The Cricket Compass for Context

The Cricket Compass for Context-Aware Mobile
Applications
Nissanka B. Priyantha, Allen K. L. Miu, Hari Balakrishnan, and Seth Teller
MIT
Laboratory
for
Computer
"!#%$%Science
'&()*&+
,"-*.0/%/)123&%$"3&(4&+/%$52$)/
8TO[Z[=BKGFO>MN8JO[A(:S?\TFOUAG8Jd[A]a^9\L7:0]`>7UC]a=@\h:0?5?@FU\h:SAG=@F0On:+KG8:0O=PM'e
`F0KaA(:SOUA\T?P:0]a]F0W:0`9`>?@=@\h:SAG=@FO9]=PO8TMN8JKGi0=PO9iq`8LKGZ:S]a=PZ8\TF0MN`>^9Aae
=@O>iq8TO[Z=BKGF0O>MN8TOUAG]B¥hµ+vj¶d9:0MN`9?P8J]=@O>\T?@^H8 zhu y³tvzS¯|
sGx:0è
~0±,=@O
~ AG7>8J=@K
`>?@=@\h:+AG=PF0O>]lAG7:SAb8JO:0<9?@8X^9]a8JKG]NAGFH9=@]a\TF+Zp8JKb² KG8T]a~ F0^9KG\T8J]
`>7UC]a=@\h:0?`9KGFhd=@MN=@AfCmB¥J¤9n5SSvn5:0\JAG=@Zp8Mb:S`>]AG7:+A:S^9AGFMb:+AG=@\h:0?@?BC
\(7:0O9i82:0]#:^>]a8JK#MNFSZ8T] 0+vn9:0O>HN:0`>`9?@=P\T:SAG=@FO9],g7>F0]a8^9]a8JK#=@Oe
AG8JKaW_:0\T8T]":0H>:S`9AAGFAG7>8%^>]a8JKh· ]?@FU\h:+AG=PF0Oj%¸]a=@iO9=@>\h:0OUA":SMNF^9O[AF0W
`9KG8JZ=@F0^>]2g#F0KGo*7>:0]W_FU\T^9]a8hHXF0O`9KGF+Z[=PH9=@O>ilH98JZ=@\T8`F]a=BAG=@FOX\h:+e
`:S<>=@?@=BADC=@OHFUF0KG]Tn=@O>\T?@^H=@O>iNAG7>8q¸2\JAG=@Zp8qk:0H9i8 0¹Svnk:SA'@¥J¤0vn
© ¸2º2¸ © ®+vn:SOH,KG=@\(op8JA 0+]C]AG8TMN]Tj
¸2Om=PMN`FSKaA(:0OUAq:0]a`8T\LA'F0W\TF0OUAG8Jd[Ahng7>=@\(7=P]KG8T?P:SAG8THAGF`97UC9]e
=@\h:0?`F0]a=@AG=@F0On=@]'AG798mz0s(txL¯9y y³tvz0¯mF0W:XH98JZ=@\T8£»³F0KN^9]a8JKL¼g=BAG7
KG8T]a`8T\LAAGFbFO>8F0KMNF0KG8?P:0OH~ Mb:SKGo[]=@OX:'KG8Ti=@F0Oj¸½`8JKGZ0:0]a=@Zp8
\TF0MN`>^9AG=@O9iN:0`9`>?@=@\h:SAG=@FO\T:0O<8TO98J>AWKGF0M¾oO9Fhg=PO9i'AG7>=@]=@O9W_FSKae
Mb:SAG=@F0OnpWF0K,=PO9]A(:0O9\T82<UC`9KGF+Z[=PH9=@O>iAG798:0<9=P?@=BADC3AGF:H>:S`9A,:^>]a8LK
=@OUAG8JKaW³:S\T8,AGFAG7>8,H9=BKG8T\LAG=PF0O=POg79=P\(7:^>]a8JK=P]]A(:0OH=@O>iF0K`F=@OUAae
=@O>ij ^9K5>KG]AMNF0AG=@Z0:SAG=@O>i:S`>`>?@=@\h:+AG=PF0O=P]\h:0?@?@8hHAG7>8N¿
¯ÂUxLs(j
]a=@FO'AG79=P],:0`9`>?@=@\h:SAG=@F0ObAGFKG^9O'FOb:7>:0O>H97>8J?Hq\T~0FÀMNÁ `9^9AG8JK
Ã:0O>8Hl8J79O8TZ[?@=@`4
]a=@i7UAG8hHbF0K<9?@=PO>H`8TF0`>?@8O>:+Z[=@ip:+AG8AGFhg:+K(H4:3H8T]AG=@O:+e
AG=@FOc=@O:SOc^>OW³:SMN=P?@=P:SK]a8JAaAG=@O9i9j ª F0K8Jd9:0MN`9?@8nAG798 Ã :TC[O>H98JK
MN=@i7UA?@8h:H:*Z[=@]a=BAGF0K3WKGFMÄAG7>8b8TOUAaKaC£?@F<><UC£F0W:<>^9=@?H=@O>i4AGF
AG7>84F0N\T8FSWAG7>8*`8LKG]aFO79F]AG=@O>imAG798*Z[=@]a=@AGFSKhnF0KbAGFc:£]a8TMN=Be
O:+KNKGFUFM*j67>8 :TC[OH8JK'i0=@Zp8T]N=@O>\JKG8JMN8TOUA(:0?H9=BKG8T\LAG=PF0O>]'AGF
AG7>8^9]a8JKF0OHCO:SÃ MN=P\T:0?@?BC4KG8JAaKG=@8TZp8TH»hD:0\JAG=@Zp8JU¼Mb:S`>] [nSSvn
^>]a=@O9i4AG7>8'^9]a8JKh· ]`F]a=BAG=@FO:SOH£FSKG=@8TOUA(:SAG=@FOmg=BAG7mKG8J]a`8T\JAAGF*:
>d8hH]a8JA%F0Wg=BKG8T?@8T]a],<8h:0\TF0O>]"`>?P:S\T8hHqAG7KGF^>i07>F0^9A"AG7>8<9^>=@?PH9=@O>ij
67>8]a8T\TFO>H4MNF0AG=@Z0:SAG=@O>iq:0`9`>?@=@\h:SAG=@F0O*=@]\T:0?@?@8hHAG7>8XÅtvx ¯ÂUxLs(j
67>82^>]a8JK#\h:0Ol`F=@OUA=BA=@O:0OUCbH=@KG8J\JAG=@FOn:SOHb]a`8T\T=BWCl:±>DÁ ]g#8T8T`
:0O9i?@8T:SOH£Mb:+d=PMq^>MÆH9=@]A(:0O9\T8j ]a=@O>i*:0O:S\JAG=@Zp8'Mb:0`£=@O[AG8Le
i0K(:+AG8hHg=BAG7q:KG8T]aF0^9KG\T8#H9=@]a\TF+Zp8JKaC]C ]AG8TM¢»³80j ij@n0AG798%fOUAG8TOUAG=PF0O:S?
È[C]AG8TM*np Èl@¥L¼LnAG7982¡2=@8JgO>H98JK%AG7>8TONKG8JAaKG=@8TZ8T]:SOH
ÇH9=@:S]a`9MN?:T=@O>Ci
]:lKG8T`KG8T]a8TOUÇ A(:SAG=@F0OcF0WAG798']a8JAFSWH98TZ[=@\T8T]:SOH£]a8LKGZ=@\T8J]
?BC=PO9i=@O9]a=H8qAG7983]a8T\JAGFSKF0W#=@O[AG8LKG8T]A]a`8T\T=B>8hHX<UC*AG798q^9]a8JK:SOH
:0?@?@Fhg]AG7>8^9]a8JKAGF=@O[AG8LK(:0\JAg=BAG7bAG7>8T]a82]a8JKGZ[=P\J8T]Z[=:AG7>8KG8T`9KG8Le
]a8TOUA(:SAG=@F0OXF0OAG7>8Mb:0`5j¸AG79=BK(H*MNF0AG=@Z:+AG=@O>il:0`9`>?@=@\h:SAG=@FO=@]=@O
AG7>8H8T]a=@iONF0WD:0^>i0MN8TOUAG8hHevKG8h:S?@=@AfCH9=@]a`>?P:TC]TnUg7>8JKG8AG7>8^9]a8JKh· ]
Z[=@8JgFSWAG7>88JOZ[=BKGFO9MN8TOUA=@]2F+Zp8LKG?:S=PH4g=@AG74=POW_FSKGMb:SAG=@FO:S<F^9A
F0AG798JKF0<ÉD8T\JAG]`9KG8J]a8TOUAg=BAG7>=@OAG7:SA8TO[Z[=@KGF0O>MN8TOUAhn):SOH:H9:0ÀG]
AGF3AG798H9=BKG8T\JAG=@F0O4AG7:+AAG798^>]a8LK2=@]?@FUFo[=@O>i'AGFhg:+K(Hm ¤9n®+vj
6798;:0<>=@?@=BADCEAGFIH98JAG8LKGMN=PO98QAG7>8RFSKG=@8TOUA(:SAG=@FOVFSWX:YH98TZ[=@\T8R=@]
Abstract
FSWW_^>O>H>:SMN8TOUA(:0?"=@MN`F0KaA(:0O9\T8b=@Oc\TFOUAG8Jd[Aaef:Tg:+KG8:SOHc?@FU\h:+AG=PF0O9e
H8T`8TO>H98TOUAMNF<9=@?P8N\JFMN`>ÂG=@O>i9jlk%Cc:SO:0?@F0i0CmAGF*:4AaK(:H9=BAG=@FO>:0?
\JFMN`:S]a]Tnpo[O>Fhg?@8hHi8F0W)FSKG=@8TOUA(:SAG=@FO3AG7KGF^9i7qAG7983rs(tvu(wpxLy"uGz0{'|
:+AaA(:0\(7>8hHAGF4:lMNF<9=P?@8qH98TZ[=@\T8q8TO>7>:0O>\J8T]Z0:SKG=@F^9]:0`9`>?@=@\h:Se
}AG=@~SF0(O> ]Tn=PO9\T?@^H=PO9i8LN\T=@8TOUAg:TC[evO>H9=@O>il:0O>HO:hZ[=Pi:SAG=@FO5nH=BKG8T\Je
AG=@F0O:0?#]a8JKGZ[=P\J84H=P]a\JFSZ8JKaCUn%:0O>H:S^>iMN8JO[AG8THevKG8h:0?@=BADCH=P]a`9?P:hC]Tj
^K'\TF0MN`:S]a]3=@O9WK(:0]AaKG^>\LAG^9KG8l8TO>7>:0O>\J8T]qAG798]a`>:SAG=P:0?=@O9W8JKG8TO9\T8
\T:0`:S<>=@?@=BADCF0WAG798,KG=@\(op8JAb=@OHFUF0Kb?@FU\h:SAG=@F0O]C]AG8TM 0+n:0OH
8JO:0<9?@8T]2O98Jg`8JKGZ0:0]a=@Zp8\TF0MN`>ÂG=PO9i':S`>`>?@=@\h:+AG=PF0O>]Tj
]a=@O>i9d8hH:0\JAG=@Zp8'<8T:0\TF0O>]:0O>HX\T:SKG8JW^>?@?BCm`9?:S\T8hH`:S]a]a=PZ8'^>?Be
aA K(:S]aFO9=P\]a8TO>]aFSKG]Tn,g#8b]a7>FhgV7>FhgEAGF8T]AG=@Mb:SAG8bAG7>8bF0KG=@8TOUA(:SAG=@F0O
FSW:MNF<9=P?@84H98TZ[=@\T8AGFg=BAG7>=@O:W_8LgH98TiSKG8T8T]Tn^9]a=@O>im`KG8T\T=@]a8n
]a^9<9e\T8TOUAG=@MN8JAG8JK#H9=B)8JKG8JO>\T8T]#=POlH=P]A(:SO>\T828T]AG=@Mb:SAG8T],WKGFM:<8T:Se
\JFOAGFX8h:S\L7]a8TO>]aFSKbFOAG7>8\TFMN`>:0]a]Tj67>8TO5ni0=PZ8TOQ:X]a8JANFSW
9d8hH5n0:0\LAG=PZ8`F]a=BAG=@FO'<8T:0\TF0O>]g7>F0]a8?@FU\h:SAG=@F0O>],:SKG8o[O>FhgO5nSg#8
H8T]a\JKG=@<8b:0Om:0?@iFSKG=BAG7>MAG7:+A\TF0M3<>=@O98T]]a8TZp8JK(:S?"\h:SKaKG=@8JKq:SKaKG=@Z0:0?
AG=@MN8T]AGF`KGF[H9^9\T83:NKGF<9^>]A8J]AG=PMb:+AG8qFSW#AG798KG=@i=PHF0KG=@8TOUA(:SAG=@F0O
FSWAG7>8MNF0<>=@?@8\TFMN`>:0]a]Tj
67987:+K(Hg:+KG8F0WAG7>8,KG=@\(op8JA\TF0MN`:0]a]=@]]aMb:S?P?58TO9F^>i07AGFq<8
=@OUAG8TiSK(:SAG8hHmg=BAG7:47>:0O>H97>8J?HXMNF<9=P?@8bH8TZ[=P\J8jlfA=@O>\T?@^H8T]Zp8
`>:0]a]a=@Zp8^9?@AaK(:S]aFO9=P\KG8T\J8T=@Zp8JKG]TnU8h:S\L7'j 0\TMI=@O'H=P:0MN8JAG8JKhnp:SKaK(:TCU8hH
=@O:f¡]a7:S`8l:4W_8Jg¢\T8TOUAG=@MN8JAG8JKG]:0\LKGF]a]Tj£,KG=@\Lo8JA3<8T:0\TF0O>]
H8T`>?@FhCU8hHbAG79KGF0^>i79FÂ:q<>^>=@?PH9=@O9i'<9KGF:H9\T:0]A2\TF^9`>?@8hH4¤¥h p¦4§2¨
`:S\Lop8LAH9:SA(:':SOH*:'¤0«§2¨^>?BAaK(:0]aF0^>OH\h:SKaKG=@8JKhng79=@\L7:+KG8
©2
`KGª FU\T8T]a]a8hHN<UCAG7>8\TF0MN`:S]a],]aFSWADg:SKG8AGFF<A(:0=@ObH9=B)8JKG8TOUAG=P:0?>H9=@]e
A(:SO>\T8#:0O>H`F]a=BAG=@FO8T]AG=@Mb:SAG8T]Tj ^K8Ld9`8LKG=PMN8JO[A(:S?0KG8T]a^9?BAG]]a7>Fhg
AG7>:SAF^9K2`9KGFSAGF0AfC9`8=@MN`>?@8TMN8JO[A(:+AG=@FO*\h:SOXH98JAG8JKGMN=@O98\JFMN`:S]a]
FSKG=@8TOUA(:SAG=@FO*AGF3g=BAG79=PO*¬NH98TiSKG8T8T]g7>8TOlAG7>8AaKG^>8:0O>i0?@8?@=@8T]<8Je
Afg8T8JO¬04H98Ji0KG8T8T]Tn:0O>HAGFlg=BAG7>=@Oc®lH98TiSKG8T8T]g798TOXAG798qAaKG^98
:SO>i0?P8?P=@8T]<8JAfg8T8JO*2¤3H8Ti0KG8T8J]Tn9g=BAG7bKG8T]a`8T\JAAGFq:9d98THb<8T:Se
\JFOj
1.
Introduction
r%zS¯>yfxa°0yv|
sGx
t³u y³tvz0¯ n%g7>=@\(7:H>:S`9AqAG7>8T=BKq<8T7:hZ[=@F0K3AGF
~0±,~ ~L}p}² ~

67>8^9OH98LKG?@C=@O>iq\h:0`>:0<9=P?@=BADCKG8hÊU^>=BKG8hHWF0KAG7>8T]a8:S`>`9?P=@\h:+AG=@FO>]2=@]
:0o[=@OAGFc:D]aF0WADg:SKG8\TFMN`>:0]a]Tn cg7>=@\(7n,8TOHFhg8hHg=@AG7:£]a8Le
Mb:0OUAG=@\Mb:0`RFSW=@AG]l\TF0O[AG8LdA4:0O>HR:0\T\J^9K(:SAG8o[O>Fhg?@8hHi8XF0W=BAG]
FhgO£`F0]a=BAG=PF0Oc:SOHF0KG=@8TOUA(:SAG=@F0On\h:0OX=@O9W_FSKGMËAG7983^>]a8LKF0W,=@O[AG8LKae
8T]AG=@O>iKG8T]aF0^9KG\T8J]:0O>Hb79FhgQAGFi8JA,AGFAG7>F]a8KG8T]aF0^9KG\T8T]Tj,679=P],`:+e
`8JK2H98J]a\JKG=@<8T]AG798H98T]a=@i0O:0O>H4=@MN`>?@8TMN8TOUA(:SAG=@F0O4F0WAG798*rsLt³u(wpxLy
uGz0{
yfxL{3n\TFO9]a=P]AG=@O9iF0W:]a8LA"F0W>:0\JAG=@Zp8<8T:0\TF0O>]Tn0`:0]a]a=@Zp8
}~S(#(ÀS
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.
7th ACM Conf. Mobile Computing and Networking (MOBICOM) July 2001,
Rome,
Italy
´\
ACM 2001
¥
7>:SK(H[g:SKG8]a8JO>]aF0KG]Tn:0O>H4:0]a]aFU\J=:+AG8hH*]aF0WADg:SKG8:0?@iFSKG=BAG7>MN]Tj,67>=@]
]C]AG8TM 8TO>:0<9?P8J]':4KGF<9^>]Aq]aF0WADg:+KG8\JFMN`:S]a]q\T:0`:S<>=@?@=BADCcWF0K3:
7>:0O>H97>8J?HH98TZ[=@\T8MNF+Z[=@O>iq:0<FÂ=PO9]a=PH98:3<9^>=@?PH9=@O>ij
6798F`8JK(:+AG=PO9i8TO[Z=BKGF0O>MN8TOUA"=@O'AG7>8,KG=@\(op8JA#:SKG\(7>=BAG8T\JAG^KG8=@]%=@O9e
]AaKG^9MN8TOUAG8hH£g=BAG7:0\LAG=PZ8l<8T:0\TF0O>]Tn%8h:0\(7F0Wg7>=@\(7<9KGF:H9\T:0]AG]
=BAG]FhgOoO9FhgO`F]a=BAG=@FOF+Zp8JK3:0O ©2ª \L7>:0O>O98T?"AGFi8LAG7>8JKqg=@AG7
:SOm^9?@AaK(:S]aFO9=P\N`9^>?@]a8* 0+vj O>8 ª KG8J\T8T=@Zp8JK:SOH]a8TZp8JK(:S?,`>:0]e
]a=@Zp8l^>?BAaK(:S]aFO>=@\`F]a=BAG=@FOKG8T\T8T=@Zp8J©KG]3
:SKG8l`9KG8T\J=P]a8J?@C`9?P:0\T8hHF0O:
\JFMN`:S]a]4<F:SK(H5j¢È[F0WADg:+KG8XKG^9O>O9=PO9iFOef<F:SK(H^9]a8T]lAG798Â0t |
xLsGxL¯>y³t
=@OH=@]A(:0O>\J8T]3KG8T`FSKaAG8hH<UC£AG7>8l^>?BAaK(:0]aF0O>=@\KG8T\J8T=@Zp8JKG]
AGF=@OW_8J~Kq² AG7>8NF0KG=@8TOUA(:+AG=PF0O»³F0K£D7>8T:H9=@O9iU¼F0WAG798H8TZ[=@\T8j6798
,KG=@\(op8JA%\TF0MN`:0]a]KG8J`F0KaAG]"`F]a=BAG=@FOb:SOHqFSKG=@8TOUA(:SAG=@FO'=@O>H9FUF0KG]WF0K
:'7>:0O>H97>8J?H)nMNF<>=@?@8H98JZ=@\T80n:0O>H=@O9WF0KGMN]2:0O:S`>`9?P=@\h:+AG=@FO*KG^>Oe
O9=@O>i3F0OAG798H98JZ=@\T82F0WAG798`F0]a=@AG=@F0O:0O>HlFSKG=P8JO[A(:+AG=@FO*=@O:q?@FU\h:0?
\JFUF0K(H9=@O>:SAG8]C]AG8TMV8T]A(:0<9?@=P]a798hH4<UCbAG7>89d8hH]a8JAFSW<8h:0\JFO>]Tj
Beacons on
ceiling
B
Compass hardware
67989KG]A\(7:S?P?@8TO9i82=POlH8JKG=@Z=@O9izSsLtxL¯9y y³tvz0¯W_FSK:]aMb:0?@?H8TZ[=P\J8
:+KG=@]a8T]WKGFMAG798'O>8T8THXW_FSK3Z8JKaCX:0\T\J^9K(:S~ AG8bH=B)8JKG8TOUAG=P:0?,H9=@]A(:0O9\T8
8J]AG=PMb:+AG8T] X8T]AG=@Mb:SAG=@O>imF0KG=@8TOUA(:SAG=@FOAGFmg=BAG7>=@OR:XW8JgÆH98TiSKG8T8T]
FSWAG7>8'\JF0KaKG8T\JAZ0:0?@^>8qKG8hÊU^>=BKG8T]H9=B)8JKG8TOUAG=P:0?,H9=@]A(:SO>\T8'8J]AG=PMb:+AG8T]
AGF3<8F0W"]a^><e\T8TOUAG=@MN8JAG8JK:S\T\T^9K(:S\JCUng7>=@\L74=P]2:SA?@8h:S]A:SO*F0K(H8JK
FSWMb:SiO>=BAG^>H983]aMb:S?@?P8LKAG7:SOXAG7983\T^KaKG8TOUAG?@C*<8T]A:hZ:S=P?P:S<>?@8'?@=@O9e
8T:SKbH=P]A(:SO>\T8l8T]AG=@Mb:SAG=@F0OAG8J\L79O>F?@F0i=@8T]Tj
8]a79F+g7>Fhg AGFXH9F
AG79=@]'^>]a=@O>iMq^>?BAG=@`>?@8\T:SKG8JW^>?@?BC`>?P:0\T8THKG8J\TÃ 8T=@Zp8JKG]Tj67984]a8T\JFOH
\(7:S?@?P8JO>i8':SKG=@]a8T]H9^98AGFbZ0:SKG=P:SAG=@F0O£=@OAG7>8]a`8T8hHF0W,]aF^9OHH9^98
AGFAG8TMN`8LK(:SAG^9KG8X:SOHR7[^>MN=PH9=BADCUng79=@\L7:+)8T\JAG]4AG798£:S\T\T^K(:0\JC
FSW`F0]a=BAG=PF0O8J]AG=PMb:+AG8T]Tj © :SAG7>8LK#AG7:SOb8Jd`>?@=@\T=BAG?@C'MN8h:0]a^KG=PO9iAG7>=@]
`>:SK(:SMN8JAG8JKg=BAG7q\J?P=@Mb:+AG8]a8TO>]aFSKG]Tnpg8#\h:0?@\T^9?:+AG8=BA"H9=BKG8T\JAG?BCWKGF0M
F0<>]a8JKGZ8hH4`9KGF0`:Sip:SAG=@F0O4AG=@MN8T]Tj
θ Heading relative to B
on horizontal plane
User device
parallel to ground
on horizontal plane
"!#$%&')(*'+,-%./101'2
$34556
$'78$9)(:7;1%&=<>,8$ $ %&,?@78%.569$((A,$@47<B$@5C
D ,FE41%4GH%&569)$ ((H(0;/(I,)!)0@6JK!$1'L
1'+,M)@%.1(M#('N$ ')7O4/'$@'PQ,)(
7;?1%.*/0$@;*RI$:%& &71'$ R:(S(@6T7VU#'?@7=!S=,?
!#$%.'(.C
6798,KG=@\Lop8LA£\JFMN`:S]a]]C9]AG8JM `9KGF`F0]a8hH=@OAG79=P]`>:0`8JK£:0He
H[KG8T]a]a8T]]a8TZp8JK(:S?`9KGF0<>?@8TMN]'g=BAG7R8Jd=@]AG=@O>iMN8JAG79F[H9]'W_FSK*FSKG=P8JO9e
A(:+AG=@FOm8J]AG=PMb:+AG=@FOj'¸IAaK(:0H9=BAG=@FO>:0?"Mb:0i0O>8JAG=@\'\TF0MN`:S]a]\h:0O£8T]e
AG=@Mb:+AG8F0KG=@8TOUA(:SAG=@F0On<9^9A8Ld979=@<>=BAG]8TO>FSKGMNF^9]8JKaKGF0KG]g7>8JO*O>8h:+K
Mb:SiO98JAG=@\lFSKqAG=@MN8JeZ0:SKaC=@O>il8T?@8T\JAaKG=@\b8T?PH9]Tn<F0AG7cFSWg79=@\L7:+KG8
K(:+AG7>8JK3\TFMNMNF0Oc=@OMNF]AqMNF[H98JKGOm<>^>=@?PH9=@O9i]qg=BAG7\TF0MN`>^9AG8LKG]
:SOHF0AG798JKN8hÊU^9=P`9MN8TOUAhj KG=P8JO[A(:+AG=@FO\h:0O<8l=POW_8JKaKG8THWKGFM :
MNF+Z[=@O>i£`F]a=BAG=@FO]a8TO9]aF0Khn<9^9A'AG79=P]b^9]a^:0?@?BCKG8hÊU^>=BKG8T]b?P:SKGi08F0K
W_:0]AN^9]a8JK'MNFSAG=@FO>]Tn%g7>=@\(7=P]q^>O>H98T]a=BK(:0<9?@84=@O]a8TZp8JK(:S?:0`9`>?@=@\h:Se
AG=@F0O>]TjN¸\JAG=@Zp83]a8JO>]aF0KG]F0O£^9]a8JKH98TZ[=@\T8T]AfC`>=@\h:0?@?BC?@8h:HAGF4]C]e
AG8JMN]AG7>:SAAaK(:0\(oX^>]a8JKG]lB¥T¤9n#S¹Svng7>=@\(7]a^9)8JKWKGF0M `F0AG8TOUAG=P:0?
\JFMN`9KGF0MN=@]a8T]AGF^>]a8JK`9KG=@Z0:0\JCB¥ [n,0Svj4DOc\TF0OUAaK(:0]Ahn,,KG=@\Lo8JA
KG8TÊ[^9=BKG8T]':*]aMb:S?P?#O^9M3<8JKFSW<8h:0\TF0O>]3:SA'o[O9F+gOm`F]a=BAG=@FO>]3=PO
8T:0\(7KGFUFM AGF£=@O>]AaKG^>MN8JO[A':£<9^>=@?PH9=@O>in<>ÂN8TO:S<>?@8T]N?@FU\h:+AG=PF0O
:SOHF0KG=@8TOUA(:SAG=@F0OW_FSK:X`>:0]a]a=@Zp8*7>:0OH7>8T?PHH98JZ=@\T8g=@AG79FÂ'KG8Je
ÊU^9=@KG=@O9i:0OUCm^9]a8JKqMNF0AG=@FO5j Ã 8N7>:hZp8N<>^9=P?BAq]a8TZp8JK(:S?#`KGF0AGF0AfC`8
<8T:0\TF0O>]b:0O>H:KG8T\T8T=@Zp8LKN\TFMN
`>:0]a]'\JFO9>i^K(:SAG=@FO5n:0O>HKG8T`FSKaA
8Ld9`8LKG=PMN8JO[A(:S?>H9:SA(:AG7>:SA%]a7>FhgAG7:SA%F0^9K%]aF0WADg:+KG82\JFMN`:S]a],\JF0Kae
KG8J\JAG?BCq8J]AG=PMb:+AG8T]"F0KG=@8TOUA(:SAG=@F0O3AGF2g=BAG7>=@O3:W_8LgQH8Ti0KG8J8T]Tj Ã 8#:0?@]aF
H8T]a\JKG=@<8:*¡=@8JgO>H98JKq:S`>`>?@=@\h:+AG=PF0OH98TZp8J?PF0`8hHc^>]a=@O9i*AG7>=@]q\T:Se
`>:0<9=P?@=BADCUj%6798,KG=@\(op8JA]C]AG8TME=@]<8T=@O>i^>]a8THb=@O4¦46· ] KGFSÉD8T\JA
[
d
C
i
J
8
4
O
@
=

O
3
:
0
Z
S
:
G
K
@
=
J
8
f
A
C
S
F
W
`
J
8
G
K
0
Z
0
:
a
]
@
=
p
Z
8
J
\
F
N
M
>
`
^
G
A
@
=
>
O
3
i
a
]
J
\
T
8
O
+
:
G
K
=PF0]qB¥hµ+vj

6798KG8T]AF0WAG79=@]`:0`8LK2=@]F0KGi:0O9=P¨J8hH*:0]WF?@?@F+g]TjÈ8T\LAG=PF0OqH8Je
A(:S=@?P]%AG7>8H8T]a=@iONFSWAG7>8,KG=@\Lo8JA%\TFMN`>:0]a]Tn[H8T]a\JKG=@<>=@O>i=BAG]AG7>8JF0KaC
FSW>F0`8JK(:SAG=@F0OnH9=B)8JKG8TOUAG=P:0?[H=P]A(:SO>\T8,8T]AG=@Mb:SAG=@FO5n0:0OH\TFUFSK(H9=@O:+AG8
H8JAG8JKGMN=@O:+AG=@FOR:S?Pi0F0KG=BAG7>MN]TjIÈ8T\JAG=@F0O¬H9=@]a\T^>]a]a8J]F0^9K=PMN`9?@8Je
MN8JO[A(:+AG=@FOX:0O>H£È[8T\JAG=@FOX¤l`9KG8T]a8TOUAG]8Ld9`8LKG=PMN8JO[A(:S?KG8T]a^9?@AG]:0OH
:SO8JKaKGF0Kb:SO:S?@C]a=@]TjÈ[8T\JAG=@FO®H9=@]a\T^9]a]a8T]']aFMN8l=@MN`9KGF+Zp8TMN8JO[AG]
<>:0]a8hHXFOXF^K8Jd`8JKG=@MN8TOUA(:0?KG8T]a^9?BAG]Tj'È[8T\JAG=@FOm¹H8T]a\JKG=@<8T]AG798
¡2=@8JgO>H98JK#:0`9`>?@=@\h:SAG=@FO5j 8\TF0MN`:+KG8F0^9K%]C]AG8TM½AGF`9KG8TZ[=@F^9]
g#F0KGol=@OÈ8T\LAG=PF0Oµ3:SOH\JFÃ O>\J?P^>H98=@OÈ[8T\JAG=@FO* j
2.=@i^KGDesign
of the Cricket Compass
¥']a79F+g]:b^>]a8JKH8TZ[=@\T8qg=BAG7c:+AaA(:0\(7>8hHX\TFMN`>:0]a]7>:SK(H[e
ªg:+KG8N84
=@Oc:lKGFUF0Mg=BAG7m<8h:S\TFO9]`>?P:0\T8TH£FOXAG7>8'\J8T=@?P=@O9i9j Ã 798TO
AG7>8'H98TZ[=@\T8'=@]7>8T?PH`:+K(:0?@?@8T?,AGFlAG7>8'79F0KG=@¨TFOUA(:S?,`9?:SO>8)
n W=@]AG7>8
:0O9i?@8W_FSKGMN8hHq<UCAG7987>8h:0H9=@O>iH9=BKG8T\JAG=@FOq]a7>FhgOn0g=BAG73AG7>8`F0=@O[A
g7>8LKG8AG7>8`8LKG`8TOH=P\J^>?P:SKWKGFMV<8h:S\TFH
O XE=@OUAG8JKG]a8T\JAG]AG7987>FSKG=Be
¨TF0O[A(:S?`9?P:0O>80j Ã 8:SKG8=@OUAG8JKG8T]AG8TH4=@O*`9KG8T\J=P]a8J?@C8T]AG=@Mb:SAG=@O9>
i Wj
67>83<:0]a=@\'=PH8h:=@]AGF4^9]a8'FO98
KG8T\T8J=PZ8JKAGFKG8T\J8T=@Zp8'\TFUFSK(H9=Be
O:+AG83=@O9WF0KGMb:+AG=PF0OXWKGFMÆAG7983<8h©2:S\Tª FO9]Tn:SOHM3^9?BAG=P`9?@8n5\h:SKG8JW^>?@?BC
`>?P:S\T8hH5n^>?BAaK(:0]aF0O>=@\KG8T\T8T=@Zp8JKG]2FO4AG798\TFMN`>:0]a]:SAaA(:S\L798hH4AGF'AG7>8
H98JZ=@\T8AGFF<9A(:S=@ObAG7983ÂSt YxLsaxL¯>y³t H9=@]A(:0O9\T88J]AG=PMb:+AG8T]#FSW:<8h:+e
\TF0OAGF'8h:S\L7^>?BAaK(:0]aF0O>=@\KG8T\T8J=PZ8JKh~0jZ² Wq=@]:W_^9O>\JAG=@F0O4F0WAG7>8H=@)8LKae
8TOUAG=P:0?H9=@]A(:SO>\T8FSW>AG798#?@=@O>8h:+K#H=@]A(:0O>\J8F0W9AG7>8#\JFMN`:S]a]WKGF0MAG7>8
<8h:S\TFO5n):0O>H4F0W"AG7>8798T=@i7UA2F0WAG7>8<8T:0\TF0O»³\J8T=@?P=@O9iU¼:0<F+Zp8AG7>8
`>?P:SO>8FSWAG7982\JFMN`:S]a]Tj Ã 8F<A(:0=@Ob`8JKae<8h:0\TF0O?@=@O>8T:SKH=P]A(:SO>\T8
8T]AG=@Mb:SAG8J]l<UCH9=B)8JKG8JO>\T=@O>i£AG7>8:SKaKG=@Z0:0?AG=@MN8T]bF0W\TF0^>`9?P8TH ©ª
:0O>H3^>?BAaK(:S]aFO>=@\]a=@iO:S?@]#]a8TOUA%WKGFMI8h:S\L7N<8T:0\TF0O SSvj%6FF0<9A(:0=@O
AG7>827>8T=@i07[AF0W5AG7>8<8T:0\TF0OlWKGFMAG798\TF0MN`:0]a]Tn[g#88T]AG=@Mb:SAG8AG7>8
`F]a=BAG=@FO4\TFUF0K(H=PO>:SAG8T]FSWAG7>82\TFMN`>:0]a]WKGF0M AG7>82`F]a=BAG=@FO*\TFUFSKae
H9=@O>:SAG8T]H9=@]a]a8TMN=@O>:SAG8hHl<[ClMq^>?BAG=@`>?@8O>8T:SKG<UCl<8h:0\TF0O>]Tj
67>8'KG8J]AqFSWAG7>=@]]a8T\JAG=@FOcH98T]a\JKG=@<8T]7>FhgIAG7>=@]=PH98h:\h:0Oc<8'KG8Le
:0?@=@¨T8hH=@O`9K(:S\JAG=@\T8j
8b]A(:+KaA3<UCmH98T]a\JKG=@<9=PO9i7>Fhg H=BKG8T\JAG=@FO>:0?
=@O9WF0KGMb:SAG=@F0OR\h:0OR<8Ã F<A(:0=@O>8THQ^>]a=@O>iH=B)8JKG8TO>\J8T]=@OH=P]A(:SO>\T8
<8JAfg8T8TO:c<8T:0\TF0O:0OHRH=B)8JKG8TOUAbKG8T\T8T=@Zp8JKG]Tj
8H98T]a\LKG=P<8X:
AG8T\(7>O9=ÊU^98AGF:S\L79=P8JZp8XAG798XKG8TÊ[^9=BKG8hH`9KG8T\J=P]a=@F0O Ã FSW'H=@)8LKG8TOUAG=:S?
H9=@]A(:SO>\T8*8J]AG=PMb:+AG8T]Tn^9]a=PO9icH=@)8LKG8TOUAG=:S?2`97:S]a84=@O9WF0KGMb:SAG=@F0OF0W
AG7>8^9?BAaK(:0]aFO9=@\g:hZp8T]KG8h:0\(7>=@O>iAG798cKG8T\T8T=@Zp8LKG]Tj ª =@O:S?@?@CUng8
]a7>Fhg7>FhgAGFF<A(:0=@O:0\J\T^9K(:+AG84`F]a=BAG=@FO\TFUFSK(H9=@O:+AG84=@O9WF0KGMb:+e
AG=@FObg=BAG7>F^A8Jd`>?@=@\T=BAo[O>Fhg?@8hHi8FSWAG7982]a`8J8hHlFSW]aF0^>OH)n[\TFM'e
`8TO9]G:SAG=@O>i3WF0K2=BAG]Z0:SKG=P:+AG=PF0O4g=BAG7*`>7UC]a=@\h:0?5\TF0OH9=BAG=@FO9]Tj

2.1
Theory
of Operation
3]a79Fhg]:3<8h:S\TFO-XNn:SOH:3\JFMN`:S]a]g=BAG7*AfgFN^>?BAaK(:+e
ª]aF=@O9i^=@\#KG83
KG8T\T8T=@Zp8LKG]TnV[\:0OHB[Q]SnSg7>=@\(7':+KG8?@FU\h:SAG8hH3:SA":2H9=@]A(:0O9\T8^
:0`>:SKaAWKGFMY8h:S\L7qF0AG798JKhj"67>8#:0O9i?@8F0W9KGF0A(:SAG=@F0O'F0W9AG7>8#\JFMN`:S]a]Tn
Beacon B (on ceiling)
d1
d2
z
x1
ding
Hea
R2
L
R1
θ
Horizontal pla
ne
θ
θ
L/2
76 98
g=BAG7lKG8J]a`8T\JA#AGFq:<8h:0\JFO?»³=¼»./] \L¼LnUAG7>8H=@)8LKG8TO>\T82=@OH=@]e
A(:0O9\T8T]FSWAG7>8#AfgFKG8T\T8T=@Zp8JKG]WKGFMAG798<8h:0\JFOnp:0O>Hl»³=@=¼=?> nSAG7>8
K(:SAG=@FlF0W%AG7>87>8T=@i07[AF0W%AG7>8<8h:0\JFOWKGF0MËAG7>87>FSKG=@¨TFOUA(:0?`9?P:0O>8
FOg79=P\(7AG7>8\TFMN`>:0]a]2=P]`>?P:0\T8THAGFNAG7983H=P]A(:SO>\T8F0W%AG7>8<8h:+e
\TF0OmWKGF0M AG798'\T8TOUAG8JKFSWAG7>8N\TF0MN`:S]a]TjfOm`K(:0\JAG=@\T8n7>Fhg8TZ8JKhn
O>FbMN8h:S]a^9KG8TMN8JO[AG]2:SKG8q`8JKaW_8J\JAhj ^KiF:0?=@]AGFb8T]AG=@Mb:SAG88h:S\L7
F0WAG798T]a8bÊU^:SO[AG=BAG=@8T]g=BAG7c79=Pi07c`9KG8J\T=@]a=PF0On"]aF:S]AGF4`9KGF[H9^9\T8N:
]a^9'\T=@8TOUAG?@C4:0\J\T^9K(:+AG88T]AG=@Mb:SAG8F0W Wj
@= i0^9KG8¬]a7>Fhg]AG7>82<8h:0\TF0O=XYWKGF0M =@i^KG8`KGFSÉD8T\JAG8hHlFOAGF
AGª 7987>FSKG=@¨TFOUA(:0?)`9?:SO>8:S?@FO>iqg7>=@\L7lAG7>ª 82\TFMN`>:0]a]=@]:0?@=@iO98hH5j%DO
AG79=@]%>i^9KG80n \,:0O>
H 5]:SKG8AG798`9KGF+É8T\JAG=@F0O>]#FSW5H9=@]A(:0O9\T8T
] \,:0OH
/]FOAGFAG7>827>F0KG=@¨TF0OUA(:0?)`>?P:0O98j Ã 8:0]a]a^>MN8AG7:+AAG7>8\JFMN`:S]a]
=@]7>8T?PHl`:SK(:S?@?P8J?AGF3AG7987>FSKG=P¨JFOUA(:0?`>?P:0O98j
]\ ]\ ]
]] ]] ]
] ]
"!$#%] '& g798TO( \")$/ ]+* ^j
ª KGFM ª =@i^KG8¬/
]\,
:SOH
^
»
- ». ]
\TF0]Wp¼

O>8g:TCIF0W4`9KG8T\J=P]a8J?@CE8T]AG=@Mb:+AG=PO9i¢.» /] \(¼Xg#F^>?PHI<8AGF
`9KG8J\T=@]a8T?BCMN8T:0]a^9KG8@\N:SOHA/]l]a8T`>:SK(:+AG8T?BCUn<>^A3AG7>:SAN=@]'8h:S]a=@8JK
]G:0=PHAG7:SOHFO98j#F0O>]a=PH98JKhn%W_FSKN8Jd9:0MN`9?@8n,:]a=BAG^>:SAG=@FOg7>8JKG8
^ ®S\JM*n[:0O>I
H W ¥T BpnUg=@AG7l:<8h:0\JFO:SA:H9=@]A(:SO>\T82F0WMN8Je
AG8JKG]#:0OHb:7>8J=Pi07UA#FSW,¥MN8JAG8JK%WKGF0M¢AG798KG8J\T8T=@Zp8JKG]Tj ª KGF0M¶%ÊU^:+e
AG=@FOc»³¤p¼Ln9AG798Z0:0?@^>8FSW»./] \G¼#=POAG7>=@]\h:0]a8=@]FO9?@C(RDC ¹S\TM*n
g7>=@\(7q=@]":S<F^9A:0OF0K(H8JKF0W>Mb:0i0O>=BAG^H8,]aMb:S?P?@8JKAG7>:0Og7:+A\T^Kae
KG8TOUAAG8T\(7>O>F0?@Fi=@8T]\h:SO:0\(7>=@8TZp8=@O4AG8LKGMN]F0W"?@=@O>8h:+KH=@]A(:0O>\J88J]e
AG=@Mb:SAG8T]2B¥T¤9n9SS \ j%È=@O9\T82F0^9K#iFp:S?=@],AGFH98TZ[=@]a82:\JFMN`:S]a]%g=BAG7
`>7UC]a=@\h:0?@?BC']aMb:S?@?H9=@MN8TO9]a=@FO>]Tnp\TFMN`>:SK(:0<9?@8=@ON]a=@¨T8AGF7:SOH7>8T?PH
"º¸]Tn:SOH]AG=P?@?%:0\(7>=@8TZ8'7>=@i7£H9=BKG8T\LAG=PF0O:S?#:S\T\T^9K(:S\JCUn5g8'O98T8hH
:0O4:0?BAG8JKGO>:SAG=@Zp8MN8JAG79F[H'AGF38T]AG=@Mb:SAG8AG7>=@]H9=B)8JKG8JO[AG=P:S?H=@]A(:0O>\J8j
»¥h¼
»0¼
^

]a=@O"Wp¼
]
- .» - ^ ]a=@O"Wp¼ ]

]
]
/ ] \ 4^]a=@O W
È[^><9]AG=@AG^AG=@O>iNW_FSK
]\ :SOH0 ]] WKGFMÆ¶,ÊU^>:SAG=@FO9]'»¥+¼:SOH»¼Lng#8
i08JA
/] - \ »./ ] \L¼
]a=@O W »v¬¼
&^ 1
]]+
»
^

\TF0]Wp¼
679=@]2Mb:TCb<8KG8JgKG=BAaAG8TO:S]
]a=PO"W
]
/] \
^2 ¥ »43 5 ¼ ]
;
<
<UCN:0O>Hn[KG8T]a`8J\JAG=@Zp8T?BCUj
ª KGFM ª =@i^KG8
:
5
4 $ /7 %.569)$ ((M0$ 7)(9 $ 7) Z4/')%&
1'+7)1($ ')%./(*!# </',=!#$%.'+$ ')7+$ %&,2,?=L
%./;4(.C D ,)1(-U O(9,8@(0M*) /%.1' ,?
!#$%.'8'R,3,4 .'R$0 0$ '-
,3%.569$((.C
W[n9g=BAG74KG8J]a`8T\JAAGF3AG7>8<8h:0\TF0O XNn>=@]KG8T?P:SAG8hHlAGF3AG7>8H=B)8JKG8TO>\J8
=@OH=P]A(:SO>\T8J] q
\ :0O>H /S
] ng798JKG8 \3:SOH /]N:SKG8NAG798bH9=@]A(:0O9\T8T]
FSWKG8T\T8J=PZ8JKG]
[
\ :SOHI[Q2
] WKGF0M b
X j%6798Zp8JKaAG=@\h:S?5:0OHl7>FSKG=P¨JFOUA(:0?
H=@]A(:0O>\J8T]WKGF0MËAG798\J8TOUAG8JKFSW,AG798q\TF0MN`:S]a]2AGFIV
X :SKG8qH98TO9F0AG8hH
g798JKG8
L/2
x2
x
I/R/&6M')1'I,$'0*4/'$@'3$0'
W
, , & '5$0- 0$ '
3)(1' 7)($')%& /( 69$@/(.C
! (;N,$ +, ,?/$ 7)1' 1(+ #/')7)1% 0$ ,
[\
01' ')1' ,?:)0$(')1%:%.569$((Q/%./;&(
$'7
[ ]
^
<>,1%&, $@4B 0$ %./7-$@
$:7)1($ ')%.
56T$%4, ,VC
x
^9K,]aF?@^AG=PF0OlAGFAG7>=@],`9KGF<9?@8TMEAaK(:S\Lo[]%AG7>8
xÂ0t Y2xLsGxL¯uLx<8Le
DA g#8T8TOAG7>8l^>?BAaK(:S]aFO>=@\*]a=@i0O:0?@]b:+A3ADg#FmH=B);} 8JE9KG8T~0OU A3KG8T\J8T=@Zp8JKG]N:SOH
`9KGFU\J8T]a]a8T]AG7>=@]=@O9W_FSKGMb:SAG=@FO5j Ã 83>OHAG7:+AAG7>=@]:0`>`KGFp:S\L7m:0?Be
?@Fhg]'^>]AGFF<9A(:S=@OH=B)8JKG8TOUAG=P:0?H=P]A(:SO>\T8l8T]AG=@Mb:SAG8J]qg=BAG7]a^><e
\T8TOUAG=@MN8JAG8JK:S\T\T^K(:0\JCUj%679=P]=@]H98T]a\JKG=@<8hH=PO*È8T\LAG=PF0O[j Uj
»³¤p¼
67>83]a8T\TFO>HmÊU^:SOUAG=@AfCUnF?> n5=@]8T]AG=@Mb:SAG8hH<UCH98LAG8JKGMN=@O>=@O>ibAG7>8
.» G)IH)JU¼\TFUFSK(H9=@O:+AG8T]"F0W>AG798,\JFMN`:S]a]g=BAG7KG8T]a`8J\JAAGF2AG798,`9?P:0O>8
W_FSKGMN8hH<[CAG798#<8h:S\TFO9]»_AG7>,
8 KH`>?P:0O98+¼Lj 8HF2AG7>=@]<UC`9?:S\T=@O>i
M3^9?BAG=P`9?@8<8T:0\TF0O>]#=@Ol:KGFUFM:0OH'8J]AG=PMb:+Ã AG=@O>iAG7>8AG=@MN8=BA,A(:0op8T]
W_FSK#AG798^9?BAaK(:0]aFO9=@\2]a=@iO>:0?AGF`KGF`:Sip:+AG82<8JAfg8T8JO'AG7>8TME:0O>H3AG7>8
\TF0MN`:0]a]Tj§Fhg8JZp8JKhn)<8T\h:S^>]a8AG7>8]a`8T8hHF0W,]aF^9OHZ0:SKG=@8T]2g=BAG7
:0Mq<>=@8TOUAAG8TMN`8LK(:SAG^9KG8':0OHX7[^>MN=PH9=BADCUng#8NM3^9]A8T]AG=@Mb:SAG83AG79=@]
ÊU^:SO[AG=BAfCl:0]g8T?@?³j,67>=@]2=@]H98J]a\JKG=@<8hH4=@OÈ[8T\JAG=@FOUj ¬j
\
67982g#F0KG]Aae\h:0]a828JKaKGF0K#=@OX».
8JKaKGFSKG]2=@O( \ :SOH( ] j
¶%ÊU^:+AG=PF0OQ»³¤p¼=PMN`9?@=P8J]AG7:+A=@A]a^9N\T8J]AGFl8T]AG=@Mb:SAG8qADgF4ÊU^:0Oe
AG=BAG=@8T]=@O£FSK(H98JKAGF4H98JAG8LKGMN=PO98qAG7983F0KG=@8TOUA(:+AG=PF0OcF0W,AG7>8'\JFMN`:S]a]
¬
]
\
¼"=P],8hÊU^:S?>AGFAG7>8]a^>MIF0W5AG7>8
From beacon
d1
From far-away beacon
d2
d
2 -d
3
d1−d2
d
1 -d
2
L
[ \
? >@%&@ ;/4(
@'5$ 0)
7 1($ ')%.- 46
[Q]
$ ')7
%&$'O69$ (
$9 $ L $<$S+!#$%&'ZC
L12
R1
L23
R3
,37) L
')(
+* \ ] ¼ C
(1'-, /%./;4(K969$(
`>7>:0]a8NH=B)8JKG8TO>\J8T]AGF48T]AG=@Mb:SAG8':0O:S\JAG^:S?#H=@)8LKG8TO>\T80jb67>8'=@Oe
AG^>=BAG=@FO=@]3AG7>:SA'=BWAG7>8bADg#F£=@OUAG8JKaevKG8T\T8J=PZ8JKNH=P]A(:SO>\T8J]Tn ^ \ ] :SOH
^Z]-,X:+KG8*\(7>F]a8JO\h:SKG8LW_^>?@?BCUnAG7>8JOAG798:0\JAG^>:0?`>7>:0]a8H9=B)8JKG8JO>\T8
<8JAfg8T8TOKG8T\T8J=PZ8JKG]*¥:SOH»³]G:TC>¼q\h:SOQ<8*H=@]G:0M3<9=@i^:+AG8hH<[C
^>]a=@O9ilAG7983`>7>:0]a83H9=B)8JKG8TO9\T8'<8JAfg8T8TOKG8T\T8J=PZ8JKG]:SOH¬n]a=@O>\T8
AG7>82ADgF3`>7:S]a8H9=B)8JKG8TO9\T8T]:SKG8O9F0A=@OH8T`8TOH8TOUAhj
2.2
Estimating Differential Distance
#F0O>]a=PH98LKADgFb^9?@AaK(:S]aFO9=P\KG8T\T8T=@Zp8LKG]K[\:0OH-[ ]?@FU\h:SAG8TH£:lH9=@]e
A(:SO>\T89^ :S`:SKaAhn:0]]a7>FhgOR=@O ª =@i^9KG8X¤9j58JA(\:SOH /]<8
AG798bH9=@]A(:0O9\T8T]AGF4KG8T\T8T=@Zp8LKG*
] [ \ :SO
H [ ] WKGFM <8h:S\TFF
O XNj58JA
\ /]b:SOHc?@8J
A F\q:0O>
H M]N<8bAG798b^>?BAaK(:0]aF0O>=@\lg:hZp8Je
WF0KGMN]KG8T\T8T=@Zp8TH4<UH
C [ \ :0O>=
H [ ] WKGF0M Xbj,67>8`97:0]a8H=B)8JKG8TO>\J8
<8LADg8J8TO*AG7>8g:hZp8LW_F0KGMN]:SAAG7>8ADg#F'KG8T\T8T=@Zp8LKG]Tn nH98T`8JOH9]FO
AG798H=@)8LKG8TO>\T82=@O4H=P]A(:SO>\T8J]#AaK(:hZp8JKG]a8hHNWKGF0M XAGFqAG798KG8T\J8T=@Zp8JKG]
<UCbAG7>8^>?BAaK(:0]aF0O>=@\]a=Pi0O:S?:SOHAG798g:hZp8T?@8TO9i0AG
7 FSWAG7>8]a=Pi0O:S?vn
:SOH4Mb:TCb<88Jd`KG8T]a]a8hH4:S]
» ¼
»®0¼
R2
1
8LA \ ]:SO.H ]-,<8#AG798:0\LAG^:0?`>7>:0]a8H=@)8LKG8TO>\T8J]F0W5:2<8T:0\TF0O· ]
g:hZp8LW_F0KGMÆ<8JADg#8T8TOKG8T\T8T=@Zp8LKG]3¥':SOHXb:0OH*KG8T\J8T=@Zp8JKG]b:0O>HX¬[n
KG8T]a`8T\LAG=PZ8T?BCUj%67>8TO5n
/ 0 1/ 0 - 2/ 0
W_FSK38T:0\(7c`:S=@KqF0WKG8J\T8T=@Zp8JKG]l» 3I)54U¼Lng7>8JKG
8 1 / 0 :SKG8b=@OUAG8Ti8LKG]3:SOH
+62/ 0876"j%k#8T\h:S^>]a8AG798:S\JAG^:S?5`97:S]a8H9=B)8JKG8JO>\T82<8JADg#8T8TO
ADg#F2KG8T\J8T=@Zp8JKG]=@]"`9KGF`FSKaAG=@FO:S?AGFAG7>8H9=@]A(:0O9\T8#AaK(:hZp8JKG]a8hH<UCAG7>8
]a=@iO>:0?"WKGFMËAG7>83<8T:0\TF0O£AGF48T:0\(7mF0W,AG7>8KG8T\T8T=@Zp8JKG]Tn9 ]-, >: \ ] .» /] ;,hI¼ >[.» \ /]T¼ O^ ]-,4>4^
\ ]#g7>8JO / * ^ / 0 j67>=@],=@]"]a7>FhgO
=@O ª =@i^KG8®[j
:SAg#82g=@?@?5]a79Fhg=P],AG7:SA=@A=P]#`F]a]a=@<>?@8AGF`>=@\(:
o ^
\ ]:SO:
H ^Z]-,
Ã]a^>\(7>7N
AG7:+AFO98\h:SOb^>]a82AfgF]a8JAG]FSWF0<>]a8JKGZp8THb`97:S]a8H=@)8LKG8TO>\T8J]
\ ] )< ]-,AGF [¯ ~ >{ =J@t ?:9:z L² À 8J]AG=PMb:+AG8AG7>8:0\JAG^>:0?`97:0]a8H=@)8LKae
8TO9\T
8 \ ] j"DO4`>:SKaAG=@\T^9?:+Khn>g#8]a7>FhgAG7>8WF?@?@F+g=@O9ilKG8T]a^9?BA ^\ ]
At z Ft~ = ¯x'Â y^ Gz ]-, ~ Hx sax sa\ x] ²@~ y³¯Ct B0>Â x ² À]-} , s(t_y{NGz x[¯ D{ >{ ² y³=Jt @t}?:² 9x :z z >z ; =JE"y y t_E ¯xL¯y t_x y
uJy } G ² x3Â0t Y
xLsaxL¯u(x ~ \ ] ¯D
L² À
~
E
Â ]-,JI ~
~ ~²;} E9~0

~
:SKGi^98NAG7>=@]<[C\JFOUAaK(:H=P\LAG=PF0Oj*È^9`>`F]a83=PO£W³:0\LAAG798JKG8b:SKG8
ÃADg#8'
F`F]a]a=@<>?@8:0\JAG^>:0?'`97:0]a8H=@)8LKG8TO>\T8J]£\TFSKaKG8T]a`FO>H9=@O>iRAGF:
i=@Zp8JOmF<9]a8JKGZp8hHX`>7>:0]a8bH9=B)8JKG8JO>\T83WF0K8h:S\L7XKG8T\T8T=@Zp8JKhj ª F0K`:S=BK
»3I)54U¼Ln9\h:0?@?)AG7>8T]a8H=B)8JKG8TO>\J8T]K L/ 0 :0OHMNL/ L0 j%67>8TO5n[AG7>8WF?@?@F+g=@O9i
]a8JAG]F0W"8TÊ[^>:SAG=@FO9]7>F?P5H L/ 0 1 L/ 0 - / 0
\h:0?@?AG7>=@]bAG7>8 uJy `97:S]a8£H=B)8JKG8TO>\J8£<8JAfg8T8JOAG7>8ADg#F
Ã]a=@i08
O:0?@]:0OHH98TO9F0AG8~ =BA<U~C² j
k,8T\h:0^9]a8=BA=@]H9=BN\T^9?BAAGF3\TFSKaKG8T\JAG?BClH98LAG8JKGMN=@O>8AG7>8]A(:+KaAF0W`8Je
KG=@F[H=P\g:hZp8LW_F0KGMN]Tn>g8\h:0OF0O>?BC*F0<9A(:0=@O8T]AG=@Mb:+AG8T]2WF0K:3g:hZp8Je
WF0KGM*· ]#`97:S]a8=PO'AG798K(:0O>i08» )¼WKGF0MIKG8J`8h:SAG8hH'?@FhgevAGF0e7>=@i07
AaK(:SO>]a=BAG=@FO9]NF0WAG7984]a=@iO>:0?³j OW_F0KaAG^9O:+AG8T?BCUn:i=@Zp8TOF<9]a8JKGZp8hH
`97:S]a8H9=B)8JKG8TO9\T8<8JAfg8T8JOADg#F3g:hZp8LW_F0KGMN]Tn#n9\h:SO4\TFSKaKG8T]a`FO>H
AGF*:0Oc=@O9>O>=BAG8'O[^>Mq<8JKFSW:0\JAG^>:0?%`>7:S]a8bH9=B)8JKG8TO9\T8T]Tn":S?@?#]a8T`>:Se
K(:+AG8hH*<UC %j679=@]=@O*AG^9KGO*?@8h:0H9]AGFNM3^>?BAG=@`>?@8`F]a]a=@<9=P?@=BAG=@8T]WF0K
j
O98g:TC4AGFN]aF0?PZ8AG79=@]2`KGF<>?@8TM¾=@]AGFNF<>]a8LKGZp8WKGFMË¶%Ê[^>:SAG=@FO
»®0¼AG7:SAq:S]q?@FO9i:0] >[n #n:0OHAG7>8JKG8N=@]O>F:SM'e
<9=@i^>=BAfCUjÈ=@O9\T8 \ )I/] )#:0O>H8^¢:SKG84AG7KG8T8*]a=PH98J]lFSW:XAaKG=P:SO>i?@8n
^ \ /] Bn:0OHg84\h:0OAG7>8JKG8JWF0KG8`9?:S\T8*AG7>8lKG8Je
8 ^!">0NAGFl^>O>:0M3<9=@i^>F0^>]a?BCH8JAG8JKGMN=@O>8
\J8T=@Zp8JKG]:+A:H=@]A(:0O>\JA
X:0O>HlAG798JKG8JW_FSKG8^>O9=ÊU^98T?BC8J]AG=PMb:+AG8N.» \ /]T¼Lj
:¤p«§¨^9?@AaK(:S]aFO9=P\g:hZp8LW_F0KGM¢:SA#:AG8TMN`8JK(:+AG^9KG8FSW0® B
ª:SOF0K#
H®0$# 7[^9MN=H=BADCUn%>0 ¤;C ¬®MNM*jX679=P]q=@]3]aMb:0?@?@8JKqAG7:0O
AG798q]a=@¨T83F0W,MNF]A:hZ0:0=@?P:0<9?P8q^>?BAaK(:0]aF0O>=@\']a=@iO>:0?KG8T\T8J=PZ8JKG]Tn)g7>=@\L7
:+KG8£AfC9`9=@\h:0?@?BCRFORAG798£FSK(H98JK4F0W3:0<FÂm¥£\TM*&
j Fhg8JKG=@O9iAG798
\T:SKaKG=@8JKWKG8hÊU^>8TO9\JCl=@]2O9F0A2:0OF0`9AG=@FO5n]a=@O>\T8AG79=@]g#F^>?PH4Mb:Sop8=BA
:S^H=P<9?@8,AGF7^9Mb:0O9]Tj 8%AG798JKG8JW_FSKG8#O98T8hH:O9=@\T8#i08TO>8JK(:S?[MN8JAG7>F[H
AGF`>?P:S\T8£KG8T\J8T=@Zp8JKG]AGÃ F^>O>:0Mq<>=@i^9F^>]a?BCH98JAG8JKGMN=@O98AG798£`97:S]a8
H=B)8JKG8TO>\J8j
L/ L0 1 L/ 0L - 2/ 0
O98g:TClF0WA(:S\Lo[?@=@O>iAG7>=@]=P]AGF3\h:SKG8JW^>?@?BC4`9?P:0\T8'y saxGxKG8T\J8T=@Zp8JKG]
:S?@FO>i:?@=PO98n[:S]]a7>FhgO'=@O ª =@i^KG8®[np:0OH^>]a8: t_E sFSWF<9]a8JKGZp8hH
}~
È=@O9\T88h:0\(7*F0<>]a8JKGZp8T
H )\ ]=P]KG8T?P:SAG8THAGF3AG7>8\JF0KaKG8T]a`F0OH9=@O9O
i ?]-,
<UCbAG7>8K(:SAG=@F:^Z]-,4>&^\ ]n9AG798:0<F+Zp88hÊU^:+AG=@FO>]\h:SO*<8KG8JgKG=BAaAG8TO
:0] 1 L]-, - ]-, » ^ ]-, >&^ \ ] ¼J» 1 L\ ] - \ ] ¼
»v¹p¼
¤
1
L]-L , - -] , »^
-, >
] &^ \ ]
¼J»1
L\ L ] - \ ]
¼
»µ¼
B1
B2
B
Y
X
θ
R1
R2
X
θ
Y
Y
W
1(:$6
XN¥
X
q
,
C
! ?)(
,9!#$%&'
X
%.$'O!#9$@>/ L
β
θ
β
[È ^><AaK(:0\JAG=@O>i¶%Ê[^>:SAG=@FO»µ¼2WKGFMÄ¶%ÊU^:+AG=PF0O»v¹¼:0O>HKG8T:SKaK(:0O9i0e
=@O9i9n>g#8i8JA
^\ ]» 1 L]-, 1 L]-L , ¼ ^ ]-,p» 1 L \ ] 1 L \ L ] ¼
»v ¼
58JA^9]8Jd`9KG8T]a] ^ / 0 :S] / 0 >0[n[g7>=@\(748Jd`KG8T]a]a8T]#AG798]a8T`>:SK(:SAG=@F0O
<8LADg8J8TOXKG8J\T8T=@Zp8JKG]:S]:0OX=@O[AG8Ji0K(:0?"Mq^>?BAG=@`>?@8qFSW >0[jq¶%Ê[^>:SAG=@FO
»v ¼=P]AG798TO48hÊU^9=PZ0:0?@8TOUAAGF/
\ ]» 1 L]-, 1 L]-L , ¼ 1]-,p» 1 L\ ] 1 L\ L ] ¼
» ¼
g798JKG88h:S\L7*FSWAG7>
8 / 0 :0O>G
H 1 / 0 :SKG8=@OUAG8Ti8JKG]Tj
X
θ
Y
5 D <B2((:Q/%./;4(:%.$'O!)$G+,(S63L
69SC
'2(I @%&@ ;/ 4 0( 0/(H' ,
L
011'?3$ ')7,?9(/%.')7(>01 @(A'8,
L
011'C
F0AG=@\T8AG7:+D
A 1 / 0 7 n9AG798]a8T`:+K(:SAG=@FO=@OH9=@]A(:SO>\T8<8JAfg8T8TO
GAÇ 798\h:+KaKG=P8LKg:hZp8JW_FSKGMN]:SAKG8T\T8J=PZ8JK 3%:0OHbKG8T\T8T=@Zp8LK 49n:SOH 7
^ / 0 / 0 >0[n>WF0K8h:0\(7`:S=@Kq» 3I)54U¼ »¥)L0¼')h» )G¬¼Lj67>=@]MN8h:0O9]
AG7>:S
A @» 1 L/ 0 1 L/ L0 <¼ V& ^/ 0 / 0:jQ»³fOcW³:S\JAhH
n B» 1 L/ 0 1 L/ 0L <¼ Mb:TC<8x yz4 ^ / 0 n<>^9A"F0O>?BCq=@W>AG7>8<8h:S\TFO3?P=@8T]%FOqAG7>8]G:SMN8
79F0KG=@¨TF0O[A(:S?[`>~?P² :0O98:0]AG7>8%\TFMN`>:0]a]Tj"679=P]]a=@AG^>:SAG=@FOq=@]^>O9?P=@op8J?@C=PO
`K(:0\JAG=@\T80n):0O>H*H98JAG8J\JA(:0<9?P8=BW"=BAHFU8T]FU\T\T^9Khj ¼b67>8JKG8LW_F0KG80n% 1 L/ 0 1 L/ L0 9 / 0 j'67^9]Tn5=@W¶,ÊU^:+AG=@FOQ» ¼2=@]AGF<8']G:+AG=@]8hH)
n \ ]q:0OH
]-, u ~ ¯>¯zSy<8KG8T?P:+AG=PZ8T?BC4`KG=PMN80j
§28TO>\J8n+=BA=@]`F0]a]a=@<>?@8%AGF^9O:0Mq<>=@i^9F^9]a?@CH98LKG=PZ8,:SO:0\JAG^>:0?p`97:S]a8
H=B)8JKG8TO>\J83F» / 0 ¼%=@ONAG7>8K(:0O9i82F0W ) ^ / 0 WKGFM:0OlF<>]a8LKGZp8hHNFO98
» / 0 ¼#<[Cb`9=@\Lo[=@O>Bi ^
\ ]:SOH ^ ]-,AGFq<8KG8T?P:SAG=@Zp8T?BCl`9KG=@MN82=POUAG8TiSK(:0?
Mq^>?BAG=@`>?@8T]FSK
W >Uj ª F0K8Jd9:0MN`9?@8ng#8N\h:0O£`>=@\(9
o ^ \ ] : c:0OH
^Z]-, ¥C ®:jN67[^>]Tn5o[O>Fhg=@O>iGn)g#8'i8JAAG7>838Ld>:S\JA *O>8J8hH98hH
WF0K28T]AG=@Mb:SAG=@O>A
i Wq=@O¶%Ê[^>:SAG=@FOm»³¤U¼Lj
1
4
2
2.2.1 Disambiguating
]a=@O>i¶%Ê[^>:SAG=@FOR»³¤p¼:0OHmAG798'AG8T\(7>O>=PÊU^>8J]qH=@]a\T^>]a]a8hHmAG7[^9]W_:SKhn
8#
g#
\h:SO3H8JAG8JKGMN=@O>8"]a=@O"W<8JADg#8T8TOAG7>8%\TFMN`>:0]a]:SOH:`:SKaAG=@\T^9?P:SK
<8T:0\TF0O Xbj%k#Â2:0] ª =Pi0^9KG8¹3]a79Fhg]Tn=@O*i8JO>8JK(:S?vn9AG7>8JKG8:+KG8ADg#F
?@FU\h:+AG=@FO>
] X \ /n X ] W_FSK:<8h:S\TFI
O X AG7>:SA%KG8T]a^>?BA=@O'AG798]G:SMN"
8 W:+A
AG798\TFMN`>:0]a]Tj67>=@]2=@]2H9^98AGFN]CMNMN8JAaKaCNF0WAG798]C]AG8TM:0<FÂ
AG798N?@=PO98
£j*¸Oc:0O>:0?BC[AG=@\h:0?%g:TCmFSW^>O>H98JKG]A(:SOH=PO9iAG79=P]=@]
AGFF<9]a8JKGZp8AG7:+A#AG7>8LKG82:+KG82AfgFZ:S?P^98T]#FS)
W W=@ONAG7>8K(:0O9i8q )L ¼
WF0K:'i=@Zp8TO*Z0:0?@^98FSW"]a=@O W[j679=P]:0Mq<>=@i^9=@AfCl=PO*AG798?@FU\h:SAG=@FOFSW
AG798<8h:S\TFO`9KG8TZ8TOUAG]#^>],WKGFMH98JAG8LKGMN=PO9=@O>iq:^9O>=PÊU^>8Z:S?P^982WF0K
AG7987>8h:0H9=@O>ij
3
5
;94/%./;4( ' $8%.569$(( &6M1'? <B
#4#/')7)% )0$@N/%./;L 4 0( -<>,1%&, $ )(/7 )'$6-!)(0SN' 3,F,$ 7)1' <A,N/(#@%& $
!#$%.' C
]aF?@Zp8AG7>=@]l<UC^9]a=@O>iy z]a8JAG]FSWO>F0O9e\TF?@?@=@O>8h:+K4KG8T\J8T=@Zp8JKae
ÃAaKG=@8
`9?P8LAG]3AGF<9KG8h:SomAG7>8l]CMN± MN8JAaKaCUj Ã 8b`>?P:S\T8AG798lAfgF]a8JAG]'FSW
®
AG7>8KGFUFM»vH9FhgOUg:+K(H9](¼Ln:S]]a7>FhgOb=@O ª =@i0^9KG8 j,#FO9]a=PH98JKWF^K
<8h:S\TFO9] X n X \ n X ] n:SO8
H X , :SAaA(:S\L798hHAGF£AG7>8*\T8J=P?@=@O>imF0W:
KGFUFM*j¶,:S\L7<8T:0\TF0O X / <KGFp:0H9\h:S]AG]=BAG]2\JFUF0K(H9=@O>:SAG8T]q.» / )IH / )G¼
FO*AG798 ©ª \L7>:0O9O>8T?³ng79=P\(7=@]]a8TO9]a8hH*<UC4AG7>8KG8T\J8T=@Zp8JKG]F0O*AG7>8
\TF0MN`:0]a]TjY¸AlAG798]G:0MN8*AG=@MN8n=BA:0?@]aF<9KGF:H9\T:0]AG]:0OR^>?BAaK(:+e
]aFO9=@\`9^>?@]a8j¸ KG8T\T8T=@Zp8LKhng7>=@\(7*=@]:+A:SO*^>O9oO9FhgO4\TFUFSK(H9=@O:+AG8
.» n Hn U¼LnMN8h:S]a^9KG8T]AG7>8AG=@MN8H9=B)8JKG8TO9\T8 /,<8JAfg8T8JOAG798:SKaKG=@Z:S?
F0W5AG7>8J]a82ADg#Fq]a=@i0O:0?@]AGF<8h:0\JFO X / j%67>8:0\JAG^>:0?)H9=@]A(:SO>\T8WKGFM
AG7>8'KG8J\T8T=@Zp8JKAGF X /2=@]AG7>8JKG8JWF0KG8b8hÊU^:S?%AGF /ng7>8LKG8 X=@]AG7>8
»³^>O9o[O>FhgO¼,]a`8J8hH4F0W]aF^>O>H5j
y
B
Beacons on
ceiling
(xi, yi, 0)
z
x
\h:SObAG798TO'gKG=BAG82AG798WF?@?@F+g=@O9iqW³:SMN=@?@C'F0W5W_F^K8hÊU^>:SAG=@FO9]#W_FSK
ÃAG7>8
8b^9O>o[O>FhgO>]b».G)JH%)J;) ¼Lj © 8T\h:S?P?,AG7:SAg8:SKG8b=@OUAG8JKG8T]AG8hH=@O
AG7>8Z:S?P^98F0
W > > ] - H ] - ] j
(x, y, z)
Compass
coordinates
5 D , %.547)1'$@ (S?(@6
)(/7 1' E41%4G
,P!#$%&')(F$ N%&'?U ?4/7 <>, ,/ .
% 547)'$ /(
$ ')7-7)1((@6M1'?$ B,)1( 1' &69$ '9' ,? :
%4,$''/0 C
>
/ ¼ ] - .» H H / ¼ ] - ] ».
] /] )m.7637Q¬
»¥h¼
8J?P=@MN=@O:+AG0
8 ] WKGFM AG7>8T]a848hÊU^:SAG=@F0O>]b<UC]a^><9AaK(:S\JAG=@O>i
Ã8h:S\L847'\h8T:0Ê[O
^>:SAG=@FO'WKGFM½AG7>8#`9KG8TZ[=@F^9],F0O>8n0AGFF<9A(:S=@O3AG7>8WF?@?@F+g=@O9i
AG79KG8J8 t_¯)x s,8hÊU^:+AG=PF0O>]=@O4AG7>82AG79KG8T8Z0:SKG=P:0<9?@8T]Tn )IHl:0OH ] ² ~
H ]
KG8J\T8T=@Zp8JKaevAaKG=@`>?@8JAG]`8JKG`8TO>H9=@\T^9?:+KAGFQ8h:S\L7 F0AG798JKX:0]]a7>FhgO =PO
=@i0^9KG8£µ[n:SOHAG798JKG8*\h:SO<8O>Fhg<8FO9?@CFO98`F]a=BAG=@FOWF0K
AGª 798<8h:S\TFO XNj Ã 8:+KG8O>Fhg;i=@Zp8TO4:0O:SO>i0?P8 W \ KG8T?P:+AG=PZ8AGF 4e
:0OBH W4]%KG8T?P:SAG=@Zp8AGF e n0g79=@\L7qMN8h:0O9]AG7:SA]a=P"O W \%:0O>H]a=@"O W4]
:+KG8o[O>FhgOjfA=@]8h:S]CbAGFq]a8T8AG7:+AAG7>8JKG82\h:0OlFO9?BCb<8:^>O>=PÊU^>8
]aF0?@^9AG=@FO3WF0KAG79=P]\JFO9>i^K(:SAG=@FO5j"67>8T]a8,ADgF2`8JKG`8TO>H9=@\T^>?P:+K]a8JAG]
FSWKG8T\T8J=PZ8JKaevAaKG=P`9?@8JAG]:SKG8\JFO9>i^KG8hH^9]a=PO9i B0x,KG8T\T8T=@Zp8JKG]F0OAG798
Á
\JFMN`:S]a]Tn:S]2]a79FhgO*=@O ª =@i^KG8q [j
g7>8LKG8AG7>8Mb:+AaKG=@d
2.3
Determining Compass Coordinates
fONAG7>8`KG8TZ[=@F^>]#H9=@]a\T^9]a]a=PF0Og#8:0]a]a^9MN8hH'AG7:+A#AG7>8KG8T\T8T=@Zp8LK\h:0O
H8JAG8JKGMN=@O>8AG7>8K(:SAG=@F4FSW7>8J=Pi07UAAGF4H=P]A(:SO>\T80n ?> n5AGF4:`>:SKaAG=@\Je
^9?P:SK<8T:0\TF0Oj6Fb8TO>:0<9?P8AG798KG8T\T8T=@Zp8JK2AGFNip:+AG7>8JKAG7>=@]=POW_FSKGMb:Se
AG=@F0Ong8=@MN`>?@8TMN8TOUA2:N\TFUF0K(H=@O:SAG8q]C]AG8TMË^9]a=@O>il:NO^9M3<8JKFSW
:S\JAG=@Zp8<8h:S\TFO9]=@O>]AaKG^9MN8TOUAG8hHcg=BAG7o[O>FhgO`F]a=BAG=@FO9]lg=BAG79=PO
AG798]a`:S\T8j 67>8\TF0MN`:S]a]H8JAG8JKGMN=@O>8J]N=@AG]bMN8h:SOQ`F0]a=@AG=@F0O:0]
:SO.» n H)n U¼#AG^9`>?@8<[C4?@=P]AG8JO>=@O>iNAGFb<8h:0\JFOAaK(:0O9]aMN=P]a]a=@F0O>]Tj267>=@]
MN8J\L7>:0O>=@]aMV:S?@]aF'8TO:S<>?@8T]^>]AGF3H98JAG8LKGMN=PO982AG798]a`8T8hHlF0W]aF0^>OH
=@O4AG798Z[=@\T=@O>=BADClF0WAG798\TF0MN`:0]a]Tj
».?\
.» ]
.» ,
]
=P]i=@Zp8JO4<UC
¼
\(¼
]
¼
]\ ] -- H \]] H ]]
]] ]\ - H ]] H \]
, ] H , H ]
]
[».H@\
[.» HV]
[.» H ,
]]\
» ]
» ,]
H
H
¼
H@\L¼
]
»¥¥h¼
]\ ¼¼
]] ¼ ]
»
¼
fW5AG7>8H98JAG8LKGMN=PO>:0OUAFSW =@]O>F0O9e¨T8JKGFnAG798TO¶,ÊU^:+AG=@FOX»] ¥¥+¼%\h:0O
<8]aF?@Zp8hHlAGFbH98JAG8JKGMN=@O98^>O>=PÊU^>8Z:S?P^98T]W_F0K G)IH)>:0O>H
jÈ[^><9e
]AG=BAG^9AG] =@O>iAG7>8J]a82Z0:0?@^>8J]#=@OUAGFq¶%ÊU^:+AG=PF0O£»¥Tp¼AG7>8TONC=@8T?PH9]:Z0:0?@^>8
W_FS+
K ng7>F]a8`F]a=BAG=@Zp8]GÊU^:SKG8KGFUFSA#C=@8T?PH9
] j ^9KaAG798JKGMNF0KG80ng8
\h:SOX^9]a8AG7>=@]8T]AG=@Mb:+AG8FSW nAGFNW_^9KaAG798JK2=PMN`KGF+ª Zp8AG7>8:0\J\T^9K(:S\JC
F0W%AG7>8 /] \8J]AG=PMb:+AG=@FOX<[C4^>]a=@O>il:N<8JAaAG8JK8T]AG=@Mb:SAG8F0W%AG7>8
g:hZp8J?P8JO>i0AG74F0WAG798^>?BAaK(:0]aF0O>=@\\h:SKaKG=@8JKhj
k F0AG7AG798*k:+Al:0O>HAG798,KG=@\Lo8JAb]C]AG8TMN]'^>]a84:£\TF0M3<9=PO>:SAG=@FO
,
FSW ©2ª :0O>H^9?BAaK(:0]aF^9OH]a=Pi0O:S?P]'AGF£MN8h:0]a^KG8*H=P]A(:SO>\T8J]Tn^>]a=@O9i
AG798KG8J?:+AG=@Zp8']a`8T8hH]<8JAfg8T8JOXAG798T]a8AfgFl]a=@iO:S?@]Tjq§2Fhg8TZp8LKhn5AGF
H8JAG8JKGMN=@O>8NAG798H=@]A(:0O>\J8:S\T\T^K(:SAG8T?BCUn%=BA3=@]3O98T\T8T]a]G:+KaCcAGFo[O>Fhg
AG798N]a`8T8hH]FSW<F0AG7£]a=Pi0O:S?P]Tj*67>8N]a`8T8THmF0W ©2ª =@]q8T]a]a8JO[AG=P:S?P?BC
=@OO>=BAG8=@O*F0^9K]a8JAaAG=@O>in<>ÂAG7>8]a`8T8TH4F0W"^9?@AaK(:S]aF^9OH*H8T`8TOH]
F0O'8TO[Z[=BKGFO>MN8JO[A(:S?pW³:S\JAGF0KG]%]a^>\(7':S]"AG8JMN`8JK(:SAG^KG8:0O>Hq7[^>MN=PH9=BAfCUj
6798k:+A]C]AG8TM\TF0MN`8TO>]G:+AG8T]WF0KAG7>=@]Z0:SKG=P:+AG=PF0O3<UCMN8h:S]a^9KG=@O>i
8JOZ[=BKGFO9MN8TOUA(:0?[W³:S\JAGF0KG]Tj,67>82,KG=@\(op8JA,]C9]AG8JME=@]"KGF<9^>]A#:0ip:S=@O>]A
]a^9\L7£Z:+KG=P:SAG=@FO£<[CZ[=BKaAG^>8qF0W=BAG]H8T`8TOH8TO>\J83FO9?BCFO£KG8J?:+AG=@Zp8
H=@]A(:0O>\J8T]Tj
§ Fhg#8TZp8JKhn)AG7>83:0<9=P?@=BADCAGFH98JAG8LKGMN=PO98n Hn 9n:0O>H ] ^>O>=PÊU^>8J?@C
WKGF0M :0<F+Zp8N]a8JAqF0W8hÊU^>:SAG=@FO9]qH8T`8TO>H9]FOmAG798NZ:S?@^>8T]b».N/ )$H$/f¼
W_FSK2D
763 7¬j#È`8J\T=B\h:S?P?BCUnFO98\h:SO]a79F+gAG7>:SA=BWAG798<8h:S\TFO9]
X n X \ n X ] n:SO9
H X , :SKG8N`9?P:0\T8hHX]a^>\(7£AG7>:SAAG7>8LCXH9F*O9F0A:0?@?%?@=P8
FOAG798]G:SMN8]AaK(:S=Pi07UA'?@=@O>84FSK'\T=BKG\T?@8n%AG7>8JOAG798JKG8l=P]3:0?Bg:TC]N:
^>O9=PÊ[^983]aF0?PÂG=@FOmAGFlAG7>8':S<F+Zp8']a8JAFSW8hÊU^:+AG=@FO>]Tj3DO£`9K(:0\LAG=P\J8n
AG7>=@]`9?P:0\T8TMN8JO[A\h:0OX<8'HFO9838h:S]a=P?BCX<UC`>?P:S\T=@O>i4¤l<8h:S\TFO9]FO
AG7>8l\TFSKGO>8JKG]qF0W:KG8J\JA(:0O9i?@8*:SOHcAG7>8TO<UCmMNFSZ[=@O>iF0O>8lF0WAG7>8
<8h:S\TFO9]]aFMN8qH9=@]A(:0O9\T8':S?PF0O>ilAG7>8qH9=P:0i0FO:S?"F0W#AG798KG8J\JA(:0O9i?@8j
¸2Ol8Jd9:0MN`9?@8`>?P:S\T8TMN8TOUAFSWAG7>8<8h:0\TF0O>]=@]]a7>FhgO4=@O ª =@i^9KG8 [j
È^9`8JKa\J=:S?@?@CUnAG7988hÊU^:SAG=@F0O>]:S<F+Zp83:+KG83]a=@MN=@?P:SKAGFbAG7>F0]a8q^9]a8hH
<UC Q,ÈKG8T\T8T=@Zp8LKG]AGFH98JAG8LKGMN=PO98KG8T\T8T=@Zp8LK`F]a=BAG=@FO5jfO Q#ÈnTAG7>8
<8h:S\TFO9],:+KG8]G:SAG8T?@?@=BAG8T]"g=@AG73`9KG8T\T=@]a8\T?@FU\(o[] U?P:SAG8TO9\JCWKGFM½]G:+AG8T?Be
?@=BAG8AGF3KG8T\T8T=@Zp8LK2=@]O>F0O9eO>8Ti0?@=Pi0=@<>?@8 >AG798`9KGF0`:Sip:SAG=@F0OZp8T?@FU\T=BADC=@]
o[O>FhgOX»_AGF9KG]AF0K(H8JKL¼#:0]AG798]a`8T8THlFSW?@=@i7UA 9:0OHl:q]C]AG8TM¢F0W
8hÊU^:+AG=@FO>]=@]]aF0?PZ8hHm:+AAG7>8qKG8J\T8T=@Zp8JKAGFlKG8T\TF+Zp8JKAG7983KG8T\T8J=PZ8JKh· ]
:0<9]aF?@^9AG8£`F]a=BAG=@FO:0OHAG=@MN8B¥+®+vjDOR\JFOUAaK(:0]Ahn=@O ,KG=@\Lo8JAhn
`9KGF0`:Sip:SAG=@F0OAG=@MN8£»_WF0K ©2ª ¼=@]'O98Ti?@=@i=@<>?@8 AG7984<8h:S\TFO9]'7:hZp8
O>F\J?PFU\(o[] 9:0OH3AG798`9KGF0`:0i:SAG=@FOl]a`8T8hH*»_WF0K#^>?BAaK(:0]aF0^>OH>¼"=@],^>O9e
o[O>FhgOj ^K]C]AG8TM:S?P]aFl]aF?@Zp8J]2W_FSKWF^9K^>O9oO9FhgO>]Tn>AG7KG8T8F0W
`F]a=BAG=@FOb:SOHFO>8WF0K"AG7>8]a`8J8hHqFSW)]aF^>O>Hq=@O3AG798?@FU\h:0?9MN8hH9=@^>M*j
]a8JO[A,:AG8T\(7>O9=PÊ[^98#AG7:+A%8TO:S<>?@8T]%^>]AGFH98LAG8JKGMN=@O>8#AG798`F0e
Ã]a=BAG8=@F`9OKG8T=@O4
AG8LKGMN]FSW».n Hn p¼#\TFUF0K(H=PO>:SAG8T]2^>]a=@O>i3¤N<8h:0\TF0O>]g=BAG79e
F0^9Ao[O9F+g?@8hHi8FSWAG798]a`8T8hHbF0W]aF^9OHbF0KKG8hÊU^9=@KG=@O9i3:0H>H9=BAG=@FO>:0?
8JOZ[=BKGFO9MN8TOUA(:0?,]a8TO>]aFSKG]Tj Ã 8l^>]a8bAG7>8bMN8h:S]a^9KG8hH`9KGF0`:Sip:SAG=@F0O
AG=@MN8 /,AGFl8h:S\L7<8h:S\TFO5n5g
79=@\L7=@] sz z0s(y³tvz0¯ AGFNAG7>8q:0\JAG^>:0?
} }
~0²
H=@]A(:0O>\J
8 /j
8=@MN`>?@8TMN8JO[A#:\TFUF0K(H=PO>:SAG8]C]AG8TMIg=BAG7>=@ObAG7>82KGFUF0MV:0]a]a^9M'e
Ã=@O9i
AG7>8\J8T=@?P=@O9iAGF<8#AG7>8+9e H`9?P:0O>8:0OH2AGF<8`F0]a=@AG=@Zp8=@O9]a=H8
¹
3.8,7>:hImplementation
=@MN`9?P8JMN8TOUAG8hH`9KGFSAGF0AfC9`8J]F0WAG7>8%<8h:S\TFOq:0O>H\JFMN`:S]a]
Ã7>:SK(H[gZp:S8,
KG8H8T]a\JKG=@<8hHl=PO4È8J\JAG=@FOUj,¶,:S\L7<8h:0\TF0O4=@]\TF0O9i0^9KG8hH
g=BAG7N=BAG]"`F]a=BAG=@FON=@ON:\JFUF0K(H9=@O>:SAG8]C]AG8TM*ng79=P\(7'=BA%<9KGF:H9\T:0]AG]
F0Om:b¤9¥T 4¦4§2¨ ©2ª \(7:SO>O>8J?vj#FO>\J^9KaKG8TOUAg=BAG7X8h:0\(7X`8JKG=@F[H9=@\
]a8TO>H9]#:3®S5]^9?BAaK(:0]aFO9=@\`>^9?P]a8:SA¤«§2¨n
©279ª =@\L<73KGFp:S:KGH8\hKG:08T]\TAh8Jn=PZ=BA
g
8hH3:+AAG7>8#\JFMN`:S]a]^>?BAaK(:0]aF0O>=@\KG8T\T8J=PZ8JKG]Tj%¶,:S\L7
<8T:0\TF0O:0OHc\JFMN`:S]a]7:0]q:0OF0O9e<Fp:+K(2
H %IMN=@\JKGFU\JFOUAaKGF?@?@8JK
AG7>:SA=@MN`>?@8TMN8JO[AG]%AG7>82\TFMNMq^>O>=@\h:+AG=@FOb`9KGFSAGFU\TF?:0O>Hl`KGFU\T8T]a]a8T]
=@OW_F0KGMb:+AG=@FOj,6798KG8T]AF0W5AG7>=@]#]a8T\LAG=PF0O4H8T]a\JKG=@<8T]#AG798H8JA(:0=@?@]FSW
AG798\TF0MNM3^>O9=@\h:SAG=@FOl`9KGFSAGFU\TF?5<8JAfg8T8TOlAG7>82<8h:0\TF0O>]:0O>H\TF0M'e
`>:0]a]Tn:SOH79FhgVAG7>8*\TF0MN`:S]a]l`KGFU\T8T]a]a8T]NAG798*F<9]a8JKGZp8hHH9=B)8JKae
8JO[AG=P:S?H9=@]A(:SO>\T88T]AG=@Mb:SAG8J]bAGFcH98hH^>\T8*AG798:0\JAG^>:0?H9=B)8JKG8TOUAG=P:0?
H=@]A(:0O>\J8T]Tj
Mapping From Observed Differential Distance to Actual Differential Distance
Observed Differential Distance (Unit: 1 wavelength)
1
0.8
0.6
0.4
0.2
0
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Actual Differential Distance Between Receivers 1-2 (Unit: 1 wavelength)
Observed Distance 2-3
Actual Distance 1-2
Observable Distance 1-2
Observable Distance 2-3
Observed Distance 1-2
:
N ?8"')7)1'P, $ %.$ 0*7) /' $0*71($'%.
[ \
[Q]
!# <@'
$')7
!S )(1':,?*! (;/7-7) Z//'5$0
»
[\ [Q]h¼
» [Q] [ +¼ C
7)1(R$')%./(A 56
$ ')7
3.1
Protocol Details
6798q<8T:0\TF0O>]=@OX,KG=@\(op8JAF0`8JK(:SAG8=@O:0OX:0ÂGFO9FMNF^9]2Mb:SO>O98JKhn
g=BAG79F^9A':0OUCc\J8TOUAaK(:0?@=@¨T8hH\TFOUAaKGF0?F0Wg7>8JOAG798JCXAaK(:0O>]aMN=BAq=@O9e
WF0KGMb:+AG=PF0O SSvjX6F*KG8hH^>\T8N=@OUAG8JKae<8h:S\TFO=@OUAG8JKaW_8LKG8TO>\T8l:+AqAG798
KG8J\T8T=@Zp8JKG]Tn#8h:0\(7<8h:0\TF0O]a8JO>]a8T]'AG798 ©2ª \h:+KaKG=@8JKb<8JW_FSKG8AaK(:SO>]e
MN=BAaAG=@O>il:b?@FU\h:0?@?BCX^>O>=PÊU^>8DºE:SOH=@AG]oO9FhgOX`F0]a=BAG=PF0O£\JFUF0K(H9=Be
O>:SAG8T]TjDOX:H9H9=BAG=@FO5n)8h:0\(7]a^><>]a8TÊ[^98TOUA2AaK(:SO>]aMN=@]a]a=@FO=@]]a8TOUA:+A
:N^9O>=BW_FSKGMN?@C\(7>F]a8JO*K(:0OHFMVAG=@MN8:SWAG8LKAG7>8`KG8TZ[=@F^>]2FO98jDO
F0^9Kb=@MN`>?@8TMN8JO[A(:+AG=@FOn%AG7>84:hZp8JK(:0i08:0MNF0^>OUA'FSWAG=@MN84<8JAfg8T8TO
]a^9\T\T8T]a]a=@Zp8AaK(:0O>]aMN=@]a]a=@FO9]N=@]b®SmMN]Tj67>8`:S\Lop8LA'W_FSKGMb:SANFSW
AG798<8h:0\TF0Ob=PO9\T?@^H8T],=@OW_F0KGMb:+AG=@FOl:0<F0^9A%AG7>8i8TF0i0K(:S`>7>=@\]a`:S\T8
»³80j ij@n5:0O*=@OUAG8TOUAG=@FO:S?O>:0MN8W_FSK2KG8J]aF^9KG\J83H=P]a\JFSZ8JKaC4=@O ÈXB¥Ln
: © :0]=@O£#FUF?P6FhgO +n58JAG\0j ¼Lj¶,:S\L7X`:S\Lop8LA=@]`9KGFSÇ AG8T\JAG8hH
^9]a=@O>i:<>?@FU\(o[e`>:SKG=BADC\TF[H980jI67>8\TF0MN`:0]a]H98LAG8T\JAG]l\TF?@?@=@]a=PF0O
F0OcAG7>8 ©2ª \L7>:0O>O98T?:SOHcH=@]a\h:SK(H]q]G:SMN`>?@8T]AG7:SAqHFO>F0A`>:0]a]
:*<9?@FU\LoUe`:+KG=@AfCX\L798T\Long7>=@\L7m7>8T?@`>]=BAqH9=@]G:0Mq<>=@i^>:SAG8N<8JAfg8T8TO
`FSAG8TOUAG=P:0?@?BC4=@OUAG8JKG?@8h:hZp8hH ©ª ^>?BAaK(:0]aF0^>OH\TFMq<>=@O:+AG=PF0O>]]a8TOUAFSW
]a8J`:SK(:+AG8<8h:0\TF0O>]Tj
)
4) ,
:
3.2 Differential Distance Estimation Algorithm
DObF0^9K`KGF0AGF0AfC`8nUAG7>82^>?BAaK(:0]aF0O>=@\KG8T\T8J=PZ8JKG]:SKG8]a8JA^>`l:S\T\TF0K(H[e
=@O>ilAGF ª =@i^9KG8' ng798JKG:
8 ^\ ] ^\ : n:SOM
H ^Z]-, ^
¥ C :® j;¸2OQ=@OUAG8JKG8T]AG=@O9i:0]a`8T\LAFSWF^Kb=@MN`>?@8TMN8TOUA(:SAG=@F0O=@]NAG7>8
MN8JAG79F[H3^>]a8hHAGFH98JAG8JKGMN=@O98AG7>8^>O9=PÊ[^98:0\JAG^>:0?>H9=B)8JKG8TOUAG=P:0?H=@]e
A(:0O9\T83WKGFMÆAG7983F<9]a8JKGZp8hHXH9=B)8JKG8JO[AG=P:S?"H9=@]A(:0O9\T8j367>8'MN8JAG79F[H
^>]a8J]AG798l=@OUAG^>=BAG=@FOcH98TZp8J?PF0`8hHc=@OÈ8J\JAG=@FO[j Un%g798JKG8l:0O½f8Jd[e
=@]AG8TO>\J8T4:+KGi^9MN8TOUA2g:0]Mb:0H98W_FSK7>FhgYAGFb\TF0O9i0^9KG8KG8T\T8T=@Zp8LKG]
AGF^>O>:0M3<9=@i^>F0^>]a?BCXKG8T]aF?@Zp8lAG7>8l:0\JAG^>:0?`97:S]a84H=@)8LKG8TO>\T80jm¸?Be
AG7>F0^>i07lAG798:SKGi0^>MN8TOUAg:0]Mb:H82=@OlAG7>84f`>7>:0]a8HFMb:0=@O5n AG7>8
KG8T]a^9?@AG]"79F?PH38hÊU^>=@Z0:0?@8TOUAG?BC=@OqAG7>8Ng:hZp8T?@8TO9i0AG7NHFMb:S=PO5n g7>8JKG8
AG7>8#MN8h:0]a^KG8hHZ0:0?@^98T]":SKG8AG798H9=B)8JKG8TOUAG=P:0?H=P]A(:SO>\T8J]%=@OAG8JKGMN]F0W
j"§Fhg#8TZp8JKhnpAG798:+KGi^9MN8TOUA#=@OÈ8T\LAG=PF0O[j =@]#O9F0A#`9KG8T]a\JKG=@ÀG=PZ8n
]aF3g#8F^9AG?@=@O>8F0^9K=@MN`>?@8TMN8TOUAG8hHl:0?@i0F0KG=BAG7>M¾<8T?@Fhgj
#FO9]a=PH98JK =@i^KG8£¥Tn%g7>=@\L7`>?@FSAG]3AG7>8lZ:+KG=P:SAG=@FOF0WF<>]a8LKGZp8hH
9H =B)8JKG8JO[AG=P:Sª ?,H=B)8JKG8TO>\J8 L :S]:lW^>O>\LAG=PF0O£FSW#AG798':0\LAG^:0?%H=@)8LKae
8TOUAG=P:0?H9=B)8JKG8JO>\T8 £W_F0KNAfgFX`:S=@KG]3F0WKG8J\T8T=@Zp8JKG]Tj O>8lF0W2AG7>8
\T^KGZp8T]»_AG7982]aF0?@=Hb?@=@O>8]a8JiMN8TOUAG](¼%]a79Fhg]#AG7>8 JL \ ] Z:+KG=P:SAG=@FObW_FSK
AG7>8,KG8T\T8T=@Zp8JK%`>:0=BK» [\ ) [ ]h¼Ln0g79=P\(7N:+KG8]a8T`:+K(:S AG8hH'<UC:H=P]A(:SO>\T8
^ \ ] $
j67>8FSAG7>8JK"\J^9KGZp8»_AG7>8#H>:0]a798hHq?@=@O>8#]a8TiMN8TOUAG](¼]a79Fhg]
AG7>8#Z:+KG=:+AG=@FO L]-, W_FSK"AG7>8,KG8J\T8T=@Zp8JK%`:S=BK» [Q] ) [ ,h¼]a8T`:+K(:SAG8hHq<[C
^ ]-, ¥ C :® j 8O>FSKGMb:0?@=@¨T8hH3AG7>8\T^KGZp8T]"AGF]a7>FhgQAG798F<>]a8LKGZp8hH
Z0:SKG=P:SAG=@FO9]F0W Ã JL \ ] :SOH JL]-, :S]:lW_^9O>\JAG=@F0OmF0W \ ] =³j 80jPn JL \ ]
Z0:SKG=@8T]=@O4AG7>8K(:SO>i08N ) 9:S] \ ] Z0:SKG=@8T]=@Om $ )L: 9j
6 798'`9KGFU\J8T]a]a=@O>iF0W#^>?BAaK(:0]aF0O>=@\N]a=@iO>:0?@]q=@]MNFSKG83=@O[ZpF?@Zp8hH)jN6798
\JFMN`:S]a]7:SK(H[g:+KG8H9FU8T]X:SO:0?@F0i0evAGF0efH9=@i0=@A(:S?'F+Zp8JKG]G:SMN`>?@=@O>iAGF
H8JAG8T\JA?PFhgevAGF0e79=Pi07AaK(:SO>]a=BAG=@FO>]WKGFM 8T:0\(74^>?BAaK(:S]aFO>=@\KG8J\T8T=@Zp8JKhj
fON:H9H9=BAG=@FO3AGF`KGFU\T8T]a]a=@O>i ©2ª =@O9W_FSKGMb:SAG=@FO5npAG7>8F0O9e<Fp:+K(A
H "a
MN=@\JKGFU\JFOUAaKGF?@?@8JK7>:0OH?@8T]lAG798^>?BAaK(:0]aF0O>=@\m]a=@iO>:0?@]KG8J\T8T=@Zp8hHR<UC
AG798]a8TZp8JK(:S?^>?BAaK(:0]aF0O>=@\KG8T\T8T=@Zp8JKG]lFORAG798\TFMN`>:0]a]bAGFF0<9A(:S=PO
`97:S]a8H9=B)8JKG8TO9\T88T]AG=@Mb:SAG8J]Tn:SOHb`:0]a]a8J]AG798T]a8AGFqAG798]aF0WADg:SKG8
KG^9O>O9=PO9i3F0O4AG7>8:+AaA(:0\(7>8hH4H98TZ[=@\T8j
679=@]]aF0WAfg:+KG8c`9KGFU\T8J]a]a8T]AG7>8K(:hg H9:SA(:AGFF0<9A(:S=PO;F<9]a8JKGZp8hH
H=B)8JKG8TOUAG=P:0?H9=@]A(:SO>\T8X8T]AG=@Mb:SAG8T]Tn:0O>HRAG798TOR\TF0OZ8JKaA4AG798TM AGF
:S\JAG^:S?bH9=B)8JKG8TOUAG=P:0?bH=@]A(:0O>\J8Q8T]AG=@Mb:SAG8J]Tj fAc:0?@]aF=@O9W8JKG]mAG798
\JFUF0K(H9=@O>:SAG8T]%F0WAG798#\TF0MN`:S]a]KG8T?P:SAG=@Zp8AGF2AG798\TFUFSK(H9=@O:+AG8]C9]AG8JM
H8JO98hH<UCAG7>8<8h:0\TF0O>]Tn:0O>HX\TF0MN`>ÂG8T]2AG7983F0KG=@8TOUA(:+AG=PF0Om^9O>=BA
Z8T\JAGF0Kl=@OQAG7>:SAl]C]AG8TM*jfAl\h:S?P\J^>?P:SAG8T]lAG7>8:SO>i0?P8KG8T?P:+AG=PZ8AGF
8T:0\(7<8T:0\TF0O¾:0OH ^9]a8T]AG798]aMb:0?@?@8T]AR:SO>i?@8AGFIH98JKG=@Zp8RAG798
FSKG=@8TOUA(:SAG=@FOZp8T\JAGFSKhj67>8lKG8h:0]aF0OW_FSK'AG7>=@]3g=@?@?<8\J?P8T:SKNWKGF0M
È[8T\JAG=@FO ¤9ng79=P\(7;]a7>Fhg]AG7:SA4AG7>8c:S\T\T^K(:0\JC;F0W3F^K]C9]AG8JM
g#F0KG]a8TO9]X:SA?P:SKGi08:0O9i?@8T]»³i0KG8T:SAG8JKAG7>:0O :0<FÂ¤U®H98TiSKG8T8T](¼Lj
679=@]3:S?P]aFMN8h:SO>]AG7:+AAG7>8N]C]AG8TMgFSKGo[]q<8T]Ag798TOc=BAq>OH]
:+A?P8T:0]AqFO>8N<8T:0\TF0O:SAq:0Oc:0O>i0?@8l]aMb:S?@?P8LKAG7>:0Oc¤p®4H98Ji0KG8T8T]
]a=@O9\T8AG798JKG8:SKG8:SAm?@8h:0]A£W_F^Km<8T:0\TF0O>]m`8LKm]a`>:0\T8FO½8h:S\L7
\J8T=@?P=@O9i£FSW2=@OUAG8JKG8T]Ahn"=BAq=@]qKG8T?P:SAG=@Zp8J?@Cm]AaK(:0=@i7UAaWF0Kag:+K(HAGF`9?:S\T8n
:SOHq>OH)n:+A%?P8T:0]A,FO>8<8T:0\TF0O'=@O3]A(:0O>H>:+K(HqKG8T\JA(:SO>i^9?P:SK"KGFUFMN]Tj
µ
¶%:0\(7\J^9KGZp8l=@]'`8JKG=@F[H9=@\g=BAG7H9=@]a\TF0OUAG=PO[^9=@AG=@8T]Tj67>8lF<>]a8LKGZp8hH
Z0:0?@^>8 L Z:+KG=P8J]=POlAG7>8K(:SO>i08N ) 95<8T\h:S^>]a8AG7:+A=@]AG7>8K(:SO>i8
F0WbMN8T:0]a^9K(:S<>?@8H=P]A(:SO>\T8<8LADg8J8TOADg#FY»_AG=@MN8Je]a7>=BWAG8TH¼g:hZp8Le
W_FSKGMN]3g7>F0]a8*]A(:SKaAG=@O9i£AG=@MN8T]':+KG8*O>FSA'o[O>FhgO5j67>8*H=@]a\TFOUAG=Be
O[^>=BAG=@8T]':+KG84H^>8bAGFAG7>8NW³:S\JA'AG7:+AqAG798F0<>]a8JKGZ0:0<9?@84H=@)8LKG8TOUAG=:S?
H9=@]A(:SO>\T8T]qW_F?@?@Fhg¾AG7>8l`8JKG=@F[H9=@\T=BADCFSW2AG798F0<>]a8JKGZp8TH`97:S]a8*H9=BWe
W_8LKG8TO>\T8J]Tj#6798:0\JAG^>:0?H9=B)8JKG8TOUAG=P:0?5H=P]A(:SO>\T8J]Z0:SKaCb=@OlAG7>8K(:SO>i8
^
\ ] ) ^\ ]LW_FSK \ ]0n:SOH=POAG7>8K(:0O9i84 ^Z]-,) ^ ]-,J"WF0K /]-,0j
k#Â<8T\h:S^>]a8g#87:hZp82O>FSKGMb:0?@=@¨T8hHNAG7>8\J^9KGZp8T]#:0]:W_^>O9\JAG=@FOlF0W
`:S\=BK]0n» AG[ 7>] 8N) [ F0<>, ]a¼q8JKG]aZp7>8TFhHmgO`>7>=P:0O ]a8b=@H9i=B^)KG8J8mKG8J¥hO[£AG=P:S:0?#?@]a\TFc^KGZ0Zp:S83KG=@8TW_FS]NKq=@OAG79AG8'79KG88T\TK(8T:S=@O>Zpi8L8K
^ ]-, ^
\ ]4>&^Z]-,) ^Z]-, ^\ ª ] >4^ ]-,J ^
\ ]) ^\ ]L2=POAG7>8*`9?PFSAhj
67>8b]a?@F1 `8bFSW8h:0\(7c?@=@O>18b]a8TiMN8JO[A=@]`9KGF0`F0KaAG=@FO>:0?#AGF4AG798NO>FSKae
Mb:0?@=@¨T8hH]a8T`>:SK(:+AG=PF0O3H=@]A(:0O>\J8,W_FSKAG7:+A`>:0=BKFSW9KG8T\J8T=@Zp8JKG]Tj§28TO>\T80n
AG7>8O9F0KGMb:0?@=@¨T8hHN\T^KGZp8W_FSK» [ \ ) [ ] ¼7:S]:]a?@F`82F0W"¥nUg79=P?@8AG7>8
\J^9KGZp8WF0Kq» [Q]
) [ ,+¼7:S]2:q]a?PF0`8F0W ^Z]-,4>&^\ ] ¬ >S¤9j
K(:SO>i08'F0W#F<>]a8LKGZ:S<>?@8'H=@)8LKG8TOUAG=:S?%H9=@]A(:0O9\T8T]=@]
© 8T) \h9:S?@j ?"AGKG7>F:SM AAG79=@8
i
9
^
KG8¥h[nSg#8#]a8T8%AG7:+A:0OUCF0<>]a8JKGZ8hHZ:S?P^98%g=BAG79=PO
AG79=@]K(:Sª O>i8\h:Sª O<8Mb:0`9`8hHlAGF'WF^9K2`F]a]a=@<9?P8]aF0?PÂG=@FO>]W_FSK2AG798
:S\JAG^:S? \ ] j 8JA ! & <8'AG798']a8JAF0W`F0]a]a=P<9?@8l]aF0?@^9AG=@FO9]qH8Je
KG=@Zp8THXWKGF0MAG7>8qF<>]a8LKGZp8hH£Z0:0?@^98 L \ ] j 2K(:0`97>=@\h:S?P?BCUnAG7>8T]a8N:+KG8
AG7982Z0:0?@^98T]FONAG798279F0KG=@¨TFOUA(:S?):Sd=@]8Jd[AaK(:0`F0?:+AG8hHNWKGFMEAG7>8W_F0^9K
=@OUAG8JKG]a8T\LAG=PF0O>]<8JAfg8T8JOXAG79
8 H JL \ ] ?@=@O>8N:SOHAG7>8F<>]a8LKGZ:S<>?@8
H=B)8JKG8TOUAG=P:0?,H9=@]A(:0O9\T8N\T^9KGZ8qW_FSKqAG798qKG8T\J8T=@Zp8JKl» [\ ) [ ]T¼Ljl67>8JOn
i0=@Zp8TO:SOF0<>]a8JKGZ8hH L \ ] nF0^9KNA(:S]ao=@]'AGFX=PH98TOUAG=BWCAG7>84:0\JAG^>:0?
H=B)8JKG8TOUAG=P:0?H=@]A(:0O>\J8WKGFM AG798]a8JA ! & j
Average Angle Estimate Using Measured D2-D1 Values
F0AG8*AG7>:SAb<8T\h:S^>]a8-^\ ]:0OH8^ ]-,:+KG8*KG8T?P:SAG=@Zp8T?BC`9KG=@MN84Mq^>?Be
AGÇ =@`9?P8J]qFSWK>UnAG7>8'`8LKG=PF[H]»v:SOH£H9=@]a\TFOUAG=@O[^>=BAG=@8T](¼W_FSKqAG7983ADg#F
\J^9KGZp8T]3:0?Bg:TC]'H=B)8JKhn,:0OHmAG798b\JC\T?@8FSW8h:S\L7\T^KGZp8»³=³j 8j@n,AG798
H=@]a\TFOUAG=@O[^>=BAG=@8T](¼H9FlO>F0AF+Zp8LKG?:S`m8h:S\L7£F0AG798JKMNF0KG8AG7:0OXFO9\T8j
#F0O>]a8hÊU^98TOUAG?@CUnAG798qAfgFl\T^9KGZp8J]H9FlO>FSA7:hZp8q:NKG8T`8h:SAG=@O9i`>:SAae
AG8LKGO4g=BAG7>=@O*AG7>8=@OUAG8JKG8T]AG8TH4K(:0O>i08N ^
\ ]) ^\ ]Lvj§8JO>\T8ng8i08JA
:'^9O>=PÊU^>8]aF0?PÂG=@FOW_FSK2AG798q:S\JAG^:S? bZ:S?P^98W_F0K ¯ i=@Zp8TO*`>:0=BK
~ À
FSW"F<9]a8JKGZp8hH JL \ ] :SOH JL]-, Z:S?@^>8T]Tj
-40
-60
-80
Average Angle Estimate
-60
-40
-20
0
20
True Angle
40
60
80
H 4.1
Differential Distance Estimation
DOAG79=@]]a8JAF0W8Jd`8JKG=@MN8TOUAG]TnTg#8,^9]a8"AG798"]a8JAG^>`]a79F+gO=@O ª =@i^KG8
AGFlMN8h:0]a^KG8AG7983:S\T\T^9K(:S\JCFSW#AG7>8H=@)8LKG8TOUAG=:S?"H9=@]A(:0O9\T83Z0:0?@^98T]Tn
] \ n):SAH9=B)8JKG8TOUAZ:S?P^98T]FSZW Wj 8`>?P:0\T8AG7>8<8h:S\TFO]a^>\(7
AG7:+Al=@Al=@]:SA:c7>8T=@i07[A ¥C ®£Ã n2:m7>FSKG=@¨TFOUA(:0?H9=@]A(:0O9\T8F0W
C :Tg:hCWKGF0M AG7>8*KG8J\T8T=@Zp8JKG]Tn:0OHR:SO:0O9i?@M
8 Wmg=BAG7
KG8T]a`8T\LAAGFAG798?@=@O>8#ÉDF=@O>=@O>iqAG7>8<8T:0\TF0O*:0O>HbAG7982KG8T\J8T=@Zp8JKhj%67>8
KG8T\T8J=PZ8JKG]:SKG8\TF0O9>i^9KG8TH:S\T\TF0K(H=@O>i3AGF ª =Pi0^9KG8®Un9g798JKGK
8 ^ \] $n ^Z]-, ¥C ®:j
9O 8\h:hZp8h:+A%:0<F0^9AAG7>=@]":S?Pi0F0KG=BAG7>M½WF0K"O>H9=@O>iAG7>8:S\JAG^:S?9`97:S]a8
H=B)8JKG8TOUAG=P:0?[H9=@]A(:SO>\T8%=@]AG7:+AMN8h:S]a^9KG8TMN8JO[A58JKaKGFSKG]Mb:TC`KGF[H9^>\J8
O9FMb:+AG\L79=PO9i2]aF0?@^9AG=@FOAG7:SA"8Ld9=@]AG]=@O<F0AG7 ! & :0O>H3:0O & j
fON]a^>\(7b:]a=@AG^>:SAG=@FO5nUg8O>HqAG7>8\T?@F]a8J]AMb:SAG\(7>=@O>i]aF0?@^9AG=@FOb<UC
\(7>FUF0]a=@O>i:SO \ ]
! & :SOH ]-,
& ]a^9\L7AG7>:SA \ ] ]-,J
=@]MN=@O>=@Mq^>M*j5 67>
8JOnSg8#KG8T`FSKaA AG7>8#
:0\JAG^>:0?H9=B)8JKG8JO[AG=P:S?[ H9=@]A(:0 O9\T8
AGF3<
8 ! &'# ] & j
-20
¥h ]a7>Fhg] AG7:+A W_F0K AG798 F0<9e
DC ®S¤pµ :0O>H JL]-,
C ¤9¥h®Un
! & ? ¥C ¤p®0¬D) C ¤p®0¬ )J C ®S¤Uµ?)+¥C ®S¤pµ :SOH & §28TO>\J8nÄAG7>8 O:S?V]aF?@^9AG=@F0O =@]
DC µ0 0¹D)LDC ®+¤Uµ )S¥C 0 pj
\ ] DC ®S¤pµ£<8T\h:S^>]a84AG79=P]3Z:S?P^9848Jd=@]AG]N=@O<FSAG7 ! & :0OH
& j
0
AG8T\(7>O9=ÊU^98T],FSWÈ[8T\JAG=@FOUj ¬[j ª =PO>:0?@?BCUnUg8\TFMq<>=@O>8AG7>8KG8T]a^9?BAG]F0W
AG7>8J]a8N8Jd`8JKG=@MN8TOUAG]AGF`8JKaW_FSKGM :SO:0O>:0?BC[AG=@\l8LKaKGF0Kq:0O>:0?BC]a=P]qF0W
¶%Ê[^>:SAG=@FOR»³¤p¼AGFH8JKG=@Zp8l:0O^9`>`8JK<F^9OHmF0OcAG7>8N8TO>HevAGF0e8TO>H
8JKaKGFSKG]F0O>8MN=@i7UAb8Jd`8T\JAl=@OQ`K(:0\JAG=@\T80j Ã 8H9FmAG79=P]b<8T\T:0^>]a8
F^Kl\T^9KaKG8TOUAl`9KGFSAGF0AfC9`847:SK(H[g:+KG8£HFU8T]lO>F0A:S?P?@Fhg^9]NAGFcF<e
A(:0=@OmAG798N:hZp8JK(:Si8b:0O>HcH9=B)8JKG8JO[AG=P:S?,<8h:S\TFOcH9=@]A(:0O9\T8T]]a=@M3^>?BA(:+e
O>8JF^>]a?BC g7>=@?@8qg#83:+KG8q<9^>=@?PH9=@O>iNAG79=P]\TF0M3<>=@O98hH*7:+K(Hg:+KG8ng8
H9Fg:SO[AAGFi8LA%:2]a8TO9]a8F0W>7>Fhg:0\T\J^9K(:SAG8#F^9K"]C]AG8TM=P]?@=@op8T?BCAGF
<8j%67982W_F0?@?PFhg=@O>i3]a8T\JAG=@FO9]H98TMNF0O>]AaK(:SAG8AG7:+AF0^9KH=@)8LKG8TOUAG=:S?
H9=@]A(:SO>\T8:SOH4`F0]a=@AG=@F0O*8T]AG=@Mb:SAG=@FO4MN8JAG7>F[H]gF0KGobg8J?P?³j
=@i^KG8
20
8
& <8AG7>8]a8JA4F0W`F]a]a=@<>?@8X]aF?@^9AG=@F0O>]*^9]a=PO9icAG7>8F<9]a8JKGZp8hH
Z0:0?@^98 L]-, jXÈ[=PO9\T8Ng8l:SKG8bi0^:SKG8JO[AG8J8hH:*^>O9=ÊU^98N]aF?@^9AG=@FOWF0K
:SOUCi=@Zp8JOR`:0=BK4F0WF<9]a8JKGZp8hHZ0:0?@^>8J] L \ ] :SOH L]-, ng8g=@?P?
>OH'8Jd9:S\JAG?BCNFO982Mb:+AG\L79=PO9i]aF?@^9AG=@F0OlAG7>:SA,8Jd=P]AG],=@Ol<FSAG7 ! &
:SOH & j%67[^>]Tn[AG7>8O:S?5:0O>]g#8JKW_FSKAG7>8:S\JAG^:S?5H9=B)8JKG8TOUAG=P:0?
H=@]A(:0O>\J8 \ ]=@] =BW%:SOHF0O>?BCl=BW
:0O>H & j
! &
40
+ I;$ -$ '03/( 69$@/(:;4()(A49$'?L
0-;/$01?@(.C D ,H/I!)$ 4(>1'7)1%.$@9,-$ ! (0-$'?L
0*/4( K$00?,A4$ 01(.C D ,*011'
0 ( ,?
17$ 0A4/0$@'(,) !#/ <//' , 4 $')7 @( 69$ R@7
$'?0-;@$ 01/(.C
k C3W_F0?@?PFhg=@O>iAG7>8:+KGi^>MN8JO[AG]"`KG8T]a8TOUAG8hH3=@OlÈ8J\JAG=@FOl[j Unpg8\h:0O
%
^9]a8NAG7>8NF<9]a8JKGZp8hH L]-, AGF7>8J?P`m^>]=H8TOUAG=BWCXAG7>8N\TFSKaKG8T\JA']aF0?@^9e
AG=@F0Oj ª KGF0M ª =Pi0^9KG8c¥TnAG798*F<9]a8JKGZp8hH JL]-, \h:SO<8*Mb:S`>`8hH
AGFAG79KG8J8`F0]a]a=P<9?@84]aF?@ÂG=PF0O>]3WF0K'AG7984:S\JAG^:S? \ ] jç2i:0=@On%?@8JA
ª
60
-80
F0K 8Jd9:0MN`9?@8n
a]ª 8LKGZp8hH JL \ ]
80
4.
Experiments
fOAG7>=@]l]a8T\JAG=@FO5n2g#8KG8J`F0KaAFOR]a8TZp8LK(:0?`8JKaWF0KGMb:SO>\T88Jd`8JKG=Be
MN8JO[AG]"\TF0OH^>\JAG8hHg=BAG7NF^9K,KG=@\Lo8JA%\TFMN`>:0]a]%=PMN`9?@8TMN8TOUA(:SAG=@FO5j
fO*È[8T\JAG=@FO*®[n[g8F^9AG?@=@O>8:W_8Lg=PMN`KGF+Zp8TMN8TOUAG]"AG7:SAg#8=@OUAG8TOH
AGFN=@MN`9?P8JMN8TOUA=@O4AG7>8W^9AG^KG8n><>:0]a8hHFO4g7>:SAg87:hZp8?P8T:SKGO>8TH
WKGFMVAG7>8J]a88Jd`8JKG=@MN8TOUAG]Tj
FSK8h:0\(7MN8h:0]a^KG8TMN8TOUA:SAAG798,]a`8J\T=B8h
H Wn+g8%A(:0op8"AG7>8{NzhÂpxF0W
GAª 7>8H=@)8LKG8TOUAG=:S?H=P]A(:SO>\T8]G:SMN`>?@8T]AGFbKG8TH9^>\J8AG7>88JKaKGF0K2\h:S^>]a8hH
<UC*^9?@AaK(:S]aF^9OH*KG8 8J\JAG=@FO>]:0O>HO9F=@]a8j67>88TOUAG=BKG8q8Jd`8JKG=@MN8TOUA
g:S]KG8J`8h:SAG8hHlW_F0KAG7KG8T8AaKG=P:0?@]Tj
H98T]a\LKG=P<8AfgFH9=@]AG=@O>\LA#]a8JAG]%F0W)8Ld9`8LKG=PMN8JO[AG]Tj =BKG]Ahnpg88TZ0:0?Be
Ã^>:S8
AG8AG7>88J'\h:0\JC3F0W5F^KH=B)8JKG8TOUAG=P:0?H=P]A(:SO>\T88T]AGª =@Mb:+AG=PF0ONAG8T\L7e
O9=PÊ[^98:S]:W_^9O>\JAG=@F0OFSWAG7>8:0O>i0?@K
8 W<8LADg8J8TOAG798\TF0MN`:0]a]:0OH
F0O>89d8hHl<8T:0\TF0O4^>]a=@O9iqAG7>82AG8T\L79O>=PÊU^>8T]#F0W"È[8T\JAG=@FO*[j [j#67>8JOn
g#8b:SAaA(:S\L7cMq^>?BAG=@`>?@8'<8h:S\TFO9]3:+AqH9=B)8JKG8TOUA`>?P:S\T8T]FOc:\T8T=@?@=PO9i
:SOHMN8h:0]a^KG8%AG798:S\T\T^9K(:S\JCF0W9\TFUFSK(H9=@O:+AG88T]AG=@Mb:SAG=@FO^>]a=@O9iAG798
67>8KG8J]a^>?BAG]%:SKG8]a7>FhgO'=@O ª =@i0^9KG8¥¥0npg7>=@\(7']a7>Fhg]"AG7>8:hZp8LK(:0i8
:0O9i?@8N8T]AG=@Mb:SAG8J]H98JKG=@Zp8hHWKGF0MAG7>83MN8T:0]a^9KG8TH /] \Z0:0?@^98T]Tj
67:+A=P]Tn9AG7>8:hZp8JK(:Si8:SO>i?@88T]AG=@Mb:SAG8J]g#8JKG8\h:0?@\T^9?P:SAG8hH*<UC:0è
`>?BC=@O>i¶%ÊU^:SAG=@F0OR»³¤U¼FOcAG7>8bo[O>FhgOZ0:0?@^>8J]qFSW n n":0O>HmAG7>8
:hZp8JK(:Si8MN8h:S]a^9KG8h
H ] \ Z:S?P^98T]:+A8h:0\(I
7 Wj ª KGF0M ª =@i^KG83¥¥0n
g8b]a8T8NAG7>:SAAG7>8NMN8h:S]a^9KG8hH /] \Z:S?@^>8T]\h:SO8T]AG=@Mb:SAG8NAG7>8
AaKG^>8:0O>i0?@8g=BAG74KG8T:0]aFO>:0<9?P8:S\T\T^9K(:S\JCUj
6:S<>?@8*¥']a79F+g]AG798N:hZp8JK(:0i08bH9=B)8JKG8TOUAG=P:0?,H9=@]A(:SO>\T8'=@OXAG8JKGMN]F0W
nAG7>8N:hZp8JK(:Si8b`8JKG\T8JO[A(:Si8N8JKaKGFSK3FSWAG7>8bH=B)8JKG8TOUAG=P:0?,H9=@]A(:0O9\T8
WF0K8JZp8JKaCm¥T B :SO>i?@8 B 7 WO7 B n5:SOH4AG7>8qH98LKG=PZ8hH:0O9i?@8
8J]AG=PMb:+AG8T]Tj
W
B
e 0
ef 0
eDµS
ef¹0
eD®S
e¤
ef¬0
eDS
eG¥T

¥h
0
¬
¤p
®0
¹
µ0

¸2\LAG^:0?
¦48T:0]a^9KG8TH
¶KaKGF0KF0W
eG¥j ¹0
eG¥j ®µS¹
eG¥j ®0S¤
eG¥j ¬ 0¹
eG¥j S¹
eG¥j pS efj 0
efj ®S¤pµ
efj µS
[j 0µ0 [j ®+¤Uµ
[j 0
¥0j 0 ¥0j 00¹
¥0j ¬0 ¹
¥0j ®S0¤
¥0j ®0µ0¹
¥0j ¹0
eG¥j ®0®
eG¥j ®+¤¤
eG¥j ®S0¤
eG¥j &¬ p
eG¥j U¥h¬
efj 0 p®
efj S¤p¬
efj ®U¥h¹
efj +¤U®
j pU¥
j 00
j ¤Uµ0µ
j µS¤.
j ¬[¥
¥j pµ0®
¥j ®S¹
¥j ¬ &
¥j ¤U®4
¥j ¤p ®
¬j 0
[j ¥0¥
ef[j 0¬¬
ef[j ¤p&® ¥j µ
¤9j@¥ 0¬
eD®Uj ¬0¬¬
®[j µ0µ
¥¥j &¹ .
/] \»5¼ /] \»5¼ /] \+»5#3¼
:
6
eD0 [j ¥+®
eG¥+Uj µµ0¬
ef¹[j ¬0¬¬
e [j ®S. eG¥+Uj ¬p0
e [j ¬®0¹
eDµUj 4® 0¤
eDµUj ¤pµ
eDµUjP¥T¹pµ
º8LKG=PZ8hH
H W
¶%]AG=@Mb:+AG8T]» W B ¼
eµS¹j pU¥
eµ+¤9j [¥
eµSj ¬p®S
eD¹0j ¤p
ef.¤ j ¬¥ eD¬0 j pU¥
eD¬[¥j µ0 0¹
e(¥T j . S¤
ef j pU¥
[j ®µ
µUjP¥T 0¤
¥hµ[j ¬p®4
0µ[j p4 ¬®[j ®µS¬
¤p[j 0
®U¥j µ®0®
¹0j ¬¥hµ
¹®[j &µ S¤
¹0 j@¥ 0¹
*
© FU\T:SAG=@FO
¸
AG=@FO9]WKGF0MAG7>8T]a8%KG8T]a^>?BAG]Tj ª =BKG]Ahn0g8:+KG8
Ã:S<>8#?@8'MbAG:SF*op:S8%\TAG\T7^KGK(8T:S8AGF08T?B<>C£]a8J8TKG]Z0AG:S=@Mb
:SAG8':SO>i0?P8J]AGFlg=@AG79=@O¬4H8Ti0KG8J8T]=PO
AG798K(:0O9i8WKGF0M¾eDµSqAGFN¬NH8Ti0KG8J8T]Tn:SOHAGF3g=BAG79=POX 3H98TiSKG8T8T]
WF0K:0O9] i?@8T]^9`AGFl®S'H98TiSKG8T8T]TjÈ8T\TF0OH)n=@O4AG8JKGMN]FSW"`8JKG\T8TOUA(:0i08
8LKaKGF0K :S?@?8T]AG=@Mb:SAG8hHNH=@)8LKG8TOUAG=:S?)H9=@]A(:0O9\T8T]2»v:0OH'798TO>\J8n:0O9i?@8T]
WF0KAG7>=@]]a8JAF0W8Jd`8JKG=@MN8TOUAG](¼7:hZp8'?@8T]a]AG7:SOQ¥h$¬ #Ä8LKaKGF0Kg=@AG7
AG79838Jd\T8J`9AG=@FOXF0W W ¥h B jq679=@K(H)n)AG7>838J]AG=PMb:+AG8T]F0W,AG7>8q`F]e
=BAG=@Zp8 WXZ:S?@^>8T]N\TF0O>]a=@]AG8TOUAG?BCQ]a79Fhg:£7>=@i07>8JKl`8JKG\T8JO[A(:Si8*8LKaKGF0K
AG7>:0ObAG7>F0]a8W_FSK2O98Tip:+AG=@ZpK
8 Wj,¦4FSKG8TF+Zp8JKhnAG7>8JCl:S?@?)KG8J`F0KaA:qZ0:0?@^98
AG7>:SA%=@]"?P8J]a]%AG7>:0O3AG798#AaKG^>8Z0:0?@^>80j ^9K%\T^KaKG8TOUA"7UC9`FSAG7>8T]a=@]Tn]AG=P?@?
^9OH8JK:0\LAG=PZ8=@OZ8T]AG=@ip:SAG=@F0On9=P]AG7>:SAAG798\h:0^9]a8T]F0WAG7>8T]a88LKaKGF0KG]
:+KG8b=PMN`8LKaW_8T\JA\T:0?@=@<9K(:SAG=@F0O>]3FSWAG7>8bH=@]A(:0O>\J8T]<8JADg#8T8TOmAG798'^>?Be
AaK(:S]aFO9=P\KG8T\T8T=@Zp8LKG]»_g7>=@\(7:<8JAaAG8LKMNF^9OUAG=PO9i`9KGFU\J8T]a]#g=@?@?)9d>¼
:SOHAG=@MN=@O>i'H98T?P:TC4=@]a]a^98T]KG8J?:+AG8hHAGFN=@OUAG8JKaKG^>`A7:SOH9?@8JKG]=@O4AG798
"aMN=@\JKGF0`9KGFU\T8T]a]aFSKF0OAG798\TFMN`>:0]a]Tj%º8T]a`9=BAG8AG7>8T]a8\T:+Z8h:SAG]Tn
g#8l>OH£AG798l:0<>=@?@=BADC£AGFX8J]AG=PMb:+AG8l:0O>i0?@8T]qAGFg=BAG7>=@O¬SevAGFSe®*H8Je
iSKG8T8T]%W_F0K#:`9K(:S\JAG=@\h:0?9K(:0O>i08F0W5:0O9i?@8T],`9KGFMN=@]a=@O>i:SOH3^9]a8JW_^9?9WF0K
Mb:SOUCb\TFOUAG8Jd[Aaef:Tg:SKG8:S`>`9?P=@\h:+AG=@FO>]Tj
º
D $@! 0
k

¸2\JAG^>:0?
8J\T8T=@Zp8JK
FU\h:+AG=PF0O© ».G)IH)Ip¼
j [n¥+U¥j n¥+µ0 [j
¥0¥+µUj [n¥+U¥j n¥+µ0 [j
j [n j n¥+µ0 [j
¥0¥+µUj [n j n¥+µ0 [j
¶%]AG=@Mb:+AG8hH © 8T\T8T=@Zp8JK
FU\h:+AG=PF0O».G)JH)$p¼
eG¥h¬[j n¥T¬0¤j [n ¥ ¬[j ¥+S¬j ¬n¥h& [jP¥0n ¥ [j ¬
eD[j µ[neD®[j ®Un;¥hµ0¹[j ¥+Sj ¤9nÄef¬j [n;¥hµ0¬[jP¥
6
:
D $ !)0 9E547)'$ +/( 69$@/(H$ H ?97
%./;:0%.$@')(.C
¶"KaKGFSK
»³\TMl¼
®Uj@¥+
¥h¹[j p®
®Uj ¹®
¹[j ¹0¬
/' L
KGF0MÆAG7>8q\TFUF0K(H=PO>:SAG8'8J]AG=PMb:+AG8T]Tng#8N:0?@]aF4H98JKG=@Zp8N:b]a8JAFS+
W ?> 0Zª :0?@^>8T]AG7:+A':+KG8b^>]a8hHm=@O¶%ÊU^:SAG=@F0OR»³¤U¼Lj6:S<>?@8b¤KG8T`F0KaAG]AG7>8
`8JKG\T8JO[A(:Si88JKaKGFSK2FSWAG7>
8 > l
H98JKG=@Zp8THWKGF0MF0^9K\TFUFSK(H9=@O:+AG88J]e
AG=@Mb:SAG8T]T
j xsax y t_¯Â0tvu yfxy yy xxLs(sazSs2t_¯ > t ~ y{'z y
C $¹ #MEx B0xL¯ E xL ¯² ¯ x s ~ E E~ ¯Â E = y ¯9y³t
=(xLy³yfxLs sL|
± 8%E ^>]a8%AG7>~ =@]g~FS±,
~Aae²_²\h:0]a~ 8MN8h :S]a^9 KG~ 8hHH9~:S²_A(² :
À =POAG7>8%O> 8LdA
y xLs
I
G
K

]
±,~0AGF
À ^>Ã O>H98JKG]A(:SOHqAG798AG798TF0KG8LAG=P\T:0?8JKaKGFSK<F^9OH'F0OlF+Zp8LK(:0?@?
]aE8T\JAG=@F0~0Ol
F0KG=@8TOUA(:+AG=PF0O8T]AG=@Mb:SAG=@FO4^>]a=@O>i'F0^9K\TF0MN`:S]a]Tj
8J\T8T=@Zp8JK
© FU\h:+AG=@FO
¸
4.2 Distance and
k 8h:0\JPosition
#
FO
».G)IHEstimation
)JU¼
§
n5¥+U¥n

¥0¥+µ[n¥+U¥n
n [n
«
¥0¥+µ[n [n
]
6:S<>?@8*¬]a7>Fhg]'AG7>8l\TFUFSK(H9=@O:+AG8*8T]AG=@Mb:SAG8T]':SAN8h:S\L7?@FU\h:+AG=PF0O>]Tj
>OHAG7:+AmF0^9Km`F]a=BAG=@FOI8T]AG=@Mb:SAG8T]£\h:0OI<8:0\J\T^9K(:+AG8AGF
Ãg=B8
AG7>=@O£®+ef¹b\T8TOUAG=@MN8JAG8JKG]Tn):SOH*=@OAG7>8gF0KG]A\h:0]a8nAGFbg=BAG7>=@O£®
\T8TOUAG=@MN8JAG8JKG]"FSWAG7>8#AaKG^98Z:S?P^98j 8\TFO>H9^>\LAG8hH3:2W^9KaAG798JK%=PO[Zp8J]e
AG=@ip:+AG=PF0Ob=POUAGFAG798g#F0KG]A#\h:0]a8]a=BAGÃ ^:SAG=@F0O :0?BAG7>F0^>i7N=BA,g:0],iFUF[H
AGF?@8T]a],AG7>:0Ob:WFUF0AhnUg8g#8JKG82=@OUAG8JKG8T]AG8TH'=PO'AG798^>O>H98JKG?BC=@O>iKG8h:+e
]aFO9]%WF0K,AG7>=@],<8J7:hZ[=PFSKhj Ã 8WF^9OH3AG7:+A%\TFO9]a=P]AG8JO[AG?BCqAG7>8gFSKG]A
\h:S]a8'7:S`>`8TO98hH*g7>8TOAG7>8KG8T\T8T=@Zp8JKg:0]O98h:SK:lg:S?@?vnF0Kg798TO
AG7>8<8T:0\TF0O4g:S]:+AaA(:0\(7>8hH4\J?PF0]a8AGFN:qg:S?@?vn9g7>=@?@8=@Ag:0]`F]a]a=Be
<>?@8AGFF<A(:0=@Ob\T8TOUAG=@MN8JAG8JKae?@8TZp8T?9:0\J\T^9K(:S\JCN:W_8LgQW_8J8JA:Tg:hC3WKGFM
g:S?@?P]Tj Ã 87:hZp8]a=@O>\T8<8T8TOXH98JZp8T?@F`9=PO9iNAG8T\L79O>=PÊU^>8T]AGFb7:SOH9?@8
KG8>8T\JAG=@FO9]WKGFMVg:S?@?P]Tn>g7>=@\L7lg8F0^9AG?@=@O>8=@OÈ8J\JAG=@FO®Uj
8T\T8T=@Zp8JK
D $@! 0M H Z@'5$ 0 7)1(R$')%./( 69$(@69/'(B$;L
$@/79/; IR& $01( ?#&%&@'5$@>4 $ ')79,?>74;/7
W
$ '0-/( 63$ /(A$ B$%4,8;/$01-
4
FSKF^9K]a8J\TFO>HX]a8JAFSW8Jd`8JKG=@MN8TOUAG]Tn)g8'`9?P:0\T8hHW_F0^9K<8h:S\TFO9]
Fª OAG798q\T8J=P?@=@O>iF0W#:'KGFUFM:+Ao[O>FhgO\TFUF0K(H=@O:SAG8J]:0]]a79FhgO£=@O
6:S<>?@8q[j¶%:0\(7*<8h:S\TFO<KGFp:0H9\h:S]AG]:'^9O>=PÊU^>8=PH98JO[AG=B>8JKhn>g79=P\(7
=@]'Mb:0`9`8hHcAGF=@AG]3oO9FhgO\TFUFSK(H9=@O:+AG8T]N<UCmAG798KG8T\T8J=PZ8JKhj67>8
KG8T\T8J=PZ8JKN=@]'`>?P:S\T8hH:SAb:]a`8T\T=B\?@FU\h:SAG=@FOQ:0O>H\JF?@?@8T\JAG]b^>`cAGF
®'H=@]AG=PO9\JAH9=@]A(:0O9\T8]G:0MN`>?@8T]WKGF0M¾8h:0\(7F0WAG798W_F^K<8T:0\TF0O>]Tj
k#8T\T:0^>]a8AG798O>F=@]a8:0O>HKG8 >8T\JAG=@FO9]2FSW"^>?BAaK(:0]aF0^>OH=PO*AG7988TO[Z[=Be
KGFO9MN8TOUA"\h:0Ob:+)8T\JA%AG7>8]G:SMN`>?@8hH'H=P]A(:SO>\T8J]TnUg8A(:0op8AG798MNF[H98
F0W#8h:0\(7cH=@]A(:0O>\J8NH9=@]AaKG=@<>^AG=PF0O£WF0K8h:S\L7£<8h:0\TF0Oc:S]AG7>8':S\JAG^:S?
H9=@]A(:SO>\T8'8J]AG=PMb:+AG8AGF8h:0\(7X<8h:0\TF0Oj 8\TF0O9i0^9KG8hHAG7>8q\TFM'e
`:S]a]:0],=@ObAG7982`KG8TZ[=@F^>],8Jd`8JKG=@MN8TOUAhnpÃ A(:0o[=@O>iMN8h:S]a^9KG8TMN8JO[AG]%:+A
W_F0^9KlH=@)8LKG8TOUAN\TFMN`>:0]a]'?@FU\h:+AG=@FO>]:0]3]a7>FhgOQ=@O6:0<9?P8*¬jQ¸A
8h:S\L7N?@FU\h:+AG=PF0On[g8\TF0?P?@8T\LAG8hHbH>:SA(::S\JKGF]a]%W_F^K=@OH8T`8TO>H98TOUA"AaKG=Be
:0?@]Tj
º
D

«
efj ®S efj ef[j j ¬
j ¬ efj@¥+® j ¬0 ¥j 0¹
eG¥j ¹® eG¥j ®µ ef[j ® efj ®S eD[j 4® eG¥j µ[¥ eG¥0j µ0® j 0 ?> * 1'O%./' 694(C
< ,3/(#@%&"RI$ %&,
>
D $ !)0 ? 4%./'$@* !#$%.'8 :$%4,%& &71'$ RM/( 69@
$ ' R& $0 C
$%.'%.547)1'$@/(
F0K:0O>i0?@838T]AG=@Mb:SAG=@F0On)AG7>8`8JKG\T8TOUA(:Si838LKaKGF0K=@]O9F0A:0]=@OUAG8JKae
8J]ª AG=PO9i'AGF3MNF0]A:S`>`9?P=@\h:+AG=@FO>]2:0]:S<>]aF?@^AG88JKaKGF0KG]Tj
e
ef
eDµ0
ef¹
eD®0
e¤p
ef¬
eD0
eG¥h

¥h
0
¬
¤p
®0
¹
µ0

A(:0O
W>4W
¤j ¹
Uj ®
¥0j ¹p®
¥0j ¬pµ
¥0j 0
¥0j@¥h
¥0j 0¤
¥0j ¥
¥0j
¥0j ¥
¥0j 0¤
¥0j@¥h
¥0j 0
¥0j ¬pµ
¥0j ¹p®
Uj ®
¤j ¹
'
;
W
4.3
Error Analysis
O>Fhgi=@Zp8:£]a=PMN`9?@8*8JKaKGF0K:SO:0?BC]a=@]FSWAG7>8*:0O>i0?@88T]AG=@Mb:Se
ÃAG=@F08*
OMN8JAG79F[H5n[F0<9A(:0=@O9=PO9i3:SO8Ld9`KG8T]a]a=@FObW_FSK7>FhgR=BAH98J`8TOH]#FO
AG7988LKaKGF0KG]'=@OAG7>8lMN8h:0]a^KG8hHÊU^:SO[AG=BAG=@8T]Tj Ã 8l^>]a8lF^9K'8Jd`8JKae
=@MN8TOUA(:S?#KG8T]a^>?BAG]WKGFM AG7>8b`9KG8JZ=@F0^>]3]a8J\JAG=@FO>]qAG7:SAq<F^9OHmAG798
:S\T\T^K(:0\JC'g=BAG7Ng7>=@\(7bF^9K,AG8T\(7>O>=PÊU^>8J]#:SOH'=@MN`>?@8TMN8TOUA(:+AG=PF0ON8T]e
AG=@Mb:+AG8N.» ¥h¼:0O
H ?> j
WN» \ ) ] ¼=@]":W_^>O9\JAG=@FOqF0WAfgFqt¯ÂUx xL¯ÂUxL¯>y |{Nx saxaÂZ0:SKG=Be
~0 8Jd`9KG8T]a]a8hH
:S<>?@8T] /\2:SOH .]0n>AG798TOAG7988JKaKGFSK=@O'n} Nn9\h² À :0O4<8
:S]q ¹[nS¬S ]
»¼
-
]
]
\ ¼ » \ ¼
»
»
]
]
.] ¼ » ] ¼
»¥h¼
¸`>`9?@C=@O>i'AG79=@]AGFNAG7>8:SO>i?@8q8T]AG=@Mb:SAG
8 Wng#8qi08JAAG798W_F?@?@Fhg=@O>i
8Ld9`KG8T]a]a=@FO4WF0KAG7>82WK(:0\LAG=PF0O:S?8JKaKGFSK2=@O W[n
*Wn>:0]:qW^>O>\LAG=PF0O4FSW
\ ] \ :0O>H
] ?> BW
W
A(:0O"W
W
»
\ ¼]
/\
»
] ¼ ] ] ]
] »¥ ] ¼
.
»¥T¬p¼
F0AG8AG7>:SA<8T\h:S^>]a8 ] \ =@]8T]AG=@Mb:SAG8TH4^>]a=@O>iqAG7>8`97:0]a8H=BWe
WÇ 8JKG8TO9\T8*F0W2AG7>8^>?BAaK(:0]aF0O>=@\4g:hZp8LW_F0KGMN]Tn:0O>H ?> c
=@]N8T]AG=@Mb:SAG8hH
^9]a=@O>i*:4H9=B)8JKG8TOUAMN8JAG79F[H\TFMq<>=@O>=@O>ilAG7>8 ©ª :SOHX^>?BAaK(:0]aF0O>=@\
]a=@i0O:0?:SKaKG=@Z0:0?NAG=@MN8T]Tn \:0OH .]]G:SAG=@]WCEAG7>8=@OH98J`8TOH8TOUAae
MN8T:0]a^9KG8JMN8TOUA\TFO9]a=PH98JK(:+AG=PF0O>]F0W%¶%ÊU^:SAG=@F0Oc»¥+0¼Lj
\ > \ »5#'¼
¬j
[j ¥
j ¬
j ¤p¹
¥j ¥
¤9j@¥ ®[j ¬¬
®[j µ[¥
¥0¥j µ0
*W>4W4»5#'¼
j ¤¤
[j ¹p
[j pµ
[j@¥h
®[j 0¬
¹j p
¹j pµ
¥¥j 0 *W B
µ[j ®®
¥j 0¤
¥j S¤
¥j p®
[j . ¥j ¥
¥j [¥
¥j@¥
S j p
¥h[j µµ
¹j ¬¬
j ®[¥
¥h[j ¬p
j ¬¹
µ[j ®&
µ[j ¤p¬
µ[j@¥+µ
0 j ¬0¬
¥h¬j ¬µ
µ[j@¥h
¥¥j ®U¥
¥h¹j 0
¥+®[j ®4
¥+µ[j S ¬j ®+¤
[j ¬
[j ¹pµ
[j@¥h¬
¤9j ¹¥
j ¤U®
j ¬¹
¥h[j . +¤9j ¤p¬
C
' 08@( 9
D $ !)0 5 Q /%.R@7 !#)')7(9 M$ W
.]
¹ 6 $ ')$@7 L
')(2$ $%4,
C D ,O$ $694(M$@4
p0®& C
& & DC
AG7>8b`8JKaWF0KGMb:SO>\T8l=@MN`:0\LA3FSW]a^9\L7MNF+Zp8TMN8JO[AF0OAG7>8,KG=@\Lop8LA
\TF0MN`:0]a]Tj
¶%ÊU^:+AG=PF0O£»¥T¬p¼#]a79F+g],AG7:SA#AG7>88JKaKGF0KMN=@i7UA#i0KGFhgRAGFq<8K(:SAG798JK
?P:+KGi8n8T]a`8T\J=:S?@?@CW_FSK4Z0:0?@^>8J]lFSWW£\T?@F0]a8AGF G>Uj 67>8`>7UC]a=Be
\T:0?"KG8h:0]aF0OmW_FSKAG7>=@]=@]q:S`>`>:SKG8TOUAWKGFM
=@i^KG8N¬ng7>=@\L7£]a7>Fhg]
AG7>:SA:SA?P:SKGi08qZ0:0?@^>8J]FSWZWn]aMb:S?@?\(7:0O9iª 8T]=@O4d>q`9KGF[H^>\T8?P:SKGi08
\(7:SO>i08T]=@I
O Wj%¶%Ê[^>:SAG=@FO»¥T¬p¼,:S?@]aF3]a7>Fhg]#AG7>:SA%AG7>88JKaKGF0KMN=Pi07UA
iSKGFhg?P:SKGi08'g7>8TO£AG7>8 >
Z:S?@^>8'=@]]aMb:0?@?³jl67>8'`97UC9]a=@\h:S?%KG8T:Se
]aF0O*=@]\T?@8h:SKWKGF0M ª =@i^9KG8Un9g79=@\L7]a7>Fhg]AG7>:SA:S]AG7982KG8T\J8T=@Zp8JK
MNF+Zp8J]\T?@F]a8JKAGFAG7>82<8h:0\TF0On>:q]aMb:S?P?\(7:SO>i08'»³F0K8JKaKGFSKL¼#=@OlAG798
H=B)8JKG8TOUAG=P:0?H=@]A(:0O>\J8`9KGF[H9^9\T8T]:3?P:+KGi8\L7>:0O9i8=@O Wj
8LA L<8AG7>8F<>]a8LKGZp8hH3g:hZp8J?P8JO>i0AG7bFSW^9?@AaK(:S]aF^9OHbH9^98AGFMNF0e
AG=@FO5n <8AG7>8AaKG^98g:hZp8T?@8TO>iSAG7F0W%^>?BAaK(:0]aF0^>O>H4WKGFMAG7>8<8h:+e
\TF0Onc<8'AG7>8'AaKG^983WKG8TÊ[^98TO>\LC£FSW^>?BAaK(:0]aF0^>O>H5n":SOH N<8'AG7>8
?@=@O>8h:+KZp8T?@FU\T=BADCFSW,AG798qKG8T\T8J=PZ8JKG]=@OXAG7983H=BKG8T\JAG=@FOAGFhg:SK(H]AG7>8
<8h:S\TFO5j#6798TOn9<8T\h:S^>]a8FSWAG7>8ºF0`>`9?P8LK8J)8T\JAhng8i8LA
L . >
¶%Ê[^>:SAG=@FO4»®¼AGFH8JKG=@Zp8#AG7>8#8JKaKGF0K» ¼\h:0^9]a8hHq<UCAG7>8
ÃºF08#`>^>`>]a?@8
8JK8J)8J\JA "¨
» ¼ 1 > . 1 g7>8LKG8 N=P]qAG7>8bZp8T?@FU\T=BADCcF0W]aF^9OH5jX§28TO>\T80n%:SAN:`8hH8T]AaKG=P:0O
g:S?@o=@O9i]a`8T8hHF0W ? C 0>£:SOH ¬0¬ 0>n>
D C 0¹ j%fOqF0^9K%=@MN`>?@8TMN8TOUA(:SAG=@F0OqFSWAG7>8]aFSWADg:SKG8\TF0MN`:0]a]Tn D C ®0®0:¹ :SQA W ¥T B n]aFlAG798q8LKaKGF0Kg=BAG7KG8T]a`8T\LAAGFNAG7>8AaKG^>8 =@]:0<FÂ¥ C $ #lj#¸"
A W ¤p B nAG7>88LKaKGF0K=@]?@8T]a]AG7:SO£¥ #lj
:0`9`>?BC¶%ÊU^:+AG=PF0Ob»¥h¬p¼AGFAG7>8%:hZp8JK(:0i08#8JKaKGFSKZ0:0?@^>8J]WKGF0M
ÃF0^98,KO98JFhdg
`8JKG=@MN8TOUA(:S?MN8h:0]a^KG8TMN8TOUAG]2AGFF<9A(:S=@Oc:0O£^>`9`8JK<F^9OH
F0OAG79848Jd`8T\JAG8TH8JKaKGFSKhj ª F0
K C :0O>H ¥ C ® £n#g#8
i08JA ] > C ¹[j Ã 8'AG7>8JO]a8JA & D C &® [n,g79=@\L7=@]
AG798gFSKG]a8:hZp8JK(:0i08\h:0]a88LKaKGF0KW_FSK > '
WKG& F0M¾6:0<9?@8¤9j Ã 8AG7>8TO
]a^9<>]AG=BAG^9AG8%AG7>8 W:0O>H ! Z:S?@^>8T]WKGFMI6:S<>?@8¥0j67>8#`9KGF+É8T\JAG8TH
AG798TF0KG8LAG=P\T:0?^9`>`8JK8JKaKGF0 K! <F^9OHl:SA8h:S\L=
7 Wq=@]?P=@]AG8hHl=@O*6:S<>?@8®[j
>OHcAG7:+A'AG7>8bAG7>8TFSKG8JAG=@\h:0?^9`>`8JKN<F0^>O>HF0O8LKaKGF0KN=@]N?@8T]a]
ÃAG7>8
:0OZp83H98TiSKG8T8T]g7>8JOMWl=P]<8LADg8J8TO2¤*H98Ji0KG8T8T]Tj Ã 8q8TM'e
`97:S]a=P¨J8AG7:+A'AG7>=@]q=P]qg7:SA3AG7>8bAG7>8TFSKaC`9KG8hH=@\JAG]N:0]':0O^>`>`8LK
<F0^>O>HXW_FSK8h:0\(2
7 Wn:0O>HXAG7>:SA=@Om`9K(:S\JAG=@\T8'AG7>=@O9i]Mb:TCg8T?@?,<8
<8LAaAG8JK»v:0O>Hb:SKG8=PObW³:S\JA<8JAaAG8LK=@O]aF0MN82\T:0]a8T]Tn9:0]#F^9K#KG8T`F0KaAG8hH
8Ld9`8LKG=PMN8JO[AG]]a79Fhg8hH>¼Lj
5.
Improvements
67>8N`KG8T?@=@MN=PO>:SKaC8Jd`8JKG=@MN8TOUAG]KG8J`F0KaAG8hHX=POXAG7>8'`KG8TZ[=@F^>]]a8J\Je
AG=@FO]a7>Fhgi0KG8h:+Ab`9KGFMN=@]a8n:0OHg84<8T?@=P8JZp8*AG7:+A'AG7>=@]b:0^9i^KG]
g8J?P?5W_FSKAG7>8ÂG=@?P=BAfC4FSW"F^9K]C]AG8TM*j%§Fhg#8TZp8JKhn>F^9KKG8T]a^9?BAG]:S?P]aF
K(:0=@]a8]aF0MN8*=@MN`F0KaA(:0OUAN=@]a]a^98T]NAG7:SAbO98T8hHAGFc<8*:0H>H[KG8T]a]a8hHQ=@O
=@MN`>?@8TMN8TOUA(:+AG=PF0ON<8JW_FSKG8:`9KGF[H^>\JAG=@F0Ol]C]AG8TME\h:SOl<8KG8h:S?P=@¨T8TH5j
67>=@]]a8T\LAG=PF0O'H8T]a\JKG=@<8T]]aFMN8,F0W9AG7>8T]a8,=P]a]a^98T]":0O>HF0^9K`KGF`F0]G:0?@]
AGFN:0H>HKG8J]a]AG798TM*j
4.4
Effect of Motion
67988Jd`8JKG=@MN8TOUAG]MN8TOUAG=@FO>8TH4:0<F+Zp82g8JKG8\TF0OH9^9\JAG8hHl<[Cl`9?:S\Je
=@O9i2AG7>8#\TFMN`>:0]a]FO3:2]A(:S<>?@8`>?P:+AaW_F0KGMV»³=³j 8j@npAG798#?@=@O>8h:+K,Z8T?@FU\T=BADC
FSW,AG798q\JFMN`:S]a]=@]¨T8JKGFp¼LjDO`K(:0\JAG=@\T80n5g#838Jd`8T\LAAG7>83,KG=@\Lo8JA
\JFMN`:S]a]AGF<8#:SAaA(:0\(7>8THAGFMNF0<>=@?@8H8TZ[=P\J8T]Tnp:SOHq:SKG8=@OUAG8JKG8T]AG8hH
=@OMN8h:S]a^9KG=@O>i=BAG]`8JKaW_FSKGMb:0O9\T8Ng7>8TO:*^9]a8JKg:0?@o[]3FSK3MNF+Zp8J]
AG798*H8TZ[=P\J84=@OAG798T=BK'7>:0OH)j Ã 8MNF[H98T?]a^9\L7MNF+Zp8TMN8TOUAq:0]':
?@=@O>8T:SKZp8T?@FU\T=BAfCm:SOH\h:0?@\T^9?P:SAG83AG7983ºF0`>`>?@8JK8J)8T\JAAGF8Jd9:0MN=@O>8
5.1
Handling Reflections
^9K:S`>`KGF`9KG=P:+AG8T?BC`>?P:0\T8THX<8h:S\TFO9]\h:SOm:S\T\T^9K(:+AG8T?BC8T]AG=@Mb:SAG8
ªAG7>F08
`F0]a=@AG=@F0O£\TFUFSK(H9=@O:+AG8T]FSW#:'KG8T\J8T=@Zp8JKhn)<>ÂF0^9K2KG8T]a^>?BAG]]a79Fhg
AG7:+AAG7>83:0\T\T^K(:0\JCmH98Ji0K(:H8T]g7>8TO£:4<8h:S\TFO£=@]g=BAG79=POm:W_8Lg
¥h
=@O9\L798T]qWKGFM :g:0?@?³j679=P]q=@]3<8T\h:S^>]a8^>?BAaK(:0]aF0^>OHmKG88T\JAG=@F0O>]
\T:0O*\h:S^>]a8AG798MN8h:S]a^9KG8hHlH9=@]A(:0O9\T8T]AGF'<8=@O>:0\T\T^K(:SAG8j%WAG7>8LKG8
=@]2:'?@=PO98JeF0Wef]a=@i07[A2`:+AG7*<8JAfg8T8TO*AG798<8h:0\JFO:0O>HAG7>8KG8J\T8T=@Zp8JKhn
g#8g=@?@?57>:hZp8:]a=@O>i?@8\JF0KaKG8T\JA , H=@]A(:0O>\J8:0MNF0O>iAG7>82]a8JAF0WH9=@]e
A(:SO>\T8J] >=BWO9F0Ahn[AG7>8TOl]a8TZp8LK(:0?)F0WAG7982KG8h:0H9=@O>i0]g=P?@?5<8=@O>\TFSKaKG8T\JAhj
O>FSA<9=@ii8LK2AG7>:0O]aFMN8AG7KG8T]a7>F0?PH*Z:S?P^98n]G:TC*j ®[j679=P]]a8T\TF0OH
\TF0OH9=BAG=@FOMN8h:SO>]AG7:+AqAG798JKG8]a79F^9?Hc<8:SA3?@8h:0]A3FO>8l<8h:S\TFO
g7>F0]a87>8T=@i07[AH9FU8T]O9F0AbHFMN=@O:+AG8TAG7>8H=P]A(:SO>\T82AGFAG798\TFM'e
`:S]a]Tn=³j 8j@nAG7>8\TFMN`>:0]a]']a79F^>?PHO>FSAb<8QH=BKG8T\JAG?BC^>OH8JKG£:0?@?
Z[=@]a=P<9?@8<8h:0\TF0O>]Tj
\h:0O]aF?@Zp8*AG798:0M3<9=@i^>=BAfC\h:0^9]a8hHQ<UCM3^9?@AG=@`9?P8*H9=@]A(:0O9\T8T]
Ã:SO8
H8JKaKGF0KG]H9^>8AGFl=PO9\TF0KaKG8J\JAH9=@]A(:SO>\T8T]<[C*^>]a=@O>i B0x2<8T:0\TF0O>]
=@O9]AG8h:HF0W2W_F^Khj Ã =BAG7Zp8l<8h:0\JFO>]Tn,AG7>8bKG8T\T8T=@ZpÁ 8LK'g=@?P?7>:+Z8
:']a8LA2FSWKG8h:H=@O>i]\TF0O[A(:S=@O>=@O>iNMq^>?BAG=@`>?@8MN8h:S]a^9KG8hH*H=@]A(:0O>\J8T]AGF
8T:0\(7R<8h:0\TF0Oj Ç FhgnWKGFM AG79=P]l]a8JAhnAG798KG8J\T8T=@Zp8JKl\h:SOR]a8T?@8T\JA
WF^K'<8h:S\TFOZ0:0?@^>8J]3:+A':*AG=@MN8n8h:S\L7Z0:0?@^98l\JF0KaKG8T]a`F0OH9=@O9iAGF
:lH9=B)8JKG8JO[A2<8h:S\TFO5n:SOH*KG^>O*AG7983:S?@iF0KG=BAG79MÆF0WÈ8J\JAG=@FO£[j ¬lAGF
H8JAG8JKGMN=@O>8=BAG]2\TFUF0K(H=PO>:SAG8`F]a=BAG=@FO5j2WAG7>8\TFUFSK(H9=@O:+AG8T]H8JAG8JKae
MN=@O98hH£WKGF0MÄADgFFSK3MNFSKG8bH9=@]AG=@O>\JAq]a8JAG]F0W<8h:S\TFO9]3:+KG8\J?PF0]a8
AGFb8h:S\L7FSAG7>8JKhng#8\h:0O]a8T?@8T\JA2AG7:+A:S]2AG7>8\TFSKaKG8T\JA\TFUF0K(H=PO>:SAG8j
AG798JKag=@]a8ng8\h:SO>O9F0A27:hZp8M3^9\L7\TFOH98JO>\T8=@O*AG7>8\TFSKaKG8T\JAae
O98T]a]F0WAG7>88T]AG=@Mb:+AG8hH4\TFUFSK(H9=@O:+AG8T]3»v:S?@AG79F^9i74AG798JCg=@?@??@=@op8T?BC
<8\JF0KaKG8T\JAAGFN:W_8Jg =@O>\(7>8T](¼Lj
FSK£MNF0]AKG8T\JA(:0O9i^9?:+KmKGFUF0MN]TnAG798T]a8\TFO>H9=BAG=@FO9]m:+KG8cK(:SAG7>8LK
]ª AaK(:0=@i07[AaWF0Kag:SK(H'AGFMN8T8JAg=BAG7>F0^9A"KG8hÊU^>=BKG=@O>i:2?:+KGi8O[^>M3<8LKF0W
<8h:S\TFO9]TjDOi8JO>8JK(:S?vn7>Fhg#8TZp8JKhn5:bMNF0KG8W_FSKGMb:0?":0`9`9KGF:0\(7g=@?@?
<8Z:S?@^:0<9?@8AGFcA(:S\Lo[?@8AG7>=@]l`>?P:0\T8JMN8TOUA`KGF<9?P8JM ^9]a=PO9i=PH98h:S]
WKGF0M AG7>8\T?P:0]a]a=@\h:S?4:+KaAaeip:0?@?@8JKaCc`KGF<>?@8TMN]3:0O>HMNFSKG8KG8T\T8JO[A
D]a8T:SKG\(7>?@=@i7UAG4`KGF<>?@8TMN]2=@OX\JFMN`>Â(:SAG=@FO>:0?i08TFMN8JAaKaCUj6FlF^9K
o[O>Fhg?@8hH9i08n)\TF0O>]AaK(:0=@OUAG]]a=@MN=@?P:SKAGFbF0^9K\JFMN`:S]a]]C]AG8TM7:hZp8
O>FSA*<8T8JOR]AG^H9=@8hH=@OAG798£?@=BAG8JK(:SAG^KG8n:0OHQAG79=@]*:SKG8T:=@]4F0`8TO
AGFQ=@OUAG8JKG8T]AG=@O9iR:0?@iFSKG=BAG7>M H98TZ8T?@F`>MN8JO[Ahn8T]a`8T\T=P:S?P?BC;W_FSK£O9FOe
KG8T\JA(:SO>i0^>?P:SKKGFUFMN]Tj
ÈF0MN8F0W"AG7>8H=@]a\T^>]a]a=@FO=@O*AG7>=@]`:S`8JK:S]a]a^>MN8T]»³`8JKG7>:0`>]A(:0\Le
=BAG?BC¼AG7>:SAAG798\TF0MN`:0]a]=@]798T?PH :+A%:0O>H`>:SK(:0?@?@8T?AGF2AG7>8,i0KGF0^>OH)j
67>=@]=@]O>F0Aq:W^>O>H>:0MN8JO[A(:S?KG8hÊU^>=BKG8TMN8TOUA g=BAG7XAG79=P]KG8hÊU^9=@KG8Le
MN8TOUAhnU:S?@?>g8O>8T8TH3=@],AG7>8FSKG=P8JO[A(:+AG=@FONg=BAG7'KG8T]a`8T\JA,AGFFO>8<8h:+e
\TF0Onpg79=P?@8F0AG798JKag=@]a8g#8O98T8hH3AG798F0KG=@8TOUA(:SAG=@FONg=BAG7'KG8T]a`8T\LA,AGF
:SA#?@8h:0]A,AG79KG8T8<8h:S\TFO9],AGF^>O9=PÊ[^98T?BCNH8JAG8JKGMN=@O>8AG798FSKG=@8TOUA(:SAG=@FO
Zp8T\LAGF0KhjlÈ[=PO9\T83g#8N7:hZp8':+A?P8T:0]AW_F0^9K<8h:0\JFO>]WF0K\TFUFSK(H9=@O:+AG8
H98LAG8JKGMN=@O:SAG=@F0OnAG7>=@]=@]2O9F0A7:+K(HlAGFN:S\T\TF0MN`>?@=@]a7j
§28JKG8nSg88J]a]a8TOUAG=:S?@?@Cq^>]a8%AG7>8%>WAG7<8h:S\TFOAGF2Z0:0?@=PH>:+AG8#AG7>8,\TFUF0Kae
H=@O:SAG8J]#F<A(:0=@O>8THb^9]a=@O>iAG7>8F0AG798JK#WF^9K UAG798KGF0<>^9]AGO>8T]a],F0W5AG7>=@]
]a\(7>8JMN8'=@]<:0]a8THmFOXAG7>8N:S]a]a^>MN`9AG=@F0OXAG7>:SAAG7>83`9KGF<>:0<9=P?@=BADCXFSW
AfgFq=PO9\TF0KaKG8J\JAKG8h:H=@O>i] \:0O>H /]2i0=@Z=@O9iKG=@]a8AGF3:0O>]g#8JKG]AG7:+A
\JF=@O>\T=PH8*=@]NO>8Ti0?P=@i0=P<9?@8jR¸OQ:SO:0?@F0i0CMN=@i7UAN7>8J?P`^>O>H98JKG]A(:SOH
g7UC*AG79=@]=@]2KG8h:S]aFO>:0<>[email protected] #FO9]a=PH98JK:l?@=@O>8]a8TiMN8JO[A2F0W,?@8TO>iSAG7 ÉDF=@O>=@O9ilAfgFl`F=@OUAG]Tn \ :SOH ] j Ã 8:+KG8AGF0?H*AG7>:SA:N`F0=POUA=PO
<8LADg8J8TO4AG7>8JMV=P]2:SA\:SOH(/]:Tg:TCWKGFMZ\:SOH)]KG8J]a`8T\Je
AG=@Zp8J?@CUjmfW<F0AG7 \3:0O>H /]l:SKG8=PO>H98T`8JOH98JO[Al»v:SOH=@O>\TFSKaKG8T\JAL¼
8J]AG=PMb:+AG8T]F0G
W \ :SO
H ] n=@A=P]79=@i7>?BCb^9O>?@=@op8T?BCNAG7:+AAG7>88JKaKGF0KG8TH
Z0:0?@^98T]g=P?@?\TF0KaKG8T]a`F0OHAGFqAG7>8]G:SMN8=H8TOUAG=@\h:0?5`F=@OUA
6.87>The
Viewfinder
8T?@F`8hHAG7>8YÅ5tx ¯ÂUxLsN:S`>`>?@=@\h:+AG=PF0OAGFH98JMNFO9e
Ã]AaK(:SAG8:hZpAG7>88lH9^>8JZp]a84
FSWAG7984?@FU\h:SAG=@F0±9OÁ :0O>HFSKG=@8TOUA(:SAG=@FO=POW_FSKGMb:SAG=@FO
`9KGF+Z[=PH98hH'<UCAG7>8]aF0WADg:SKG8\JFMN`:S]a]Tj"67>8^9]a8JKH8JO98T]%:]g#8T8T`
:0O9i?@
8 R:SOH£:*H9=@]A(:0O9\T:
8 [ :SOH£`F0=@O[AG]:*H8TZ[=@\T83KG^>O9O>=@O>ilAG7>8
¡=@8Jg>OH8JKN=@OAG798*H98J]a=@KG8THQH9=BKG8T\LAG=PF0OjQ67>8*¡2=@8JgO>H98JK'AG798TO
7>=@i07>?@=@i7UAG]AG798]a8JKGZ[=@\T8T]H9=@]a\TF+Zp8LKG8hHg=BAG7>=@O4AG798]g8TÀ]a8T\JAGF0Khj
5.2
Handling Diffractions
¸O>FSAG7>8JK2`F0AG8TOUAG=P:0?\h:0^9]a8qFSW%8JKaKGF0K2=@]2AG7>8H=@K(:S\JAG=@FO»³<8TO>H9=@O>i
:+A8hH9i08T](¼2FSW]aF^9OHg:hZp8T]:+KGF^9OHF<>]A(:S\T?@8T]Tj'È^>\(7F<9]A(:0\T?@8T]
Mb:TCNO9F0A<9?@FU\LoNAG7>88TOUAG=BKG8`:+AG7b<>^9A\h:0^9]a82AG7>82]a=@iO:S?5AGF<8TO>H5j
W[AG7>8%]a=Pi0O:S?[:SKaKG=@Z[=PO9i:SAAG798KG8T\T8T=@Zp8JK=@]<8TOUAhnhAG7>8TOAG798"MN8h:0]a^KG8
:SO>i0?P8lAGFAG7>8b<8h:0\JFOg=@?P?7>:hZp84:\TFSKaKG8T]a`FO>H9=@O>i8JKaKGFSKhj6798
H=B)8JKG8TO>\J8=@OH=@]A(:0O>\J8H9^>8AGF3<8TOH=PO9i'\TF0^>?PH4<8FO4AG798F0K(H8JK
FSWMN=@?@?@=PMN8LAG8JKG]Tn#g79=P\(7g=P?@?O>FSAN<8H98LAG8T\JAG8hH<UCcAG7>8MN8JAG7>F[H
H8T]a\JKG=@<8hHb:0<F+Zp8]a=@O>\T8AG7>88JKaKGFSK=@O'AG7>8H9=@]A(:SO>\T8gF^9?PHb<8AG798
]G:SMN82FSK(H98JK#F0W5Mb:0i0O>=BAG^H8»³F0K8JZp8TON?@8T]a](¼"AG7>:0ONAG7>8:S\T\T^9K(:S\JCNFSW
H=@]A(:0O>\J8MN8h:0]a^KG8TMN8TOUA=BAG]a8T?BWDj
6FI8TO>:0<>?@8AG7>=@]W_^>O9\JAG=@FO>:0?@=BADCUn*AG798;¡2=@8JgO>H98JKQ:0`9`>?@=@\h:SAG=@FO
ÊU^>8JKG=@8T]:NKG8J]aF^9KG\J8NH9=@]a\TF+Zp8JKaC*]a8JKGZp8JKhn)]a^9\L7X:0]2AG7>F]a8q`9KGF0`F]a8hH
=@O¢B¥0Vn n9¥h¬+n0AGFF0<9A(:0=@OAG7>8i0?@F<:S?9\JFUF0K(H9=@O>:SAG8T]"F0W9AG7>8#:+Z0:0=@?P:0<9?@8
]a8JKGZ[=@\T8T]Tj6FbW_:0\T=@?@=BA(:SAG8'AG798q<FUFSAG]AaK(:0`>`9=@O>il`9KGFU\T8T]a]Tn)AG798O>:0MN8
F0W%AG7>8]a8JKGZ8JKWF0KAG798q]a`>:0\T8=@]:HZp8JKaAG=@]a8hHFOAG7>8 ©2ª \(7:SO>O>8J?
<UCqAG798<8h:0\TF0O>]Tj 8:0?@]aF3:S]a]a^>MN8AG7>:SA,=PO>H9=@Z[=PH9^:S?>]a8JKGZ[=@\T8T],^>]a8
AG7>8J=@K3FhgO]aFSWADg:SÃ KG8*\JFMN`:S]a]qAGFF<A(:0=@OAG7>8T=BK'\JFUF0K(H9=@O>:SAG84=@Oe
W_FSKGMb:SAG=@FO5n":0O>HXAG7>:SAAG7>8LCX:H9Z8JKaAG=@]a8'AG7>=@]=@O9W_FSKGMb:SAG=@FO£AGF4AG7>8
KG8T]aF0^9KG\T8H9=@]a\TF+Zp8JKaCN]C]AG8TM*j AG7>8JKag=@]a8n:]C]AG8TM:0H9MN=@O>=@]AaK(:+e
AGF0K\T:0O:S]a]a=Pi0O*i?@F0<:0?\TFUF0K(H=@O:SAG8J]AGF38h:0\(74=@OH=@Z=PH^:0?"»³]A(:+AG=P\h¼
]a8JKGZ[=@\T8j
§2Fhg8TZp8LKhnAG798KG8J\T8T=@Zp8JK\T:0OH98JAG8JKGMN=@O982=BAG]FSKG=P8JO[A(:+AG=@FOg=BAG7bKG8Je
]a`8J\JAAGF':>d8hHbF0KG=@i=@O4^9]a=@O>i38T:0\(74F0WAG7>8<8T:0\TF0O>]=BA\h:0O7>8h:+K
WKGFM*n):SOH^>]a8Z0:0?@^>8J]2AG7:+A\JF=@O>\T=PH8AGFb<8AG7>8KG=@i7UAF0O>8j Ã 8
=@OUAG8TO>HAGFMNF[H9=BWC*F^9K\T^9KaKG8TOUAMN8LAG7>F[H*F0W#^>]a=@O>ilAG7>8]aMb:0?@?@8T]A
:SO>i0?P8:SOHlKG8J`>?P:0\T8=BAg=BAG74AG7>=@]bD`9?@^9K(:0?@=BADCN]a\(7>8TMN80j
67>8,¡=@8Jg>OH98LK"ÊU^>8JKG=@8T]AG798,]aFSWAfg:SKG8\JFMN`:S]a]W_FSK"\T^9KaKG8JO[AZ:S?Be
^>8J]#F0W)AG798KG8T?P:+AG=PZ8:SO>i?@8 Wg=@AG7NKG8T]a`8J\JA#AGFAG7>8<8h:S\TFO XNnpAG7>8
\TFUFSK(H9=@O:+AG8T]'F0W XNn%:0O>HmAG7>8b\TFUF0K(H=@O:SAG8J]'F0WAG7>8lH8TZ[=P\J8· ]3\T^Kae
KG8TOUA?@FU\h:+AG=PF0O3j,67>8JOnUAGFAG8T]Ag7>8LAG7>8JK:]a8JKGZ[=@\T8
m=@]#g=BAG7>=@O
AG7>8q^>]a8JKae]a`8T\J=@>8hH£]g#8T8T`m:0O>i0?@8nAG7983¡2=P8LgOH8JK8Jd[AG8TO>H9]AfgF
Zp8T\LAGF0KG]F0KG=@i=@O:+AG=@O>ibWKGFMVAG798qH8TZ[=@\T8· ]2\JFUF0K(H9=@O>:SAG8T] F0O>8AG:
F X
:0O>HmFO98'AGF
#j ª KGFMAG7>8J]a8lZ8T\JAGF0KG]TnAG7>8'¡2=P8LgOH8JK=@OZFop8T]
AG7>82\TF]a=@O98?:TgRAGFOHl:q^9O>=PÊU^>8]aF?@^9AG=@F0O W KXNn>g79=P\(7
=@]AG7>82:0O9i?@8F0WAG7>8]a8JKGZ[=@\T8
£g=BAG7lKG8J]a`8T\JAAGFAG7>8:0O>\(7>FSK<8h:+e
\TF0Oj67>8JO*AG7>8¡=@8Jg>OH98LK]a=@MN`>?BC`8JKaW_FSKGMN]:']a8JKG=@8T]F0W%\TFM'e
`:+KG=@]aFO>]2<8JADg#8T8TO*AG798KG8J?:+AG=@Zp83:SO>i0?P8Z0:0?@^>8T] Wn W[n):0O>
H 4AGF
AG8T]Ag798JAG7>8LK
m?@=@8T]#g=BAG7>=@ObAG7>8\T^9KaKG8TOUA#]g8T8T`:0O9i?@8n9:0O>H:+A:
H9=@]A(:SO>\T8]aMb:S?P?@8JKAG7>:0O4AG798^>]a8JKae]a`8T\J=@>8hH4H=@]A(:0O>\J8j
5.3
Beacon and
Compass Placement
AG7:+A:q`KGF[H9^9\JAG=@FO9e]AfC9?@8H98T`9?PFhCMN8TOUAFSWAG798
\JFO9MN8`FS:SW]aAG]7>=@O982W=PK(]a:S]a]^9Aa8TKG]
^>\JAG^KG8M3^9]A`>:hC\J?PF0]a8:SAaAG8JO[AG=@F0OqAGF=P]<8T:0\TF0O
`9?P:0\T8TMN8JO[Ahj ª KGF0M ¶,ÊU^>:SAG=@FOQ¥h[n=BA=@]q\J?P8T:SKAG7:SAAG798N8JKaKGF0K=@]
?P:+KGi83g798TOMWN=@]?P:SKGi08n:SOH:0?@]aFlg7>8TO =@]\J?PF0]a83AGF j 7:+A
g#8gF^9?PH4?@=Po8=P]AGF'8TO9]a^9KG8AG7>:SAhn>WF0K8TZp8LKaC4\TF0MN`:S]a]?@FU\h:+Ã AG=@FOn
AG798JKG8b=@]3:+Aq?@8h:S]A'F0O>8b<8h:0\JFOcg7>F0]aI
8 W4WKGFMÄAG7>:SA?@FU\h:SAG=@FO=@]
]aMb:S?@?P8LKAG7:SO¤U®NH98TiSKG8T8T]TjDO:H9H9=BAG=@FO5ng8gF^9?PHX:S?@]aF4?@=@op8AGF
8JO>]a^9KG8AG7:+AAG7>8JKG82=@]:SA?@8h:S]AFO>82Z[=P]a=@<9?P8<8h:0\TF0Olg79F]a
8 > ' =@]
, §8JKG8XD\TFSKaKG8T\JAGbKG8JW_8LKG]AGFl:H=P]A(:SO>\T8AG7:+A=@]`KGF`FSKaAG=PF0O:S?"AGF
AG798:0\JAG^>:0?H9=@]A(:0O9\T8j
=@i^KG8 ¥+ ]a7>Fhg] : ]a\JKG8J8TO \T:0`9AG^KG8 FSWAG7>8 `9KGFSAGF0ADC`8
¡ª =@8Jg>OH8JKN:S`>`>?@=@\h:+AG=PF0Oj¸ Mb:S`F0WAG7>8l]a8JKGZ[=@\T84:SOH<8h:S\TFO
¥¥
?@F<>:0?? F]a=BAG=@FO>=@O9ilÈ[C]AG8TMÆ» Q,È>¼@¥h[n¥+®+vng7>=@\(74=@]=@O>\JKG8h:S]e
@= O>i0?@C<8J=PO9i^>]a8hH=@O\J=PZ[=@?@=P:0O:0`>`9?@=P\T:SAG=@FO9]N=PO:0H>H9=BAG=@FOAGF=BAG]
AaK(:H=BAG=PF0O:S?#MN=@?@=@A(:+KaCX^>]a8j Q,ÈmH9FU8J]O9F0A`KGFSZ[=PH98qAG7>8NH8Ti0KG8T8
F0W`9KG8T\T=@]a=@FOqKG8hÊU^>=BKG8hHWF0K%MNF<9=@?P8:0`>`9?@=P\T:SAG=@FO9]%=@O>H9FUF0KG]"<8T\T:0^>]a8
F0W)AG798?PFhg
]a=@iO:S?]AaKG8TO9i0AG7np7>=@i7 ª O>F=@]a8n:SOHqAG798KG8 8T\Le
AG=@FO9]F0W ©2ª ©ª ]a=@iO>:0?@]H9^98AGFbAG798`9KG8T]a©2
8TO9\T8F0W,MN8JA(:0?@?@=@\qF0<ÉD8T\JAG]Tj
k#^9?P^9]a^;xLy IH98T]a\LKG=P<8l:*?@Fhge\TF]AN?@FU\h:+AG=@FO]C]AG8TMÄW_F0K3FÂae
H9FUFSK^>]a8N µ+~vn>² g798JKG8AG7>88TO[Z=BKGF0O>MN8TOUA=@]=@O>]AaKG^>MN8JO[AG8THbg=BAG7:
O[^>Mq<8JK"F0W9d98TH ©ª ]A(:+AG=PF0O>]%AG7:SA%`8JKG=@F[H=P\T:0?@?BCNAaK(:0O>]aMN=BA"AG7>8J=@K
^>O9=PÊ[^98DºE:0O>H*`F]a=BAG=@FO5j6798KG8J\T8T=@Zp8JKG]2^>]a8
\TF0O>O>8J\JAG=@Z=BAfC
AGFm8J]AG=PMb:+AG8AG798T=BKb`F]a=BAG=@FOKG8J?:+AG=@Zp8*AGFXAG7984o[©O>ª FhgO>d8hH ©ª
]A(:SAG=@F0O>]Tj
D
ºF07>8JKaAfCYxLy IRMNF[H98T?AG798`F]a=BAG=@FO8T]AG=@Mb:+AG=PF0O`9KGF0<>?@8TM =@O
:HX7>FU\N]a8TO9]aF0~K² O>8LADgFSKGo[]:0]:\TF0O[Zp8JdXFÀG=PMN=@¨h:+AG=@FOm`KGF<9?P8JM*n
]a7>Fhg=@O>icAG7>:SAb^9OH98LKb]aFMN8*\TF0OH=@AG=@F0O>]b=BA=@]b`F]a]a=@<9?P8WF0KbAG7>8
O>F[H8T]AGFH=P]a\JFSZ8JK"AG7>8T=BK"`F]a=BAG=@FO9]%KG8J?:+AG=@Zp8AGFFO98:0O9F0AG798JK@¥TSvj
È9:hZ[Z[=PH98T]lxLy IbH98T]a\JKG=@<8b:SO>F0AG798JKq:0`9`9KGFp:S\L7XAGF4AG7>=@]`KGF<>?@8TM
AG7:+AKG8T]a8TMq<>?@~8T² ]F^K\TFUF0K(H=PO>:SAG88T]AG=@Mb:SAG=@F0OY]a\L798TMN8cFSWlÈ8T\Le
AG=@FOQ[j ¬j Ã 848Jd`8T\JA3Z:+KG=P:0OUAG]'F0W2AG7>8T]a84:0`9`9KGFp:S\L798T]3AGFX<8*:
iFUF[H£]A(:SKaAG=@O>i`F=@OUAW_FSK=PO9]AaKG^>MN8TOUAG=@O>ib<8h:S\TFO9]=POXF^K8TO[Z[=Be
KGFO9MN8TOUA3g=BAG7>F0^9AN7>:hZ=@O9iAGFX`9KGF0i0K(:SM 8h:0\(7<8h:0\TF0Og=BAG7=BAG]
?@FU\h:SAG=@F0On%<>Âq`KGFiSK(:0MNMN=@O>iFO>?BCm]aFMN8NF0WAG798TM :0O>Hm7:hZ[=@O>i
AG7>8FSAG7>8JKG],H9=@]a\TF+Zp8LK,AG798T=BK#\TFUFSK(H9=@O:+AG8T],WKGFM½AG7>8FSAG7>8JK,<8h:S\TFO9]
=@O4AG7>8J=@KZ[=@\T=@O>=BAfCUj
?%.@' %.$@)FK,
<*U#'7=$ ))01 L
%&$ 'ZC H ,$ 8, 41'T1(+$ , )#O0 %&4'9 ,?63$ N$ ')7P,F$'0 F1(=/#/7 1'P4$/L
7$')( #<A,4 , $'0-;@$ 013($ (A$@
27) $ (
$ ')7 1'%./$ (/(>%.)'54% 0%&G5<>1(C
?@FU\h:+AG=@FO>]=@]bH9=@]a`>?P:TCU8hHFOQAG798*?@8JWAl`:SO>8T?³j6798*AG=@`:0O>HAG798
<F[H[C*FSW%AG798`>=@8Je]a7:S`8>i^9KG8Mb:+KGo]AG7>8H8TZ[=P\J8?@FU\h:+AG=@FO£:0OH
=BAG]q\T^9KaKG8TOUAq]g8T8J`Q:SO>i?@8jcÈ8LKGZ=@\T8J]qAG7:+A':+KG8lg=BAG79=POAG798l\J^9Kae
KG8JO[A']g8T8T`Q:0O9i?@8:0`9`8h:SKbF0OAG798KG=@i7UAN`>:0O98T?³j6798*<F0AaAGF0M
`>:0O98T?H9=@]a`9?:TC]2AG798q\JFUF0K(H9=@O>:SAG8':SOH:SO>i?@8qZ:S?P^98T]2KG8J`F0KaAG8hH<UC
AG798]aF0WADg:+KG8\TFMN`>:0]a]Tj
67>8q#F0O>]AG8T?@?P:SAG=@FO]C]AG8TMV^9]a8T]:q\TFMq<>=@O:+AG=PF0O*F0W%:S\T\T8T?@8JKGF0M'e
8JAG8JKG]Tn[iSC[KGF]Tn9:0O>H'^>?BAaK(:0]aF0O>=@\]a8TO9]aF0KG]#AGF8T]AG=@Mb:+AG82`F0]a=@AG=@F0O4:SOH
F0KG=@8TOUA(:+AG=PF0O½B¥¥Jvj =@op8,KG=P\(op8JAhnAG798#FO9]AG8T?@?P:SAG=@FORKG8T?@=@8T]lFO
:0O£:0\LAG=PZ8']a8JAFSW^>?BAaK(:S]aFO>=@\N<8h:S\TFO9]AGF4H8JAG8JKGMN=@O>8AG7>8q=@O>=BAG=P:0?
AaK(:0\(o[=@O>il`F]a=BAG=@FOcFSW,AG798'H98JZ=@\T83:0O>HAG798TOXKG8J\T^9KG]a=@Zp8T?BCKG8J>O>8T]
AG7>8%F0KG=@8TOUA(:+AG=PF0Oq8J]AG=PMb:+AG=@FO^>]a=@O>i=@O9WF0KGMb:SAG=@F0Oi:SAG798JKG8hH<[C2AG7>8
=@O>8JKaAG=P:S?]a8TO>]aFSKG]Tj§Fhg#8TZp8JKhnAG7>8AG=@i7UA2\TFUF0K(H=@O:SAG=@F0OAG7>:SA=@]KG8Le
ÊU^>=BKG8hH<8JADg#8T8TO3AG798KG8T\T8T=@Zp8JKG]%:SOHqAaK(:SO>]aMN=BAaAG8JKG]"F0WAG79=@]%]C]AG8TM
Mb:0o8T]=@A^9O>]a^>=BA(:S<>?@8W_FSK?P:SKGi08Je]a\h:0?@8q=PO>H9FUFSKH8T`>?@FhCMN8TOUAhj"fA=@]
:0?@]aF^9O>\T?@8h:+KAG7:SAAG79=@]%\T:0O3<8=@MN`9?P8JMN8TOUAG8hH=PO3:7:SOH7>8T?PHe?@=@op8
W_FSKGMVW³:0\LAGF0Khj
7.:0OUARelated
Work
xLy IP· ],¸2\JAG=@Zp8k:Hi8]C9]AG8JM*npH8TZp8T?@F`8TH3^>]a=@O>i=@OWK(:SKG8TH
Ã?@=@O>o[]Tng
~:S]² FO>8F0WAG7988h:+KG?P=@8T]A=@OHFUF0K]C]AG8TMN]#WF0K`F]a=BAG=@FO=@O9e
W8JKG8TO9\T8b S¹SvjAG]2:+KG\L79=BAG8T\JAG^9KG8=@O>]a`9=BKG8hHW_ÂG^9KG8i8JO>8JK(:+AG=PF0O>]=@O9e
\J?P^>H9=@O>iAG798k:SA,]C]AG8TM¾ 0µ+):SO>
H "=@O F=@OUAh· ]#?@FU\h:S?`F]a=BAG=@FO9=PO9i
]C]AG8TMB¥h [n4 Svj"DO'AG798T]a82:SKG\(7>=BAG8T\JAG^KG8T]TnUAG7>87:+K(Hg:SKG82A(:Si:SAae
A(:S\L798hHAGFlMNF0<>=@?@8'H8TZ[=P\J8T]=@]:0\LAG=PZ8n:0OH*KG8T]a`F0OH]AGF4ÊU^98JKG=@8T]
WKGFM :m\T8TOUAaK(:S?\TF0O[AaKGF0?@?P8LK:0O>HQ?@FU\h:SAG=@F0O H9:SA(:S<:0]a8X:S<F^9Al=BAG]
g798JKG8h:S<F^9AG]Tj Ã 79=@?P8AG7>8qk:SA]C]AG8TM^>]a8J]:l\TF0M3<9=PO>:SAG=@FOFSW
:0O>H£^9?@AaK(:S]aF^9OHXAGF48T]AG=@Mb:SAG8NH=P]A(:SO>\T8B¥J¤9n%0µ+vn "=@OF=@OUA
©2
^9]aª 8T]"]a`9KG8h:0He]a`8T\JAaKG^9M K(:0H9=@F]a=@iO>:0?@]#:SOHM3^>?BAG=@`>?@8#:0OUAG8TO>O>:08:+A
AG798N\TFOUAaKGF0?P?@8JKAGF`9KGFU\J8T]a]qMN8J]a]G:0i8J]WKGFM :A(:0ij O98'F0WAG798
`KGF<9?P8JMN]g=@AG7XAG7>8T]a8':SKG\(7>=BAG8T\JAG^KG8T]=P]AG7>:SAAG798JCAaK(:0\(o^>]a8JKG]Tn
:SOH4?@8h:0HAGF']a=@iO9=B\h:SO[A`KG=PZ0:0\LC\JFO>\J8JKGO>]B¥ +j
67>8§2=Pk:0?@?>]C]AG8TM^>]a8T]"FÀGF0e8T?@8T\JAaKGF0O>=@\AaK(:0\(o[=PO9iF0W7^9OH[KG8hH9]
F0KAG7>F0^>]G:SOH9]F0W=@OWK(:SevKG8hH ¶%º]qMNF0^>OUAG8hH£=@Oc]a`8J\T=P:0?\T8J=P?@=@O>i
`:SO>8T?@] S SvjcA3`KGF+Z=PH8T]qK(:S`>=PH^>`)H>:+AG8T]F0WKG8T\T8T=@Zp8JK3`F]a=BAG=@FO
:0O>HlFSKG=@8TOUA(:SAG=@FO5n9<9^9A,KG8hÊU^>=BKG8T]AG7>8=@O>]A(:S?P?P:+AG=PF0O*F0W?P:SKGi8:SKaK(:TC]
F0W ¶%º]"=@O'AG7>8\J8T=@?P=@O9iq:SOH3\T:SKG8JW^>?@?BCNMb:0\(7>=@O>8THq\h:SMN8JK(::SA%AG7>8
\T?@=@8TOUAhn9g79=@\L74g=@?@?]a=@i0O>=B\h:SOUAG?@C=@O>\JKG8T:0]a8H98T`9?@F+CMN8TOUA\JF]AG]Tj
#FMNMN8LKG=P\T:0?Mb:0i0O>8JAG=@\XMNF0AG=@FORAaK(:S\Lop8LKG]*7:hZp8X<8T8TO^>]a8TH;=@O
Z[=BKaAG^:0?KG8h:S?P=BAfC:SOH;]a=PMq^>?P:SAG=@F0O½:0`9`>?@=@\h:SAG=@FO9]]a^>\(7Y:0]798h:H[e
MNF^9OUAG8hHYH9=@]a`9?:TC]£:0OHY<9=@FMN8T\(7:SO>=@\MNF0AG=@FO½\h:S`9AG^KG.8 ½¸]e
\T8TO9]a=@FO½ +vnÈ[A(:+KaAaK(:0o S¤0vn:0O>H¸2^KGF0K(:Q ¬S:SKG8*AG7KG8T8`9KGF[H[e
^>\LAG]:hZ:S=@?:S<>?@83AGF[H9:hCUj67>8JC*`9KGF+Z[=H8KG8h:0]aF0O:0<9?BCm:S\T\T^K(:SAG838J]e
AG=@Mb:SAG8T]F0W"AG798`F0]a=BAG=PF0OX:0OH*FSKG=@8TOUA(:SAG=@FOF0W"AG798A(:+KGi8JAF<[É8T\LA
<UC]a8TOH=PO9iMb:0i0O>8JAG=@\`9^>?@]a8T]%:0O>H'H98LAG8T\JAG=@O>iAG798\(7:0O9i8FSW8T?PH
]AaKG8TO9i0AG7q:0?@FO9iAG79KG8T8,F0KaAG79FiF0O:S?>:+d98J]Tj"67>8T]a8#]C9]AG8JMN]^>]a^>:0?@?BC
KG8hÊU^>=BKG8T]*:\J8TOUAaK(:0?@=@¨T8hH\TFUF0K(H=PO>:SAG=@FO <8JADg#8T8TORAG7>8XMb:0i0O>8JAG=@\
AaK(:0O9]aMN=BAaAG8JKG]:0O>HXKG8T\T8J=PZ8JKG]:0O>Hm:SKG8N]a^9]a\T8TÀG=P<9?@83AGF*Mb:0i0O>8JAG=@\
=@OUAG8JKaW_8JKG8JO>\T8WKGF0MEAG798`KG8T]a8TO9\T8F0W5MN8JA(:0?@]%F0K#F0AG7>8LK#\TF0OH^>\JAG=@Zp8
Mb:SAG8LKG=:S?@]=@ObAG79828JOZ[=BKGFO9MN8TOUA@¥T¹Svng7>=@\L7b\h:S^>]a8T]#`9KGF<9?@8TMN]#=@O
Mb:0OUCb=@OHFUF0K8TO[Z[=BKGFO>MN8JO[AG]Tj
k#:07>?[:SOK
H :0H9Mb:0O>:0<97:0OH8T]a\JKG=@<8 ¸º¸ ®+vn0:0O=@OHFUF0K
e
>< :0]a8hH?@FU\h:+AG=PF0Oq]C]AG8TMRAG7>:SA^>]a8T]:0O© :0?BKG8h:0H© C[e8Jd=@]AG=PO9iH>:SA(:O9©28Jª Aae
g#F0KGoAGFl8T]AG=@Mb:SAG83`F0]a=BAG=PF0Oj3§8JKG8n)AG798 ©2ª ]a=@iO:S?"]AaKG8TO>iSAG7£=@]
^9]a8hH:0]:NMN8h:0]a^KG8FSW,H9=@]A(:0O9\T8<8JADg#8T8TO ©ª AaK(:SO>]aMN=BAaAG8JK:0OH
:*KG8T\J8T=@Zp8JKhjX67>=@]q=POW_FSKGMb:SAG=@FO=@]qAG798TOc^>]a8THmAGFX?@FU\h:+AG84:^9]a8JK
^9]a=@O>i£AaKG=P:SO>i^9?P:SAG=@FO5n#ADC`9=P\T:0?@?BC^>]a=@O>i£:0O ©ª ]a=Pi0O:S?]AaKG8JO>i0AG7
Mb:S`4F0<9A(:0=@O98hH4<UCl:3`9KG=@FSK2=@O9]AaKG^>MN8TOUA(:SAG=@F0O4`9KGFU\J8T]a]Tj
^K"\TFMN`>:0]a]]C]AG8TM½8TO97:SO>\T8T]AG798\h:S`:0<9=@?P=BAG=@8T]%F0WAG798,KG=@\Lo8JA
@? FU\h:+AG=@FO]C]AG8TM*ng79=P\(7^>]a8T]*:\JFM3<9=@O:SAG=@F0O;FSW3`>:0]a]a=@Zp8KG8Je
\J8T=@Zp8JKG]*»³\h:S?@?P8THEf?P=@]AG8TO98JKG]aU¼q:0OH:S\JAG=@Zp8<8T:0\TF0O>]Tn%g7>=@\L7`KGF0e
Z[=PH98=@O9WF0KGMb:SAG=@F0O:S<FÂ:]a`:S\T8q SSvj =@op8AG7>82k:SA#]C]AG8TM*nU=BA
^9]a8T]:'\JFM3<9=@O:SAG=@F0OF0W
:SOH*^>?BAaK(:S]aF^>O>H4AGFN8T]AG=@Mb:SAG8`F]a=Be
AG=@F0On5<>Â^>]a8J]M3^9?BAG=P`9?@8q©^9ª ?@AaK(:S]aFO9=P\KG8T\T8T=@Zp8LKG]?@FU\h:SAG8hHX\T?@F]a83AGF
8T:0\(7FSAG7>8JK,AGF=@OW_8JKFSKG=@8TOUA(:SAG=@FOlFO:MNF<>=@?@87:0O>H9798T?PHlH8TZ[=@\T8j
F^>MN8J?P=@FSAG=P]qxLy I,H8T]a\JKG=@<8AG7>8=@MN`9?P8JMN8TOUA(:SAG=@FOlF0W%:SO4F0KG=@8TOe
(A© :SAG=@F0Oq]a8TO9]aF0KAG7>~:SA² ^9]a8T]:«:0?@Mb:0O?BAG8JKAGF2\JFM3<9=@O>8,:\TF0MN`:S]a]
:0O>HKGF<F0AF[H9FMN8LAaKaCg=BAG73:SO:0<>]aF0?@^9AG8#FSKG=@8TOUA(:SAG=@FO]a=@iO:S?UWKGFM
:f]a^>O]a8TO>]aFSKG3 [¥Lvj%67>=@]]C]AG8TMg#F0KGo[]^>O>H98JKo[=PO98TMb:SAG=@\,\TFOe
6798<8T]Aaeo[O>FhgO]C9]AG8JM W_FSK"FÂ(H9FUF0K"^9]a8#=@]AG7>8,]G:SAG8T?@?@=BAG8Je<:S]a8hH
¥+
Y ¸º¸ ¸O
D" O9efk##U^9=@?H[ =@O> i ©2ª e<[:S ]a8hH ]a8JK\U FU\h:+AG] =PF0 O© :0O>H46©K(:S\Lo[=@O>i
È[C]AG8TM*j[DO / szhuI A?^*^*^ AM_a` 4rb4c1 »v68T?Bef¸2Z[=@ZnD]K(:08J?vn
¦*:SKhj)S0p¼Lj
¹+ " K &
¯9y³sazhÂ:9uJy³tvz0¯£yzby x xaz0s z ^ s(saz0s(j
¸H>H=@]aFO9d e Ã 8TA ]a?@8JCUn © 8h:0H9=@O>in¦*E ¸n¥E p®0µ[j À
µh " X X&TX
KGY &f ' #F]A Â(H9FUF0. K 5FU \h:0?@=@¨h:SAG=@F0 O ª F0Kg ¡, 8LKaC
Q## ÈUef?@8T]aK
] e5F+ gY
ÈMb:0?@?)º8TZ[=@\T8T]Tj>68T\(7j 8T`j>+eµ0&[n)#FMN`9^9AG8JK2È[\T=@8TO>\J8
º8T`:+KaAGMN8TOUAhn O9=PZ8JKG]a=B© ADClF0W%È[FÂG7>8JKGO*:0?@=BW_F0KGO9=P:n5¸2`Khj
00j
+q#FUF?P6FhgOj 7:8:8+;*=?>+>$@:@:@*A?D+I:I:S<89I$@:F*AP7+;*AMD+ITNU> n"S[j
+i
hj+ & K&
&TGm
p$o % ¸2 !O4k!¸ KG\(7> =BAG" 8T\J AG^' KG8W_FSK!:'l È8T!\T^. KG8È8LKGnZ =@\T8 º=@]a\TF+Zp8J KaC4È8JZ KGZ[ =@\T8j9DO / szhu I*qSy 0!r 1r154cs A br 4*1
r%z0¯ I5»È8h:+AaAG?P80n Ã ¸n¸^>i9j)¥ ..E ¼Ln`>`5j>S¤ U¬p®Uj
B¥h+ U, (
t&f o wv X ( #FO[Zp8Jd
ug=BKG8T ?@8T ]a]]a8JO>]aF0K O98JADg# F0KG o[]Tj>fO
`g F]a =BAG=@F O8T] AG=@Mb !:S[AG=@F0O4=@O4
/ szhu I A?^*^c^ AM_a` 4br 4c1 »v¸2`KG=@?S¥h¼Lj
B¥¥L
x*y z
K v
#FO>]# AG8J?P?P!:+AG=PF0 !?O '¸ Ã =PH98Le © :0O9i{ 8 Ã =@KG8J?P8J]a[}] | |9| u ¦4F0AG=@FOeD65K(:0\(o=@O9ilÈ[C]AG8TMWF0K2¸2^9iMN8TOUAG8hH © 8T:0?@=BADC:0O>H
¡=BKaAG^:S?È[8JA¸2`9`>?@=@\h:SAG=@FO9]TjfO / sazhu I0!
r 132 A$~~c 0 /
» KG?:SOHF9n ª %n ^>?BCX¥ .0 p¼Lj
B¥+hi
vKUz
6798 ?PF0<:S)
? F]a=BAG=@FO9=@O>ilÈ[C]AG8TM*j A?^*^*^
2 } xauJy³s [
{ - S n5¥+4»³º8J\T8TM3<8LK¥ &¬p¼Ln¬¹ p¤UµUj
B¥h¬+i
v h (n
vX
#$ tz d È=@MN`>l ?@8 È[8JKGZ[=P\J8nº=@[ ]a\T F+ Zp8JKaH
d KG FSAG FU\TF? ¥j j
C "
®h
H=BAG=PF0O>]Tn):SOH4=BAG]2:0`9`9KGFp:S\L74Mb:hC<8\TF0M3<>=@O98hHlg=BAG7X,KG=@\Lo8JA2AGF
=@MN`KGFSZ8F^K]C9]AG8JM*j
8.
Conclusion
6798,KG=@\(op8JA#\TFMN`>:0]a]#]C]AG8TM¢H98J]a\JKG=@<8hHN=PONAG79=P]%`:S`8JK#KG8J`F0KaAG]
`F0]a=BAG=PF0O*:SOH'F0KG=@8TOUA(:+AG=PF0O4=@OHFUF0KG]Tn[W_FSK:7:SOH9798T?PH5nUMNF0<>=@?@8H8Je
Z[=@\T8n#:0O>Hc=@O9W_FSKGMN]':SO:S`>`9?P=@\h:+AG=@FOKG^>O>O9=@O>iFOAG7>8lH8TZ[=P\J8FSW
AG798`F]a=BAG=@FO:0OH'FSKG=@8TOUA(:SAG=@FOb=@Ob:?PFU\T:0?\TFUFSK(H9=@O:+AG82]C]AG8TME8T]e
A(:S<>?@=@]a7>8hH<UCAG7>89d8hH]a8JAbF0W<8h:0\TF0O>]Tj6F£F0^9Kbo[O>Fhg?@8hHi8n
AG79=@]=@]AG798*>KG]A7:SOH9798T?PHe=@OUAG8Ti0K(:+AG8hHQ]C]AG8TM AG7:+A4`KGF+Z=PH8T]
:\TF0M3<>=@O>:SAG=@FORFSW3FSKG=P8JO[A(:+AG=@FO :0OHR`F0]a=@AG=@F0O =@O9WF0KGMb:+AG=PF0O;AGF
g=BAG79=POQ:W8JgH98Ji0KG8T8T]NFSWAG798lAaKG^984Z0:0?@^>8=PO>H9FUFSKG]TnMb:0o[=@O>iX=BA
:SO;:SAaAaK(:0\LAG=PZ8XAG8T\(7>O9F?@FiSCW_FSK*Z0:SKG=@F^9]4\TF0OUAG8Jd[AaeD:Tg:SKG8X`8JKGZ:+e
]a=@Zp8#\TFMN`9^9AG=@O>i2:0`9`>?@=@\h:SAG=@FO9]Tj"fA"HFU8T]"O>FSAKG8hÊU^>=BKG8?P:SKGi08F0KW_:0]A
^9]a8JKqMNF0AG=@FO9]3:SOH£g#F0KGo[]38TZ8TOmg7>8JO:4AaK(:H9=BAG=@FO>:0?Mb:SiO98JAG=@\
\JFMN`:S]a]W³:S=P?@]Tj#67>87>:SK(Hg:SKG8\JFO9>i^K(:SAG=@FO*\JFO>]a=@]AG]F0W:qMN=Be
\LKGFU\TFOUAaKGF?@?@8JKhnFO98 ©2ª KG8J\T8T=@Zp8JKhn):SOH*Z8^>?BAaK(:0]aF0O>=@\qKG8T\J8T=@Zp8JKG]
`9?P:0\T8hH=@OX:D¡l]a7:S`83:'W8Jg½\T8TOUAG=@MN8JAG8JKG]2:0\LKGF]a]Tn5`9KGFU\T8J]a]a=PO9i
¤¥h l¦4§¨ ©2ª H>:SA(:3:0OH*¤'«§¨^9?@AaK(:S]aFO9=P\]a=@iO>:0?@]]a8TOUAWKGF0M
:S\JAG=@Zp8<8h:S\TFO9]Tj
6798,\(7:S?@?P8JO>i8J]=@OqH8JKG=@Z[=PO9iF0KG=@8TOUA(:SAG=@F0OWF0K:]aMb:S?P?pH98TZ[=@\T8,:SKG=@]a8
WKGFMÄAG7>8NO98T8hH£WF0Kq]a^><ef\J8TOUAG=PMN8LAG8JKH9=B)8JKG8JO[AG=P:S?H9=@]A(:SO>\T8b8T]AG=Be
Mb:+AG8T]Tn5:0O>H4WKGF0MËAG7>8O98T8hH4W_FSK:0\J\T^9K(:+AG8q`F0]a=@AG=@F0O£8T]AG=@Mb:+AG=PF0Oj
H*AG7>89KG]A`KGF<>?@8TM¾^9]a=PO9ibM3^>?BAG=@`>?@8\h:+KG8JW_^9?@?@C*`>?P:0\T8TH
ÃKG8J\T88T=@]aZpF8J?@ZpKG]T8hn2
H98LKG=PZ[=@O>icAG798Mb:SAG798TMb:SAG=@\h:S?\JFOH=BAG=PF0O>]bW_FSK*`>?P:S\T8Je
MN8JO[Ahj Ã 8]aF?@Zp8THAG798]a8T\TF0OH`9KGF0<>?@8TM¾<UC*H8TZp8T?@F`9=@O>ib:'`F]a=Be
AG=@F0Oq8T]AG=@Mb:+AG=PF0OAG8T\L79O>=PÊU^>8AG7:+A\TF0MN`8TO>]G:+AG8T]WF0KAG798,^9O>o[O>FhgO
Z8T?@FU\T=BADCFSW,]aF0^>O>H=@O:SOX8JOZ[=BKGFO9MN8TOUA<[CF<9]a8JKGZ[=@O>ib`9KGF0`:0i:Se
AG=@F0OAG=@MN8T]q:0O>Hc8Jd`>?@=@\T=BAG?BC\h:0?@\T^9?P:SAG=@O>iX=BAhj ^K38Ld9`8LKG=PMN8JO[A(:S?
KG8J]a^>?BAG]']a7>Fhg AG7>:SAqg84\T:0OF<9A(:S=@O:SO>i0?P8J]'AGFg=BAG79=PO:0<F0^9A'¬
H8Ti0KG8J8T]2FSWAG7>8AaKG^98Z0:0?@^>8=@O*MNF0]A`9K(:S\JAG=@\h:0?]a8JAaAG=@O>i]Tj
O © 8JCO>F?PH]WF0KN^9]a8JW_^9?H9=@]a\T^>]a]a=@F0O>]NFOAG798
Acknowledgments
ÃMNFS8lAG=@AGZ7>:+:0AGO9=PF0o Omª W_K(FS:0KqO9AGo[79?P=@8b
,KG=@\Lo8JA\TFMN`>:0]a]Tj 8'AG7:SO>oº:hZ[=PHm¸2Oe
H8JKG]a8TO5n © ^>= ª :SOnÈ[AG8T`97>8TO :SKG?P:SOH5n Ã :+KG]eD¸op
8 :SKG¨TF0On:0OH
È[^>\(7>=BAaK(: © :0Mb:0OcWF0K3]a8TZp8JK(:S?7>8T?@`W_^>?#\TFMNMN8TOUAG]:0O>Hc]a^>i0i8T]e
AG=@F0O>]FO*`KG8TZ[=@F^>]Zp8LKG]a=PF0O>]F0WAG7>=@]`:0`8LKhj
B¥T¤S
9.@¥LReferences
!
&
)
*
(
,
6
9
7
8H98T]a=@iO*:0OH
% 8TOUA( :+AG=P F0OFS' W%:0 O* =@OUAG8TOUAG#+=@F# O>:0?5O. :0 MN=@O9i3]C]AG8TM*jDO
=@" MN`>#$?@8TMN
0 r!132 À { } z tC[{Ëz0¯54 } xLs ~ y³t¯;?62 À0 yfxL{
/ sasLzht_¯uIuJt
x »³«=:Tg:07*f]a?:SOH)nÈ92n>º8J\j¥.&p¼Ln
`>/ `5j)¥h }¹ ² S ¥j
798:8<;*=?>:>$@+@:@*A?B9C+D<E<FGC:H<I$FKJK8:E-DL7*AMD<ION>
»È8h:+AaAG?P80n Ã ¸n¸^>i9j5¥&.¼Lj
Y K (n GKz!z!
' 5|9| ha & #+# ~ z = |/ " z t_ y³tvz0¯9Ut_¯;?2 yfxL{ u' xa z0 s
¯Â / s #<uJy³# tvu(x E !` . z: [sLy ² ^ ~ÂS² t_y³tvz0¯9 j)È`KG=@O>i8LKaÀSef¡% 8JKG?P:0in¥E .µ[À j
~
~
E
B¥h¹+oi G :S?@=P<K(:SAG=@FOFSW"¶%?@8T\LAaKGFMb:0i0O>8JAG=@\
6K(:0\(o[=PO9 i'º8T% Z[=@\T8T]T] j Å5t_sLy x ty x x sau E
~² ~² À
~ E
x B0x ² z } {NxL¯>yE ~ ¯Âi0 }p}² tvu ~ y³tvzS¯ a »¥..¼Ln¥h¬& >¥+®0[j
B¥+µh dCi08TO479FMN8`>:0i08j 798+8+;*=?>:>+I<::R9E$F*A?S9D:CANH$8nAE+Q+VK> j
B¥h +%=@O>`F0=@O[A79FMN8`>:0i80j 798+8+;*=?>:>L@:@:@*AP;KHLF:;KI9HOF98KD+IA?D+ITN> j
B¥+®h
679=@]qgFSKGo£g:0]qW^>O>H98hHm<UC 66EDO>\0j*^>O>H98JKAG7>8 66#eD¦46
KG8J]a8h:SKG\(7\TF?@?P:0<FSK(:SAG=@FO5n<UÇ2Ç \T8JKfO>\j@n9º8T?BA(:'¶"?@8T\JAaKGÇ FO9=@\T]fO>\j@n
§ ½#F0KG`5j@n Ç 66¢fO>\j@n Ç F0o[=: © 8T]a8h:+KG\L7#8TOUAG8JKhn%:SO2
H "7>=@?@=@`>]
T
8
a
]
h
8
+
:
G
K
L
\
£
7
>
^
>
O
9
H
J
8
K
G
A
9
7
b
8
4
¦

6
KGF+É8T\JA
[
d
C
i
T
8
X
O
`
+
:
a
K
G
A
>
O
J
8
G
K
a
]
©<UClk¦ #FSKG`j%^>O>H98JK:q^>O>=@Zp8LKG]a=@AfCbW³ :0\J^>?BADC:Tg:+K(H5j 79=@`n:0OH
h¸2]a\J8TO>]a=@FO*68T\(7>O>F0?@Fi0C)j
798:#<8+\U;* =>:>9 C<E9B$!WK DL 7*AMH$E+8:nA?I$W:R->9HLF:n 89E+^>W+O9FK83E+89¥JK&Q9.W-B<j+D8KOUC:AG8J> KGO>8LA
Q:ºW-K(B<:S:WAh89n>J8JD+dB9`9H<=@JKG8JC:]C$Q<º;K8TJK\T8TOMqJG<98JKAP8:¥:&8 .j mGmK
Kz!z G&
' u &f '
6u79 8¸2 O>:S AGFMCbF0# W":'!#[ F OU AG 8Jd[Aaef ¸g :+KG8 ¸2`>`9?@=P \T:SAG=@\ FO5j>fuO !/ [ sa zhuIn0q y 0 r!1r154cs A rb4c1 r%z0¯ I
E
B¥+"KG=@Z0:0\JCl=@OUAG8JKGO:+AG=PF0O:S?]a^9KGZ8JCUj
0+
n"S0j
798:8+;*=>:>$@:@:@nAP;9WKH$9B9D$Kj HLF:89E+W+FKB$8KH+I$FGB:S!A?I<W9R->9COV-W:9E+->
89E-DL7:F-I:S:I<RKH$E-C!AP798ONS
, h
U,
["} & * e 6%798,\ KG=P\( op8JA 5FU\h :SAG =@FOeDÈ^>`9`F0KaA
% j[DO / sazhuIn' S y E 0 r!11)4cs A rb4c1 r%zS¯ I)»vk#F]AGF0On
È[C]#<AG8TM*
¦*¸n>¸2^>ij>00p¼Lj
¬+ Ç FSKaAG7>8JKGOº=@i=BA(:0?DO9\j9eZKGF[H9^9\JAG]G¸ © © ¸j
798:8<;*=?>:>$@+@:@*APF9Q-H$RKH$8-B+SAMD+ITNU>:B$V9W-I+W9BAP798$NS "n 00¥0j
[¥L
¤S+XY
6K(:0\(o[=PO9i3KG8hÊU^>=BKG8TMN8JO[AG]WF0K2:0^9iMN8TOUAG8hH
{Iz y x0r!1n>µ» ^>?BC£¥.0¬p¼Ln)®S [®®[j
KG8h:S?P=BAfC5*j,r%Z z0{3
E
¥h¬
XY tt&
X Y v -, v
ZÈMNFUF0AG79# 8JKae<:S]a8h!H4 ¬+!eDH :S%AaAG=BAG ^H88T ]AG=@Mb :S AG=@F0O4" W_FSK% MNF0<> =@?@8 KGF<F0A?@FU\h:S?P=@¨h:+AG=@FOj)fO / sazhuI A?^c^*^ A ¯9yfxLsL¯ y³tvz0¯ r%z0¯ I
² ¥.0 p¼Lj
z0¯ z=Gz0y³t³u ¯ÂiK
0 [yz0{ ~ y³t³z0¯»³º8JAaKGF0=@Ahn¦4~ Ln¦*:T~C£
~
t
GtY
º=@]a]a8TMN=@O:SAG=@O9iN¸2\JAG=@Zp8
:0 `4# DO9WF0KG" Mb :+AG =PF0O4AGl Fb ¦4F0<>=@?@u8§{ F] AG]Tj A?^c^*^ _ xLy z0sGw
¦*
±
»È8J` \LA¥ .S¤U¼Ln50 U¬p[j
S¬S
z! 1 y xL{ y³tvu 0¯ t z
4 = xL s B y³tv# z0¯ jD" ?@=B )8k#~ FUE Fo[] ~ 5A(H5~j@² n F0O~H9² ÀSF0 O n5¥ 0¹p®[j
~

KG=@i=@O:S?@?@Cl`9^><>?@=@]a7>8TH'=PObAG7>8 j Èj Èj © jU=@O¥ 0¹» © ^>]a]a=P:SO¼Lj
+¤0F?@798TM3^9]È[A(:SK26K(:Soj
798:8<;*=?>:>$@+@:@*AP;KI+S$7-EONKVKC!AMD+ITNU>9C$8-B<W9Q-C$89E-D$7*A 798$N n"S0j
0+
0®+
S¹S
X XK
,&T& ,& )( l AG=@?@=@]G:SAG=@FOFSl W Ã![ =BKG8T?@8T]a]2¸2# `>`9!?@=Pl \T:S AG=@F O KGF0 AGFU\J% F?#<AG*F !l DMN`9?@8TMN8TOUA¦4F0<>=@?@8q¸^>i0MN8TOUAG8hH © 8h:S?P=BAfC4k#:0]a8hHÈ[8JKGZ[=P\J8T]Tj
DO / szhuI¿ > r ¯Â¿0 / ¿*z0saw z z0¯ / z t_y³t³z0¯
~
JE }

Z0x }:0=@xL?P¯:0ÂU<9xL?@8¯>y WKGA F¯ M z0s({ ~ y³t³z0¯ )2 xLs Bhtvu(x » ª 8T<KG^:+KaC*S0p¼Lj
¸2
798:8<;*=?>:>$@+@:@*AP@ A?I<W:R-> KI GH+S<E9>$;KI9C<Q:E<;K> <VKSLV*A798LNS j
mGmK
x
wv &
67>8¸2Z \L AG=PZ' 8k:Hiu88 FU \T :SAG=@F#+OG ÈUC]!AG] 8TM* j 0r!1 \U\ . > s ~ ¯ L~ uJy³tvzS¯ z0¯ A ¯ zSsL{ ~ y³tvz0¯ 2 À0 yfxL{
S n¥N» :0O[^:+KaC
¥&p0¼Ln5¥ ¥h[j
0µ+
S S
4S
K&
mKmG
¸ 8Jg
FU\T:SAG=@F O6 8J\L. 79O>=PÊU^> 8WF0 KAG 7>8¸' \JAG=@Zp8 uN \T80 j A?^*Ç ^c^
/ xLs z0¯ ~² r%z0{q{OI n®» \JAGF0<8JK¥.µ¼Ln>¤U p¤UµUj
v
& m v
(
XY
oi #+U * o " w
hj X ] 67>8 §2" = k#:0?@?5\GAaK(:S\L%*ou8JK :0 O9\T8g=PH9# 8Jef:SKG 8T:qAag K(:0 \(o[=PO9i3W_FSKZ[=BKaAG^:S?5:0OH
§=@i0#+79# e`u8JKa W_FSKGMb
:0^9iMN8TOUAG8hHl8TO[Z[=@KGF0O>MN8TOUAG]Tj[fO / sazhu(xGxGÂSt_¯;? z y x
0 r!1
2 À { } z t {Ëz0¯Å5t_s(y ~0² x ~0² t_y À 2 z y ±,~ sGx ~ ¯Â E
)xau ¯z z ? »³º8T\T8TMq<8JK¥..¼Lj
E
² À
)( h º8J]a=Pi0O>=@O>i':3`F]a=BAG=@FO9=PO9i
] C]AG8TM \!W_. FSK OH=@O>iq AG79=@O>#Ui ]:S OH`8JF`>?@8=@OHFUF0KG]Tj A?^c^*^
2 } xauJy³s [{ 9qSn 4»È[8T`9AG8TMq<8JK¥ . ¼Ln)µU¥ µS j
¥T¤

Download Report

The Cricket Compass for Context

Paperzz.com

Your Paperzz