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1 N ΦT Z §N "K
O (5)
5.7 9C{ 5.8 ' { {
θIV = (Z T Φ)1 Z T Y θIV = (Z T Φ)1 Z T (Φθ + e) = θ + (Z T Φ)1 Z T e OθIV ìC ^
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1 N ΦT Z §N "K
O (5)
5.7 9C{ 5.8 ' { {
θIV = (Z T Φ)1 Z T Y θIV = (Z T Φ)1 Z T (Φθ + e) = θ + (Z T Φ)1 Z T e
(12)
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\9C§=
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y(D) u(n) u(0) . . . . Z= . . y(n D + N 2) y(N D 1) u(n + N 1) u(N 1) (15) òD ≥D( .MA g" y(n D 1)
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ü
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k^ {o θ§2òθ“\(9)§ w(k)"2(8) E9C §|^(5) θ 9C OθIV §, 2òθIV “\ (9)2g w(k)"Xd4í O9Cê§ ÷ E(J" {2gA{ ù{¤J 9Cw(k)9C Z /{ §9 .êθ O{{k¤ " θ(k) = (1 α)θ(k 1) + αθ(k d) (10) α 0.01 0.1§d 0 10§θ(k)k¤ ê O" .(1) D(e(k)u(k)'§…u(k)±Y-y&§¤ 9C÷vü^"
k=0
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§m
'XdWiener–Hopf§5§=
N 1
Ruy (τ ) =
i=0
g(i)Ru (i τ )
(25)
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X \ ê § X J ò e Ru (τ ) |“ê§"dd§ Ruy (τ ), τ = 1, 2, , p.Kd§(25) )óA G = [g(1) g(1) g(p)]T ù0 L '{"
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θCORLS = (ΦT ΦN )1 ΦT Ruy,N N N e±xD(&–‘ &X XA^ OXê . ê"
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1. xD(\& \&xD(§g'ê Ru (τ ) = ù§Wiener–Hopf§{z Ruy (τ ) = g(τ )Ru (0) = σ 2 g(τ ) ù §§(27) (32) σ2 0 τ =0 τ =0 (31)
y(k)r
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u(1) u(2) . . . u(N )
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A(z 1 )w(k) = B(z 1 )u(k) A(z )B(z ) Xê LS“{)"
1 1
(9) w(k)Q±
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θIV = (Z T Φ)1 Z T Y θIV = (Z T Φ)1 Z T (Φθ + e) = θ + (Z T Φ)1 Z T e OθIV ìC ^
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(1) lim (2) lim
1 T N Z Φ N →∞
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1 T NZ e N →∞
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\&u(k)±Y-y&§…D(e(k)'§K9C÷ vü^"
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{4Tally n XJD(e(k)w¤e
MA .
1
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e(k) = D(z )ε(k) ε(k)" '‘D(§… D(z 1 ) = 1 + d1 z 1 + + dm z m K9C A w(k) = y(k D), 9C |^ò D≥m
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Ruy,N = ΦN θ + EN
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Ruy,N = [Ruy (1) Ruy (2) Ruy (N )]T EN = [e(1) e(2) e(N )]T T (1) T ΦN = (2) T (N ) ù^ { '¨ { OθCORLS (30)
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3. 9C4í{ X5 § .
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A(z 1 )y(k) = B(z 1 )u(k) + e(k) N *ê O
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T T θ = [WN ΦN ]1 WN YN
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= 0§=Zeá"
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Z9C §Z 9C"Z JD( '§ ê Φ;—'"XJ¤^ 9C÷vü^§ Kk N →∞ θIV → θ w.p.1 (7) θIV 9Cê O"§ J9C§ ÷vü^§ê OθIV ± — O"
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3'– {§2|^óAS 5 OX ê ." X ê . gn ‘ §
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y(k) = a1 y(k1) an y(kn)+b0 u(k)+b1 u(k1)+ +bn u(kn)+e(k) (26) b \ & {u(k)} ‘ D ( S {e(k)} ' " ü > ±u(k τ )§ "§ Ruy (τ ) = a1 Ruy (τ 1) an Ruy (τ n)+b0 Ru (τ )+b1 Ru (τ 1)+ +bn Ru (τ n) (27)
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P0 = α2 I, θ0 = 0,
α"
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x0 = x1 = = xn = 0 éa"
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":éP0
U?50*100:^4í
§2=\IV4í§K
J
"
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5.7 9C{
1. g ¤{ 9C{óC{(Instrumental Variable, IV)"éu5 A(z 1 )y(k) = B(z 1 )u(k) + e(k) l\ =\ {u§ W =Z Z W é "8Iê J = eT W e K\ O θW LS = (ΦT Z Z T Φ)1 ΦT Z Z T Y (4) (3)
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5.7 9C{
¤
Ruy (τ ) = T (τ )θ + e(τ ) (28) "…