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The document of SLAM study. from 4.1 to 4.3.2

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SLAM SLAM
4.1.1 SLAM • • • → SLAM → •
4.1.2 P38 4.1 SLAM
4.2 P39 40 2D 2 2 SLAM ICP
4.2 P39 40 2D 2 2 SLAM ICP ! "#:%, '|)*:%, +*:%, ,*:% 4.1
4.2 P39 40 2D 2 2 SLAM ICP ! "#:%, '|)*:%, +*:%, ,*:% 4.1
4.3.1 SLAM !" !#!$ %"%$ & '"'$ (#"($$ ("" )"#)$" !* )* (* '* & SLAM %$, ⋯ , %- • SLAM SLAM • SLAM
4.3.1 SLAM !" !#!$ %"#%$" !& %& • SLAM %$#
4.3.2 SLAM SLAM ! "#:%, '|)*:%, +*:%, ,*:% ! "%|"%-*, +% ! )% . |"%, ', ,% . "#:% ' "#:% '
4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* 4.1 4.1.3 4.1.4 4.2 P41 (4.1) (4.2) "%/* "%"%/5 656* ' ,%,%/* )%)%/5 )%/* +%+%/* "% +% )% ,% ' 6*, ⋯ , 68
4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* 4.1 4.1.3 4.1.4 4.2 P41 (4.1) (4.2) ! "#:%, '|)*:%, +*:%, ,*:% = 5 6 7 ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* = 5 6 7 5 6 − 1 7 ! "#:%/9, '|)*:%/9, +*:%/9, ,*:%/9 = 5 6 7 5 6 − 1 ⋯ 5 1 7 ! "# (4.2) ! "%|"%/*, +% ! )% ; |"%, ', ,% ;
4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* ! "#:%, '|)*:%, +*:%, ,*:% = ! "#:%, '|)*:%/*, )%, +*:%, ,*:% = ! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% ! )%|)*:%/*, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% 4.1 4.1.3 4.1.4 4.2 4.1 4.1.1 P41 (4.1) (4.1.3) 4.1.2 4.1.3 P41 (4.1) (4.2)
4.3.2 SLAM !":$, &":$, '":$(" '$ )*:$, + ⇔ - )*:$, +|'":$(", '$, !":$, &":$ - '$|'":$(", !":$, &":$ = - '$|)*:$, +, '":$(", !":$, &":$ - )*:$, +|'":$(", !":$, &":$ ⇒ - )*:$, +|'$ - '$ = - '$|)*:$, + - )*:$, + × = × (4.1.1) (4.1.2) - )*:$, +|'":$(", '$, !":$, &":$ = - '$|)*:$, +, '":$(", !":$, &":$ - )*:$, +|'":$(", !":$, &":$ - '$|'":$(", !":$, &":$ 4.1.1 4.1.2 4.1.1′ 4.1.2′ !":$, &":$, '":$(" 4.1.1′′ 4.1.2′′
4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* 4.1 4.1.3 4.1.4 4.2 (4.1.3) (4.1.3.1) 4.1.3.1 4.1.3 P41 (4.1.3) (4.1.4) = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "#:%, '|)*:%/*, +*:%, ,*:% "%/* "%"%/5 656* ' ,%,%/* )%)%/5 )%/* )% "% ' ,% +%+%/*
4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* 4.1 4.1.3 4.1.4 4.2 (4.1.3.1) (4.1.3.2) 4.1.3.1 4.1.3 P41 (4.1.3) (4.1.4) = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% ⋯ 4.1.3.2
4.3.2 SLAM (4.1.3.1) (4.1.3.2) 4.1.3.1 4.1.3= &' ()|+,:), /, (0:)10, 20:), 30:) ' +,:), /|(0:)10, 20:), 30:) = &' ()|+), /, 3) ' +,:), /|(0:)10, 20:), 30:) = &' ()|+), /, 3) ' +)|+,:)10, /, (0:)10, 20:), 30:) ' +,:)10, /|(0:)10, 20:), 30:) ⋯ 4.1.3.2 20:), 30:), (0:)10 +) +,:)10, / = × ' +,:), /|(0:)10, 20:), 30:) = ' +)|+,:)10, /, (0:)10, 20:), 30:) ' +,:)10, /|(0:)10, 20:), 30:) ⇒ ' +,:), / = ' +)|+,:)10, / ' +,:)10, / 20:), 30:), (0:)10 4.1.3.1′ ⋯ 4.1.3.2′ +,:), /
4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* 4.1 4.1.3 4.1.4 4.2 (4.1.4) (4.1.4.1) 4.1.4.1 4.1.4 P41 (4.1.4) (4.2) = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%, '|)*:%/*, +*:%, ,*:% "%/* "%"%/5 656* ' ,%,%/* )%)%/5 )%/* "% "%/* +% +%+%/*
4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* 4.1 4.1.3 4.1.4 4.2 (4.1.4) (4.1.4.1) 4.1.4.1 4.1.4 P41 (4.1.4) (4.2) = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* "%/* "%"%/5 656* ' ,%,%/* )%)%/5 )%/* "% ,% +% +%+%/* 4.1.4.2
4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* 4.1 4.1.3 4.1.4 4.2 P41 (4.1) (4.2)
4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% 0 ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* = .! )%|"%, ', ,% ! "%|"%/*, +% 0 .! )%/*|"%/*, ', ,%/* ! "%/*|"%/1, +%/* ! "#:%/1, '|)*:%/1, +*:%/1, ,*:%/1 ⋯ = 3 % .! )%|"%, ', ,% ! "%|"%/*, +% ! "# = .! "# ∏% ! "%|"%/*, +% ! )%|"%, ', ,% = .! "# ∏% ! "%|"%/*, +% ∏5 ! )% 5 |"%, ', ,% 5 4.3 4.1 4.2
4.3.2 SLAM 4.3 P41 (4.3) $ %&:(, *|,-:(, .-:(, /-:( = 1$ %& ∏( $ %(|%(3-, .( ∏4 $ ,( 4 |%(, *, /( 4 4.1
4.3.2 SLAM 4.3 P41 (4.3) $ %&:(, *|,-:(, .-:(, /-:( = 1$ %& ∏( $ %(|%(3-, .( ∏4 $ ,( 4 |%(, *, /( 4 %(3- %(%(35 656- * /( /(3- ,(,(35 ,(3- .(.(3- %(3- %( .( 4.1
4.3.2 SLAM 4.3 P41 (4.3) $ %&:(, *|,-:(, .-:(, /-:( = 1$ %& ∏( $ %(|%(3-, .( ∏4 $ ,( 4 |%(, *, /( 4 %(3- %(%(35 656- * /( /(3- ,(,(35 ,(3- .(.(3- $ %(|%(3-, .( = 1 29Σ;< =%$ − 1 2 %( − ? %(3-, .( @ A ;< 3- %( − ? %(3-, .( 4.4 4.1
4.3.2 SLAM 4.3 P41 (4.3) $ %&:(, *|,-:(, .-:(, /-:( = 1$ %& ∏( $ %(|%(3-, .( ∏4 $ ,( 4 |%(, *, /( 4 %(3- %(%(35 656- * /( /(3- ,(,(35 ,(3- .(.(3- %( /( 4 * ,( 4 4.1
4.3.2 SLAM 4.3 $ %&:(, *|,-:(, .-:(, /-:( = 1$ %& ∏( $ %(|%(3-, .( ∏4 $ ,( 4 |%(, *, /( 4 %(3- %(%(35 656- * /( /(3- ,(,(35 ,(3- .(.(3- $ ,( 4 |%(, *, /( 4 = 7 29Σ;< =%$ − 1 2 ,( 4 − ℎ %(, 6AB C D ;< 3- ,( 4 − ℎ %(, 6AB ∵ 6AB /( 4 ,( 4 * 4.5 P41 (4.3) 4.1
4.3.2 SLAM 4.3 $ %&:(, *|,-:(, .-:(, /-:( = 1$ %& ∏( $ %(|%(3-, .( ∏4 $ ,( 4 |%(, *, /( 4 = 1$ %& ∏( 5 6 - 789:; <%$ = > − - 7 %( − @ %(3-, .( A ∑C; 3-D E %( − @ %(3-, .( ∏4 F 789G; <%$ − - 7 ,( 4 − ℎ %(, IJK A ∑L; 3- ,( 4 − ℎ %(, IJK (4.3) (4.4) (4.5) 4.1
! "#:%, '|)*:%, +*:%, ,*:% = .! "# ∏% 0 1 * 23456 7"! − * 2 "% − 9 "%:*, +% ; ∑=6 :* "% − 9 "%:*, +% ∏> ? 234@6 7"! A B − * 2 C D )% > − ℎ "%, FGH ; ∑I6 :* )% > − ℎ "%, FGH 4.3.2 SLAM 4.3.1 − ln ! "#:%, '|)*:%, +*:%, ,*:% = − ln .! "# + ⋯ + 1 2 S % "% − 9 "%:*, +% ; S =6 :* "% − 9 "%:*, +% + 1 2 S % S > )% > − ℎ "%, FGH ; S I6 :* )% > − ℎ "%, FGH − 4.3.2 ln T* U T2 U ⋯ U TV = lnT* + lnT2 + ⋯ + lnTV ln W % T% = lnT* + lnT2 + ⋯ lnT% = S % lnT% ln W % 7"!T% = ln7"!T* + ⋯ + ln7"!T% = T* + ⋯ + T% = S % T% ∵ 4.1
− ln $ %&:(, *|,-:(, .-:(, /-:( = − ln 1$ %& + ⋯ + 1 2 6 ( %( − 7 %(8-, .( 9 6 :; 8- %( − 7 %(8-, .( + 1 2 6 ( 6 < ,( < − ℎ %(, >?@ 9 6 A; 8- ,( < − ℎ %(, >?@ 4.3.2 SLAM 4.3.2 4.3.3 = %& 9 Σ& 8- %& + 6 ( %( − 7 %(8-, .( 9 6 :; 8- %( − 7 %(8-, .( + 6 ( 6 < ,( < − ℎ %(, >?@ 9 6 A; 8- ,( < − ℎ %(, >?@ = F $ %& = 1 G H%$ − 1 2 %& 9 Σ& 8- %& → F %&:( *

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SLAM_study_document

  • 5. 4.2 P39 40 2D 2 2 SLAM ICP ! "#:%, '|)*:%, +*:%, ,*:% 4.1
  • 6. 4.2 P39 40 2D 2 2 SLAM ICP ! "#:%, '|)*:%, +*:%, ,*:% 4.1
  • 7. 4.3.1 SLAM !" !#!$ %"%$ & '"'$ (#"($$ ("" )"#)$" !* )* (* '* & SLAM %$, ⋯ , %- • SLAM SLAM • SLAM
  • 9. 4.3.2 SLAM SLAM ! "#:%, '|)*:%, +*:%, ,*:% ! "%|"%-*, +% ! )% . |"%, ', ,% . "#:% ' "#:% '
  • 10. 4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* 4.1 4.1.3 4.1.4 4.2 P41 (4.1) (4.2) "%/* "%"%/5 656* ' ,%,%/* )%)%/5 )%/* +%+%/* "% +% )% ,% ' 6*, ⋯ , 68
  • 11. 4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* 4.1 4.1.3 4.1.4 4.2 P41 (4.1) (4.2) ! "#:%, '|)*:%, +*:%, ,*:% = 5 6 7 ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* = 5 6 7 5 6 − 1 7 ! "#:%/9, '|)*:%/9, +*:%/9, ,*:%/9 = 5 6 7 5 6 − 1 ⋯ 5 1 7 ! "# (4.2) ! "%|"%/*, +% ! )% ; |"%, ', ,% ;
  • 12. 4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* ! "#:%, '|)*:%, +*:%, ,*:% = ! "#:%, '|)*:%/*, )%, +*:%, ,*:% = ! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% ! )%|)*:%/*, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% 4.1 4.1.3 4.1.4 4.2 4.1 4.1.1 P41 (4.1) (4.1.3) 4.1.2 4.1.3 P41 (4.1) (4.2)
  • 13. 4.3.2 SLAM !":$, &":$, '":$(" '$ )*:$, + ⇔ - )*:$, +|'":$(", '$, !":$, &":$ - '$|'":$(", !":$, &":$ = - '$|)*:$, +, '":$(", !":$, &":$ - )*:$, +|'":$(", !":$, &":$ ⇒ - )*:$, +|'$ - '$ = - '$|)*:$, + - )*:$, + × = × (4.1.1) (4.1.2) - )*:$, +|'":$(", '$, !":$, &":$ = - '$|)*:$, +, '":$(", !":$, &":$ - )*:$, +|'":$(", !":$, &":$ - '$|'":$(", !":$, &":$ 4.1.1 4.1.2 4.1.1′ 4.1.2′ !":$, &":$, '":$(" 4.1.1′′ 4.1.2′′
  • 14. 4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* 4.1 4.1.3 4.1.4 4.2 (4.1.3) (4.1.3.1) 4.1.3.1 4.1.3 P41 (4.1.3) (4.1.4) = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "#:%, '|)*:%/*, +*:%, ,*:% "%/* "%"%/5 656* ' ,%,%/* )%)%/5 )%/* )% "% ' ,% +%+%/*
  • 15. 4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* 4.1 4.1.3 4.1.4 4.2 (4.1.3.1) (4.1.3.2) 4.1.3.1 4.1.3 P41 (4.1.3) (4.1.4) = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% ⋯ 4.1.3.2
  • 16. 4.3.2 SLAM (4.1.3.1) (4.1.3.2) 4.1.3.1 4.1.3= &' ()|+,:), /, (0:)10, 20:), 30:) ' +,:), /|(0:)10, 20:), 30:) = &' ()|+), /, 3) ' +,:), /|(0:)10, 20:), 30:) = &' ()|+), /, 3) ' +)|+,:)10, /, (0:)10, 20:), 30:) ' +,:)10, /|(0:)10, 20:), 30:) ⋯ 4.1.3.2 20:), 30:), (0:)10 +) +,:)10, / = × ' +,:), /|(0:)10, 20:), 30:) = ' +)|+,:)10, /, (0:)10, 20:), 30:) ' +,:)10, /|(0:)10, 20:), 30:) ⇒ ' +,:), / = ' +)|+,:)10, / ' +,:)10, / 20:), 30:), (0:)10 4.1.3.1′ ⋯ 4.1.3.2′ +,:), /
  • 17. 4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* 4.1 4.1.3 4.1.4 4.2 (4.1.4) (4.1.4.1) 4.1.4.1 4.1.4 P41 (4.1.4) (4.2) = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%, '|)*:%/*, +*:%, ,*:% "%/* "%"%/5 656* ' ,%,%/* )%)%/5 )%/* "% "%/* +% +%+%/*
  • 18. 4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* 4.1 4.1.3 4.1.4 4.2 (4.1.4) (4.1.4.1) 4.1.4.1 4.1.4 P41 (4.1.4) (4.2) = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* "%/* "%"%/5 656* ' ,%,%/* )%)%/5 )%/* "% ,% +% +%+%/* 4.1.4.2
  • 19. 4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"#:%, ', )*:%/*, +*:%, ,*:% ! "#:%, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"#:%/*, ', )*:%/*, +*:%, ,*:% ! "#:%/*, '|)*:%/*, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* 4.1 4.1.3 4.1.4 4.2 P41 (4.1) (4.2)
  • 20. 4.3.2 SLAM ! "#:%, '|)*:%, +*:%, ,*:% = .! )%|"%, ', ,% ! "%|"%/*, +% 0 ! "#:%/*, '|)*:%/*, +*:%/*, ,*:%/* = .! )%|"%, ', ,% ! "%|"%/*, +% 0 .! )%/*|"%/*, ', ,%/* ! "%/*|"%/1, +%/* ! "#:%/1, '|)*:%/1, +*:%/1, ,*:%/1 ⋯ = 3 % .! )%|"%, ', ,% ! "%|"%/*, +% ! "# = .! "# ∏% ! "%|"%/*, +% ! )%|"%, ', ,% = .! "# ∏% ! "%|"%/*, +% ∏5 ! )% 5 |"%, ', ,% 5 4.3 4.1 4.2
  • 21. 4.3.2 SLAM 4.3 P41 (4.3) $ %&:(, *|,-:(, .-:(, /-:( = 1$ %& ∏( $ %(|%(3-, .( ∏4 $ ,( 4 |%(, *, /( 4 4.1
  • 22. 4.3.2 SLAM 4.3 P41 (4.3) $ %&:(, *|,-:(, .-:(, /-:( = 1$ %& ∏( $ %(|%(3-, .( ∏4 $ ,( 4 |%(, *, /( 4 %(3- %(%(35 656- * /( /(3- ,(,(35 ,(3- .(.(3- %(3- %( .( 4.1
  • 23. 4.3.2 SLAM 4.3 P41 (4.3) $ %&:(, *|,-:(, .-:(, /-:( = 1$ %& ∏( $ %(|%(3-, .( ∏4 $ ,( 4 |%(, *, /( 4 %(3- %(%(35 656- * /( /(3- ,(,(35 ,(3- .(.(3- $ %(|%(3-, .( = 1 29Σ;< =%$ − 1 2 %( − ? %(3-, .( @ A ;< 3- %( − ? %(3-, .( 4.4 4.1
  • 24. 4.3.2 SLAM 4.3 P41 (4.3) $ %&:(, *|,-:(, .-:(, /-:( = 1$ %& ∏( $ %(|%(3-, .( ∏4 $ ,( 4 |%(, *, /( 4 %(3- %(%(35 656- * /( /(3- ,(,(35 ,(3- .(.(3- %( /( 4 * ,( 4 4.1
  • 25. 4.3.2 SLAM 4.3 $ %&:(, *|,-:(, .-:(, /-:( = 1$ %& ∏( $ %(|%(3-, .( ∏4 $ ,( 4 |%(, *, /( 4 %(3- %(%(35 656- * /( /(3- ,(,(35 ,(3- .(.(3- $ ,( 4 |%(, *, /( 4 = 7 29Σ;< =%$ − 1 2 ,( 4 − ℎ %(, 6AB C D ;< 3- ,( 4 − ℎ %(, 6AB ∵ 6AB /( 4 ,( 4 * 4.5 P41 (4.3) 4.1
  • 26. 4.3.2 SLAM 4.3 $ %&:(, *|,-:(, .-:(, /-:( = 1$ %& ∏( $ %(|%(3-, .( ∏4 $ ,( 4 |%(, *, /( 4 = 1$ %& ∏( 5 6 - 789:; <%$ = > − - 7 %( − @ %(3-, .( A ∑C; 3-D E %( − @ %(3-, .( ∏4 F 789G; <%$ − - 7 ,( 4 − ℎ %(, IJK A ∑L; 3- ,( 4 − ℎ %(, IJK (4.3) (4.4) (4.5) 4.1
  • 27. ! "#:%, '|)*:%, +*:%, ,*:% = .! "# ∏% 0 1 * 23456 7"! − * 2 "% − 9 "%:*, +% ; ∑=6 :* "% − 9 "%:*, +% ∏> ? 234@6 7"! A B − * 2 C D )% > − ℎ "%, FGH ; ∑I6 :* )% > − ℎ "%, FGH 4.3.2 SLAM 4.3.1 − ln ! "#:%, '|)*:%, +*:%, ,*:% = − ln .! "# + ⋯ + 1 2 S % "% − 9 "%:*, +% ; S =6 :* "% − 9 "%:*, +% + 1 2 S % S > )% > − ℎ "%, FGH ; S I6 :* )% > − ℎ "%, FGH − 4.3.2 ln T* U T2 U ⋯ U TV = lnT* + lnT2 + ⋯ + lnTV ln W % T% = lnT* + lnT2 + ⋯ lnT% = S % lnT% ln W % 7"!T% = ln7"!T* + ⋯ + ln7"!T% = T* + ⋯ + T% = S % T% ∵ 4.1
  • 28. − ln $ %&:(, *|,-:(, .-:(, /-:( = − ln 1$ %& + ⋯ + 1 2 6 ( %( − 7 %(8-, .( 9 6 :; 8- %( − 7 %(8-, .( + 1 2 6 ( 6 < ,( < − ℎ %(, >?@ 9 6 A; 8- ,( < − ℎ %(, >?@ 4.3.2 SLAM 4.3.2 4.3.3 = %& 9 Σ& 8- %& + 6 ( %( − 7 %(8-, .( 9 6 :; 8- %( − 7 %(8-, .( + 6 ( 6 < ,( < − ℎ %(, >?@ 9 6 A; 8- ,( < − ℎ %(, >?@ = F $ %& = 1 G H%$ − 1 2 %& 9 Σ& 8- %& → F %&:( *