Least Square (LS) Similar to linear model,assume s=H J(0)=(cn]-snl)2 =(x-H0)T(x-H0) whxiong@uestc.edu.cn 11
whxiong@uestc.edu.cn Least Square (LS) 11 Similar to linear model, assume J(µ) = X(x[n] ¡ s[n]) 2 s = Hµ = (x ¡ Hµ) T (x ¡ Hµ)
Least Square (LS) Similar to linear model,assume s=H J(0)=(n-sm)2 =(x-H0)T(x-H0) -xTx-2xTH0+0THTHO whxiong@uestc.edu.cn 12
whxiong@uestc.edu.cn Least Square (LS) 12 Similar to linear model, assume J(µ) = X(x[n] ¡ s[n]) 2 s = Hµ = (x ¡ Hµ) T (x ¡ Hµ) = x Tx ¡ 2x T Hµ+ µ T HT Hµ
Least Square (LS) Similar to linear model,assume s =I0 J(0)=入(cm-sm)2 =(x-H0)T(x-H0) -xTx-2xTH0+0THTHO 0J(0=-2Hx+2HTH0 80 whxiong@uestc.edu.cn 13
whxiong@uestc.edu.cn Least Square (LS) 13 Similar to linear model, assume J(µ) = X(x[n] ¡ s[n]) 2 s = Hµ = (x ¡ Hµ) T (x ¡ Hµ) = x Tx ¡ 2x T Hµ+ µ T HT Hµ @J(µ) @µ = ¡2HTx + 2HT Hµ
Least Square (LS) Similar to linear model,assume s =I0 J(0)=入(cm-sn)2 =(x-H0)T(x-H0) -xTx-2xTH0+0THTHO 0J(0=-2Hx+2HTH0 80 0=(HTH)-HTx whxiong@uestc.edu.cn 14
whxiong@uestc.edu.cn Least Square (LS) 14 Similar to linear model, assume J(µ) = X(x[n] ¡ s[n]) 2 s = Hµ = (x ¡ Hµ) T (x ¡ Hµ) = x Tx ¡ 2x T Hµ+ µ T HT Hµ @J(µ) @µ = ¡2HTx + 2HT Hµ µ ^ = (HT H) ¡1 HTx