOH$YHUDJH1XPEHURI7UDFNV
)LJXUHVKRZVWKHDYHUDJHVSHHGXSSORWWHGDJDLQVWYDULRXVQXPEHUVRIWDUJHWV,WFDQEH VHHQIURPILJXUHWKDWDVWKHDPELJXLW\LQFUHDVHVWKHVSHHGXSGHWHULRUDWHVWRDUDWLRRIWR 7KHUHIRUHWKHDGYDQWDJHRIXVLQJDQȽെȾILOWHUXQGHUKLJKFRUUHODWLRQLVQRWUHDOO\JUHDW 2QH RI WKH PDLQ UHDVRQV IRU H[FHVVLYH EUDQFKLQJ LQ WKH FDVH RI Ƚ െ Ⱦ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ȽെȾILOWHUV ZHUH XVHG WR WUDFN WKHVH VFHQDULRV IRU WKH WZR YDOXHV RI FRUUHODWLRQ %DVLFDOO\ HDFK UXQ FRQVLVWVRILWHUDWLRQVDQGDQHZVHHGLVVHOHFWHGIRUHYHU\LWHUDWLRQ7KHVXSSRUWIXQFWLRQ DQGWKHPHDVXUHPHQWDFFHSWDQFHYDOXHVDUHREWDLQHGGXULQJWKHVHLWHUDWLRQVDQGILQDOO\WKH DYHUDJHLVFRPSXWHG
,+
"%# & ' (
)LJ.DOPDQ $OSKD%HWD)LOWHU6SHHG8S&RPSDULVRQ
DE
,
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Ƚ െ Ⱦ ILOWHUNHSWRQWUDFNLQJWKHWDUJHWDVVXPLQJLWLVWKHEHVWVXSSRUWHGWUDFN
,,
"%# & ' (
)LJ6FHQDULR*HRPHWU\ 6FDQ1R ,QLWLDO$QJOH ,QWHUVHFWLRQ$QJOH
&RUUHODWLRQ5DQJH
$YHUDJH&RUUHODWLRQ
&RUUHODWLRQ5DQJH
$YHUDJH&RUUHODWLRQ
7DEOH/RZ&RUUHODWLRQ 6FDQ1R ,QLWLDO$QJOH ,QWHUVHFWLRQ$QJOH
7DEOH+LJK&RUUHODWLRQ
DE
)LJ/RZ&RUUHODWLRQ%HKDYLRXU
,-
%QPENWUKQP
,Q WKLV SDSHU ZH KDYH FRPSDUHG WKH UHODWLYH PHULWV RI WKH RSWLPDO .DOPDQ ILOWHU ZLWK WKH VXERSWLPDOȽെȾ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ȽെȾILOWHUGXHWRWKHVKDSHRIWKH SUHGLFWLRQ HOOLSVH ,W KDV EHHQ VKRZQ WKDW LQ D KLJK FRUUHODWLRQ VFHQDULR WKH GHFRXSOHG Ƚ െ Ⱦ ILOWHU LV PRUH OLNHO\ WR DFFHSW XQUHDOLVWLF PHDVXUHPHQWV FRPSDUHG ZLWK WKH .DOPDQ ILOWHU 7KHUHIRUH WKH VSHHG RI FRPSXWDWLRQ ZKHQ XVLQJ DQ Ƚ െ Ⱦ ILOWHU LQ D PXOWLWDUJHW VFHQDULR LV QRW KLJK DV RQH ZRXOG SUHGLFW IURP VLQJOH WDUJHW FRQVLGHUDWLRQV ,Q IDFW LW ZDV IRXQG WR EH RQO\ WR WLPHV IDVWHU WKDQ D VWDQGDUG .DOPDQ ILOWHU IRU FURVVLQJ WDUJHW
-.
"%# & ' (
VFHQDULRVFRQWDLQLQJXSWRWDUJHWV7KHFOXVWHULQJWHFKQLTXHVZKLFKDUHPRUHVWUXFWXUHG DQG LQWHOOLJHQW WKHUHIRUH LQ WKH FDVH RI Ƚ െ Ⱦ ILOWHU OHVV EUDQFKLQJ LV REVHUYHG DOWKRXJK QXPEHUV DUH QRW YHU\ VLJQLILFDQW KRZHYHU WKH WHFKQLTXHV KDYH WKH SUHPLVH WR SURGXFH EHWWHU UHVXOWV IRU VXFK VFHQDULRV )XUWKHU RQH LPSRUWDQW DVSHFW PXVW EH NHSW LQ PLQG WKDW QXPEHURIEUDQFKHVGHSHQGVRQFRXSOHRIIDFWRUVIRUH[DPSOHWKHWLPHWKHWDUJHWFURVVHDFK RWKHU WKHLU DQJOH RI LQWHUVHFWLRQ DW WKH WLPH RI FURVVLQJ DQG WKH RUGHU LQ ZKLFK VLPLODULW\ FULWHULRQ LV H[HFXWHG ,Q IXWXUH ZH ZRXOG OLNH WR FDUU\ RXW RXU UHVHDUFK ZRUN IRU PRUH LQ GHSWKDQDO\VHVRIWKHVHWZRILOWHUVFRQVLGHULQJWKHUHVXOWVREWDLQHGLQRXULQYHVWLJDWLRQKHUH SOXVZLWKPRUHUHDOLVWLFVFHQDULRV
)LJ+LJK&RUUHODWLRQ%HKDYLRXU
DE
-/
4GHGTGPEGU
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