١
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ ﺕﺎﻈﺣﻼﻣ ) ﯽﺘﺸﮔﺯﺎﺑ ﯼﺎﻫ ﺵﻭﺭ (
ﺱﺭﺪﻣ : ﺩﻮﻨﺷﻮﺧ ﺪﻴﺠﻤﻟﺍﺪﺒﻋ ﻥﺍﻮﻨﻋ ﺯﺍﻭﺮﭘ ﯼﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻦﻴﻤﺨﺗ ﻭ ﻢﺘﺴﻴﺳ ﻲﻳﺎﺳﺎﻨﺷ
ﻪﺘﺧﺎﻨﺷﺎﻧ ﻢﺘﺴﻴﺳ ﻢﺘﻳﺭﻮﮕﻟﺍ
ﻲﻳﺎﺳﺎﻨﺷ
ﻢﺘﺴﻴﺳ ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ
ﻲﺘﺸﮔﺯﺎﺑ ﻲﻳﺎﺳﺎﻨﺷ• Recursive Least Square (RLS)
؟ﺖﺴﻴﭼ ﻑﺪﻫ• ﻱﺍﺮﺑ ﻂﺧ ﻱﻭﺭ ﺩﺮﻜﻳﻭﺭ ﻪﺑ ﻂﺧ ﺝﺭﺎﺧ ﺩﺮﻜﻳﻭﺭ ﻞﻳﺪﺒﺗ
ﻲﻳﺎﺳﺎﻨﺷ
ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﺭﺎﻛ ﻦﻴﺣ ﺭﺩ ﻲﻜﻴﻣﺎﻨﻳﺩ ﻱﺎﻫ ﻢﺘﺴﻴﺳ
؟ﻪﻧﻮﮕﭼ • ﻱﺎﻫ ﻩﺩﺍﺩ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ ،ﻪﻈﻓﺎﺣ ﻱﺍﺭﺍﺩ ﻢﺘﺴﻴﺳ ﻭ ﻢﺘﺴﻴﺳ ﻥﺩﻮﺑ ﻚﻴﻣﺎﻨﻳﺩ ﻡﻮﻬﻔﻣ
ﻱﺎﻫ ﻩﺩﺍﺩ ﺯﺍ ﻲﺗﺭﺎﺒﻋ ﻪﺑ ،ﻪﺘﺷﺬﮔ ﻱﺎﻫ ﻩﺩﺍﺩ ﺯﺍ ﻪﻜﻠﺑ ﻢﻴﻨﻛ ﻲﻤﻧ ﻩﺩﺎﻔﺘﺳﺍ ﻲﻳﺎﻬﻨﺗ ﻪﺑ t
t-1
ﻢﻳﺮﻴﮔ ﻲﻣ ﻩﺮﻬﺑ ﺰﻴﻧ .
ﻢﻳﺭﺍﺩ ﻱﺭﺎﻣﺁ ﺮﻴﺒﻌﺗ ﺯﺍ• :
ﻢﻴﻨﻛ ﻲﻣ ﻒﻳﺮﻌﺗ ﺲﻧﺎﻳﺭﺍﻮﻛ ﺲﻳﺮﺗﺎﻣ ﻥﺍﻮﻨﻋ ﻪﺑ ﺍﺭ ﺲﻳﺮﺗﺎﻣ ﻦﻳﺍ• .
1 1
2[ ] ( ) [ ]
ˆ T P t T Cov
٢
ﻦﻤﻟﺎﻛ ﻩﺮﻬﺑ ﻭ ﻦﻴﻤﺨﺗ ﻱﺎﻄﺧ
) 1 ˆ( ) ( ) ( ) 1 ˆ( ) (
) 1 ˆ( ) 1 ( ) ( ) ( ) ˆ( ) ( ) ( ) (
)]
( ) ( ) ( ) ( )[
( ] ) ( ) ( )[
( ) ˆ(
) ( ) ( ) 1 ( ) ( ) ( )
(
1
1 1
1
1
1
1 1
1 1
t t t t
t p
t t
p t y t t t p i y i
t y t i y i t
p i y i t
p t
t t t
p t t t
p
T t
i
t
i t
i
T T
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ ﯽﺘﺸﮔزﺎﺑ ﯽﯾﺎﺳﺎﻨﺷ حﻼﺻا• )
ﺎﻄﺧ ﺲﯾﺮﺗﺎﻣ ﯽﺘﺸﮔزﺎﺑ ﺪﻧور (
ﺲﯾﺮﺗﺎﻣ يزﺎﺳ نوراو ﻢﻟ•
٣
ﯽﻠﺒﻗ ﺕﺎﻋﻼﻃﺍ ﺱﺎﺳﺍ ﺮﺑ ﺭﻮﺳﺮﮔﺭ ﻥﺎﻴﺑ ﻑﺪﻫ ﺎﺑ ﺭﻮﺳﺮﮔﺭ ﯽﻓﺮﻌﻣ ﺭﺩ ﺭﺍﺩ ﺮﻴﺧﺎﺗ ﺕﺭﺎﺒﻋ ﺯﺍ ﻩﺩﺎﻔﺘﺳﺍ •
ﺏﺎﺨﺘﻧﺍ ﻪﺑ ﻁﻮﺑﺮﻣ ﺕﺎﻜﻧ• )p(0)
ﻲﻧﺎﻤﻫ ﺲﻳﺮﺗﺎﻣ ،ﻦﻴﻌﻣ ﺖﺒﺜﻣ ﻭ ﮒﺭﺰﺑ ﻱﺎﻄﺧ (
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ
ﻥﺎﻣﺯ ﺎﺑ ﺮﻴﻐﺘﻣ ﻱﺎﻫ ﻢﺘﺴﻴﺳ ﻢﺘﺴﻴﺳ ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻲﻧﺎﻬﮔﺎﻧ ﺮﻴﻴﻐﺗ•
ﺲﻧﺎﻳﺭﺍﻮﻛ ﻲﻧﺎﺸﻧﺯﺎﺑ- Covariance Resetting (P(t))
ﻚﻳﺩﻮﻳﺮﭘ ﻲﻧﺎﺸﻧﺯﺎﺑ- ﻢﺘﺴﻴﺳ ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﺭﺍﻮﻤﻫ ﺮﻴﻴﻐﺗ•
ﻲﺷﻮﻣﺍﺮﻓ ﺭﻮﺘﻛﺎﻓ- Forgetting Factor
۴
ﻲﺷﻮﻣﺍﺮﻓ ﺭﻮﺘﻛﺎﻓ Forgetting Factor
ﻚﻳ ﻭ ﺮﻔﺻ ﻦﻴﺑ• ﻲﻧﺎﻣﺯ ﺮﻴﺧﺍ ﻱﺎﻫ ﻩﺩﺍﺩ ﺮﺘﺸﻴﺑ ﻥﺯﻭ• ﻲﺷﻮﻣﺍﺮﻓ ﺭﻮﺘﻛﺎﻓ ﻲﻳﺎﻤﻧ ﺭﺎﺘﻓﺭ•
2
1
] )
( 2 [
1
t
i
T i
t y t
J
1
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ هﺪﺷ هدﺎﺳ يﺎﻫ شور ﺪﻨﻨﮐ ﯽﻣ بﺎﻨﺘﺟا ﺲﻧﺎﯾراﻮﮐ ﺲﯾﺮﺗﺎﻣ ﯽﻧﺎﺳر زوﺮﺑ زا ﻪﮐ ﯽﯾﺎﻫ ﻢﺘﯾرﻮﮕﻟا
. زرﺎﻣزﺎﮐ ﺮﮔﺮﯾﻮﺼﺗ ﻢﺘﯾرﻮﮕﻟا
ﺖﺳا ﮋﻧاﺮﮔﻻ ﺐﯾﺮﺿ ﺎﻔﻟآ ﺐﯾﺮﺿ ﺪﯿﻘﻣ ﮋﻧاﺮﮔﻻ شور ﻖﺑﺎﻄﻣ خﺎﻧﺎﺑ يﺎﻀﻓ و ﯽﺷﻮﮐ ﻪﻟﺎﺒﻧد ﻪﻟﺎﺴﻣ رد ﯽﻧﺎﻣز مﺎﮔ ود يﺎﻄﺧ ﻢﻬﻣ ﻪﺘﮑﻧ. ﻪﺑ ﺖﺒﺴﻧ يﺮﯿﮔ ﻖﺘﺸﻣ وTeta
Alphab
۵
لﻮﻬﺠﻣ ود ﻪﻟدﺎﻌﻣ ود ترﻮﺻ ﻪﺑ قﻮﻓ ﻪﻟدﺎﻌﻣ ﻞﺣ زا Teta , Alphab
ﻢﯾراد :
شور حﻼﺻا ياﺮﺑ ﺐﯾﺮﺿ ﮏﯾ زا هدﺎﻔﺘﺳا :
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ ﺮﮔﺮﯾﻮﺼﺗ ﻢﺘﯾرﻮﮕﻟا Projection
هﺰﯿﻟﺎﻣﺮﻧ ﺎﯾ
جﺮﺨﻣ نﺪﺷ ﺮﻔﺻ زا يﺮﯿﮔﻮﻠﺟ ياﺮﺑ
يراﺪﯾﺎﭘ ياﺮﺑ تﺎﺒﺛا ﺲﯾﺮﺗﺎﻣ هﮋﯾو راﺪﻘﻣ ﮏﯾ: ﺖﺳا ﺮﯾز ترﻮﺻ ﻪﺑA
:
ﺮﺘﻤﮐ ﺎﻣﺎﮔ ﺮﮔا 2
زا ﺮﺗ گرﺰﺑ و 0
و دﻮﺑ ﺪﻫاﻮﺧ ﮏﯾ زا ﺮﺘﻤﮐ ﺲﯾﺮﺗﺎﻣ هﮋﯾو راﺪﻘﻣ ﺪﺷﺎﺑ
دﻮﺑ ﺪﻫاﻮﺧ راﺪﯾﺎﭘ ﻢﺘﺴﯿﺳ ) .
ترﺎﺒﻋ ﻖﻠﻄﻣ رﺪﻗ (
۶
ﯽﻗﺎﻔﺗا ﺐﯾﺮﻘﺗ ﻢﺘﯾرﻮﮕﻟا Stochastic Approximation
ﺎﺠﻨﯾا رد ﺖﺳا ﺮﻟﺎﮑﺳا ﮏﯾP
.
ﻦﯿﮕﻧﺎﯿﻣ تﺎﻌﺑﺮﻣ ﻦﯾﺮﺘﻤﮐ ﻢﺘﯾرﻮﮕﻟا LMS
ﺎﺠﻨﯾا رد ﺖﺳا ﺮﻟﺎﮑﺳا ﮏﯾ y
.
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ
ﻞﻳﺪﺒﺗ ﻊﺑﺎﺗ ﯽﻣﻮﻤﻋ ﻝﺪﻣ ﺪﻴﻔﺳ ﺰﻳﻮﻧ ﯽﺟﻭﺮﺧ ﯼﺎﻄﺧ ﺎﺑ ﻝﺪﻣ (Equation error)
ﯽﺟﻭﺮﺧ ﯼﺎﻄﺧ ﺎﺑ ﻝﺪﻣ (Output error)
ﺪﻴﻔﺳ ﺮﻴﻏ ﺰﻳﻮﻧ ﺽﺮﻓ ﺎﺑ ﻝﺪﻣ )
ﺎﻄﺧ ﯽﮕﺘﺴﺒﻤﻤﻫ (
ﺭﺍﺩ ﺱﺎﻳﺎﺑ ﻦﻴﻤﺨﺗ
٧
ﻕﻮﻓ ﻝﺪﻣ ﺭﺩ ﺐﻳﺍﺮﺿ ﻭ ﻩﺩﻮﺑ ﺪﻴﻔﺳ ﺰﻳﻮﻧe
ﻪﺑ ﺍﺭ ﺎﻄﺧ ﻉﻮﻤﺠﻣ ﺭﺩ ﻪﮐ ﺖﺳﺎﻬﻧﺁ ﯽﮕﺘﺴﺒﻤﻫ ﺮﮕﻧﺎﻴﺑc
ﺖﺳﺍ ﻩﺩﺮﮐ ﻞﻳﺪﺒﺗ ﯽﮕﻧﺭ ﺰﻳﻮﻧ .
ﻥﺍﻮﺗ ﯽﻣ ﯽﻤﺘﺴﻴﺳ ﻦﻴﻨﭼ ﯼﺍﺮﺑ • ﺩﺍﺩ ﺀﺎﻘﺗﺭﺍ ﺍﺭ ﺭﻮﺳﺮﮔﺭ ﻝﺪﻣ :
ﺪﻨﻣﺎﻧ ﯽﻣ ﻪﺘﻓﺎﻳ ﻪﻌﺳﻮﺗ ﺵﻭﺭ ﺍﺭ ﻥﺁ ﺎﻣﺍ ﺩﺭﺍﺪﻧ ﺕﻭﺎﻔﺗ ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﯽﻠﮐ ﻝﺪﻣ ﺎﺑ ﺵﻭﺭ ﻦﻳﺍ ﻪﭼ ﺮﮔﺍ • .
Extended Least Square (ELS)
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ ﺍﺭ ﺵﻭﺭ ﻦﻴﻤﻫ ﻊﺑﺎﻨﻣ ﯽﺧﺮﺑ ﺭﺩ ﻲﺘﺸﮔﺯﺎﺑ ﺲﻧﺎﺷ ﺮﺜﻛﺍﺪﺣ ﺵﻭﺭ
ﺵﻭﺭ ﺍﺭ ﻥﺁ ﺎﻳ ﺪﻨﻣﺎﻧ ﯽﻣ
ﻲﺘﺸﮔﺯﺎﺑ ﺲﻧﺎﺷ ﺮﺜﻛﺍﺪﺣ )
۱ ( ﺪﻨﻨﮐ ﯽﻣ ﯼﺭﺍﺬﮕﻣﺎﻧ .
ﻲﺘﺸﮔﺯﺎﺑ ﺲﻧﺎﺷ ﺮﺜﻛﺍﺪﺣ ﺵﻭﺭ ﺎﺑ ﻲﻳﺎﺳﺎﻨﺷ •
Recursive Maximum Likelihood
(RML)
٨
ﺕﺎﮑﻧ ﯽﺧﺮﺑ ﺵﻭﺭ • ﺵﻭﺭ ﻪﺑﺎﺸﻣ ﺰﻴﻧRLS
ﺩﺭﺍﺩ ﺱﺎﻳﺎﺑ ﯽﮕﻧﺭ ﺰﻳﻮﻧ ﺭﻮﻀﺣ ﺭﺩOLS .
ﺵﻭﺭ ﺭﺩ ﺕﺎﺒﺳﺎﺤﻣ ﺖﻋﺮﺳ • ﺖﺳﺍ ﺮﺗﻻﺎﺑ ﻪﻤﻫ ﺯﺍ RLS
.
ﺵﻭﺭ ﺯﺎﻴﺘﻣﺍ • ﻪﺑ ﺖﺒﺴﻧRELS
ﺖﺳﺍ ﺱﺎﻳﺎﺑ ﻥﻭﺪﺑ ﻦﻴﻤﺨﺗRLS .
ﺵﻭﺭ • ﺖﺳﺍ ﺮﺗﺪﻨﮐ ﺎﻫ ﺵﻭﺭ ﻪﻤﻫ ﺯﺍRELS
.
ﺵﻭﺭ ﻲﻳﺍﺮﮕﻤﻫ ﺕﺎﺒﺛﺍ • RLS
ﺵﻭﺭ ﻲﻳﺍﺮﮕﻤﻫ ،ﺩﺭﺍﺩ ﯽﺸﻫﺎﮐ ﯼﺪﻧﻭﺭ ﻩﺭﺍﻮﻤﻫ ﺎﻄﺧ ﺲﻧﺎﻳﺭﺍﻮﮐ ﺲﻳﺮﺗﺎﻣ ﻪﮑﻨﻳﺍ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ﺩﻮﺷ ﯽﻣ ﺕﺎﺒﺛﺍ ﯽﺘﺸﮔﺯﺎﺑ .
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ ﺵﻭﺭ ﯼﺎﻫﺮﻴﻐﺘﻣ ﯽﮑﻤﮐ
(Instrumental Variable)
ﺪﻳﺎﺑ ﻞﺒﻗ ﺚﺣﺎﺒﻣ ﻖﺒﻃ ﻦﻴﻤﺨﺗ ﻥﺩﻮﺑ ﺱﺎﻳﺎﺑ ﻥﻭﺪﺑ ﯼﺍﺮﺑ ﻭy
ﺪﻨﺷﺎﺑ ﻪﺘﺴﺒﻤﻫﺎﻧe .
ﻪﺑ ﺮﮔﺍ
ﺩﻮﺷ ﯽﻣ ﻞﺣ ﻪﻟﺎﺴﻣ ﻦﻳﺍ ﻢﻴﺷﺎﺑ ﻪﺘﺷﺍﺩ ﯽﺳﺮﺘﺳﺩ ﺰﻳﻮﻧ ﻥﻭﺪﺑ ﯽﺟﻭﺮﺧ .
ﻡﺪﻋ ﻞﻴﻟﺩ ﻪﺑ ﺎﻣﺍ
ﻢﻴﻨﮐ ﯽﻣ ﻩﺩﺎﻔﺘﺳﺍ ﯽﮑﻤﮐ ﺮﻴﻐﺘﻣ ﺯﺍ ﯽﺟﻭﺮﺧ ﻦﻳﺍ ﻪﺑ ﯽﺳﺮﺘﺳﺩ
. y ﻦﻳﺰﮕﻳﺎﺟ ﻪﮐ ﺮﻴﻐﺘﻣ ﺮﻫ ﻊﻗﺍﻭ ﺭﺩ
ﻢﻴﻣﺎﻧ ﯽﻣ ﯽﮑﻤﮐ ﺮﻴﻐﺘﻣ ﺍﺭ ﺩﻮﺷ .
ﻪﻧﻮﻤﻧ ﻥﺍﻮﻨﻋ ﻪﺑ :
ﯽﮑﻤﮐ ﺮﻴﻐﺘﻣ ﻝﺎﺣ ﺰﻳﻮﻧ ﻥﻭﺪﺑ ﻦﻴﻤﺨﺗ ﺯﺍ ﻪﮐ ﺍﺭz
ﯼﺎﺟ ﻪﺑ ﻩﺪﺷ ﻞﻴﮑﺸﺗy ﯽﻣ ﻦﻳﺰﮕﻳﺎﺟy
ﻢﻴﻳﺎﻤﻧ ﯽﻣ ﻩﺩﺎﻔﺘﺳﺍ ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﯽﻣﻮﻤﻋ ﻂﺑﺍﻭﺭ ﺯﺍ ﻭ ﻢﻴﻨﮐ :
θ
=u ˆ ˆyt tT
] x x x yˆ ˆy ˆy [
ztT = ¬ t¬1¬ t¬2¬ t¬n t t¬1 t¬m ] x x x y y y [
uTt = ¬ t¬1¬ t¬2¬ t¬n t t¬1 t¬m ˆ Ay (ZTU) ZTy
IV
1
= ¬
= θ
٩
ﯽﻠﮐ يﺪﻨﺑ ﻊﻤﺟ ﮏﯾ ﺪﻨﺘﺴﻫ ﻪﭼرﺎﭙﮑﯾ ﻢﺘﯾرﻮﮕﻟ ﮏﯾ ياراد هﺪﺷ ﻪﯾارا يﺎﻫ شور ﻪﯿﻠﮐ :
ﺮﯾدﺎﻘﻣ ﻢﺘﯾرﻮﮕﻟا ﻦﯾا رد و و
ﺪﻨﻨﮐ ﯽﻣ ﺮﯿﯿﻐﺗ .
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ ﺎﻳﺎﭘ ﻚﻳﺮﺤﺗ ،ﻝﺎﻨﮕﻴﺳ ﻱﺎﻨﻏ
Persistency Excitation
ﻲﻳﺎﺳﺎﻨﺷ ﻱﺍﺮﺑ ﻱﺩﻭﺭﻭ ﻝﺎﻨﮕﻴﺳ ﺏﺎﺨﺘﻧﺍ ﻲﻠﺻﺍ ﻪﻟﺎﺴﻣ• ﻱﺭﺎﺘﻓﺭ ﻱﺎﻫﺩﻮﻣﻭ ﺎﻫ ﻢﺘﺴﻴﺳ ﻚﻳﺰﻴﻓ ﻪﺒﻨﺟ ﺯﺍ ﻉﻮﺿﻮﻣ ﺢﻴﺿﻮﺗ•
ﻩﺎﮔﺪﻳﺩ ﺯﺍ ﻉﻮﺿﻮﻣ ﺢﻴﺿﻮﺗ • )LS
ﺹﺎﺧ ﺖﻟﺎﺣ
( ﻲﻠﺻﺍ ﺲﻳﺮﺗﺎﻣ
ﻱﺎﻫ ﻢﺘﺴﻴﺳ ﺭﺩ ﺩﻭﺪﺤﻣ ﺦﺳﺎﭘ ﻥﺩﻮﺑ ﻞﻣﺎﻛ ﻪﺒﺗﺭ • ﺎﺘﮑی ﻢﻤیﻨیﻣ •
١٠
ﺲﻟﺎﭘ يدورو•
ﻪﺒﺗﺮﻣ زا يراﺪﻘﻣ ﭻﯿﻫ ياﺮﺑ ﺖﺴﯿﻧ ﺎﯾﺎﭘ ﮏﯾﺮﺤﺗ n
.
ﻪﻠﭘ يدورو •
ﺪﺷﺎﺑ ﯽﻣ ﮏﯾ ﻪﺒﺗﺮﻣ زا ﺎﯾﺎﭘ هﺪﻨﻨﮐ ﮏﯾﺮﺤﺗ .
ﯽﺳﻮﻨﯿﺳ يدورو •
ﺪﺷﺎﺑ ﯽﻣ ود ﻪﺒﺗﺮﻣ زا ﺎﯾﺎﭘ هﺪﻨﻨﮐ ﮏﯾﺮﺤﺗ .
ﯽﻗﺎﻔﺗا يدورو • )
ﺪﯿﻔﺳ ﺰﯾﻮﻧ
ﺪﺷﺎﺑ يا ﻪﺒﺗﺮﻣ ﺮﻫ زا ﺎﯾﺎﭘ هﺪﻨﻨﮐ ﮏﯾﺮﺤﺗ ﺪﻧاﻮﺗ ﯽﻣ( .
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ ﻲﺴﻧﺎﻛﺮﻓ ﻩﺎﮔﺪﻳﺩ ﺯﺍ ﻝﺎﻨﮕﻴﺳ ﻱﺎﻨﻏ ﺮﻴﺴﻔﺗ• )
ﻝﺎﻨﮕﻴﺳ ﻱﺎﻨﻏ ﻪﺒﺗﺮﻣ
( ۲ ﻪﺒﺗﺮﻣ ﺯﺍ ﺎﻳﺎﭘ ،ﻲﺴﻧﺎﻛﺮﻓ ﻒﻴﻃ ،ﻩﺩﺎﺳ ﻲﺳﻮﻨﻴﺳ ﻝﺎﻨﮕﻴﺳ
ﺎﻫ ﻪﺒﺗﺮﻣ ﻪﻤﻫ ﺯﺍ ﺎﻳﺎﭘ ،ﺪﻴﻔﺳ ﺰﻳﻮﻧ ﻝﺎﻨﮕﻴﺳ
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ﻝﺎﺜﻣ : ﺏﻭﺎﻨﺗ ﻩﺭﻭﺩ ﺎﺑ ﯽﻌﺑﺮﻣ ﺝﻮﻣ ﯼﺩﻭﺭﻭ ﻭ ﺲﻟﺎﭘ ﯼﺩﻭﺭﻭ ۱۰۰
ﻪﻧﻮﻤﻧ
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ ﻝﺮﺘﻨﻛ ﻪﻘﻠﺣ ﺭﺩ ﻦﻴﻤﺨﺗ
ﻲﻠﺻﺍ ﺲﻳﺮﺗﺎﻣ ﻥﺪﺷ ﻩﮋﻳﻭ ﺐﺟﻮﻣ ﺪﻧﺍﻮﺗ ﻲﻣ ﺭﻮﺨﺴﭘ ﻲﻄﺧ ﻁﺎﺒﺗﺭﺍ ﻭ ﻲﮔﺩﺎﺳ • ﺩﺩﺮﮔ
.
ﻝﺎﺜﻣ • : y(t)=-ku(t) ﺎﻳ
y(t)=-ku(t-1)
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ﻞﺒﻗ ﻝﺎﺜﻣ ﻱﺯﺎﻓ ﻪﺤﻔﺻ ﺭﺍﺩﻮﻤﻧ
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ ﺎﻫ شور ﻪﺴﯾﺎﻘﻣ
LMS
PA
SA سرد لوا هژوﺮﭘ
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ﻪﺴﻳﺎﻘﻣ ﻱﺎﻬﺷﻭﺭ RLS (a LMS (b PA (c SA (d
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ ﻝﺎﺜﻣ : ﻦﻴﻣﺯ ﻪﺑ ﻦﻴﻣﺯ ﻚﺷﻮﻣ ﻚﻳ ﻢﺘﺴﻴﺳ
ﭻﻴﭘ ﻝﺎﻧﺎﻛ ﻞﻳﺪﺒﺗ ﻊﺑﺎﺗ ﻱﺎﻫﺮﺘﻣﺍﺭﺎﭘ ﻲﺘﺸﮔﺯﺎﺑ ﻩﺩﺎﺳ ﺵﻭﺭ
0 200 400 600 800 1000 1200
-0.4 -0.2 0 0.2 0.4 0.6 0.8 1
0 200 400 600 800 1000 1200
-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5
١۴
ﺲﻧﺎﻳﺭﺍﻮﻛ ﻲﻧﺎﺸﻧﺯﺎﺑ ﺵﻭﺭ
ﺯﺍﻭﺮﭘ ﻝﺎﺣ ﺭﺩ ﻲﻠﺻﺍ ﻢﺘﺴﻴﺳ ﻂﺧ ﻱﻭﺭ ﻲﻳﺎﺳﺎﻨﺷ ﺭﺩ ﻥﺩﻮﺑ ﺎﻳﺎﭘ ﻪﻟﺎﺴﻣ
!
0 200 400 600 800 1000 1200
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
0 200 400 600 800 1000 1200
-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
ﺵﻭﺭ ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ تﺎﻌﺑﺮﻣ ﻦﯾﺮﺘﻤﮐ شور يزﺎﺳ هدﺎﯿﭘ ﯽﮑﯿﻣﺎﻨﯾدوﺮﯾآ ﺐﯾاﺮﺿ ﻦﯿﻤﺨﺗ رد ﯽﺘﺸﮔزﺎﺑ
ﻒﻟﺍ ( ﯼﺭﺎﮑﺘﺑﺍ ﺵﻭﺭ ﻲﻳﺎﻀﻓ ﻞﻣﺎﺣ ﮏﻳ ﺖﮐﺮﺣ ﺕﻻﺩﺎﻌﻣ
١۵
ﺵﻭﺭ ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ
١۶
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ
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ﺏ ( ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﯽﻟﻮﻤﻌﻣ ﺵﻭﺭ
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ
١٨
ﺕﺎﻌﺑﺮﻣ ﻦﻳﺮﺘﻤﮐ ﺵﻭﺭ
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