3 ()

         1 ؼ(2)

   
 

1.1   Ư

1.2   zero ʽ

1.3    ʽ

1.4   1

1.5   Ư 

 

 

  1.1  Ư                                                             

  ý Էμ ȣ 踦 ̿, ޼ϰ ִ.  ȣμ ̿Ǵ ڴ, Ư 迡 ִ ̴.  ׷, 谡 ƴϰ Ƿ,  θ ϴµ Ͽ ϰ ȴ. 

  parameter  ׸ ý noise ⿡
Ҿ ¿ ִ Ÿ ִ. Է ȣ Ư ̻ , δ noise ̻ ()  ȴ. parameter , noise ü ʰ Ư y noise z
1, z2, ..., zk ʴ(Ȥ ޴ ), parameter x1, x2, ..., xn ϹǷ ¸ ϴ ̴.

 
 

   ȣ ȭ Ư ȭ , л 2 ϸ  dB SN
                  
= 10 log ( 2 / 2 )                                                                                       ()
Ѵ. 
                                                                                                                        

   y M 谡 y = M ũٴ ῡ ؼ ϰ ȴٴ ̸(ȿ )  A B ϴ. A. C ϸ A . Ư ̿ ² / ² ̴ Ʈ̴.


   Ư 3 ִ.
zero ʽ : Է (ȣ ) M̶ ϰ, M = 0 y = 0 иϿ, y = M   ̻    
ʽ : Ǵ Ms ְ, ġħ zero ǵ , zero ʽ yys = (MMs) ̻ .
1 : ȣ ڿ ̿, Ư y = ᣫM 踦 ϴ .  ÿ Ͽ л Ѵ. 

Ͽ Ѵ

    1.2   zero ʽ                                                   

  ȣ, Է M ϰ M = 0 y = 0 ̶ иϸ(̷ Ǵ zero ߱ ) M y ̻ 谡 ʽ
               y = M
츦 Ѵ. y ȣ M x
1, x2, , xn Լ̴ 
     

             y = f ( M, x1, x2, , xn )
̰ e̴, ,
               e = f ( M, x1, x2, , xn ) - M

Ҹµ, ⿡ e SN .

             1 / = [ { f ( M, x1, x2, , xn ) - M } / ]2
δ ȣ M  k M
1, M2, Mk κ  r0 ϰ y д´. ʹ ǥ .
 

Ϳ ʻ SN Ѵ.  
 

 1) zero ʽ

л ּҰ ǵ ⸦ ϸ
             = ( M1y1 + M2y2 + + Mkyk ) / r                                                                         ()
, ⼭  r ȿ⦶ Ҹ
             r = r0 ( M12 + M2 2 + + Mk2 )                                                                               ()
̴.  ̶ y M (zero ʽ)
             y = M
ȴ.

 2) zero ʽ SN

SN ϱ лм Ѵ.  ST ȣ 1ȿ S Ϲݽ Ѵ.
           ST = = y112 + y122 + + ykr02
             S = ( M1y1 + M2y2 + + Mkyk )2 / r                                                                      ()


             Se = ST - S
Ǹ л ̸ (kr
0 - 1)
             Ve = Se / ( kr0 - 1 )
ȴ.

лмǥ ϸ .  

 

л 밪 2 ²
             ² = ( S - Ve ) / r
             ² = Ve
̴.   SN
             = ² / ² = { ( S - Ve ) / r } / Ve                                                                                                ()
ȴ.

 

 3) zero ʽ

SN Ѵ. ȣμ οǴ е Ͽ ߴ. ڸ ٲپ 2ȸ ͸ . M y ζ ˰ ־ zero ʽ Ѵ.  
лм Ѵ.
      
          ST = 652 + 742 + + 1972 = 131, 879      (f = 6)
             r = 2 × ( 302 + 602 + 902 ) = 25,200
             S = ( 30 × 139 + 60 × 283 + 90 × 405 )2 / r
                  = 57, 6002 / 25,200 = 131, 657       (f = 1)
             Se = ST - S = 131, 879 - 131, 657 = 222      (f = 5)
             Ve = Se / 5 = 222 / 5 = 44.4
̸ ϸ лмǥ ȴ.

 

SN
             = { ( 131657 - 44.4 ) / 25200 } / 44.4 = 0.1177
ȴ. ú ȯŰ
             = 10 log 0.1177 = - 9.29  (dB)
̴.
             = 57600 / 25200 = 2.285
Ǹ, M y
             y = 2.285M
ȴ.

 

  1.3    ʽ                                                     

 Ǵ Ms ǥ ְ ġħ ΰ ǵ zero ʽ ̻ ̴.  y M ̻ 踦
             y - ys = ( M - Ms )
ȴ. ϴ ȣ ηκ ũ ŻǾ  Ǵ
y bar y ǥ )

 

 1) ʽ ó

zero ʽ ġǥ ǥ ͷ ȯѴ. հ ϴ 쿡 Ѵ. ǥ Ms ǵ ys1, ys2, , ysro ϸ հ ys
            
ys = ( ys1 + ys2 + + ysro ) / ro
ȴ. ǵκ
ys ǥ ٽ ͸ Ѵ. ׸ ǥذ Ms ,   Mi - Ms ģ. Mi - Ms ̳ʽ Ǵ 쵵 ִ. ׸ yi ٽ ̴.

 

հ ysſ ǵ Ͽ ϰų ݺ 1ȸ° ǵ ϴ Ǽ ִ

 2) ʽ

ʽ Ѵ.
             = { y1 ( M1 - Ms ) + y2( M2 - Ms ) + + yk ( Mk - Ms ) } /r                                    
()
ȿ
             r = r0{ ( M1 - Ms )2 + ( M2 - Ms )2 + + ( Mk -Ms )2}                    
                          ()
̴. ȸͽ
             ( y -
ys ) = ( M - Ms )
ȴ.
 

 3) ʽ SN

ǥ ͸ ġ zero ʽ Ϳ Ѵ. ٸ zero ʽ Ѵ.

ȣ 1ȿ Ϲݽ ȴ
             ST = (yij -
ys)
             S = { y1 ( M1 - Ms ) + y2 ( M2 - Ms ) + + yk ( Mk - Ms ) }2 / r                              
()

             Se = ST - S
л
             Ve = Se / ( kr0 - 1 )
̸ лм ϸ ǥ .
SN
             = { ( S - Ve ) / r } / Ve
ȴ.


   


ٽ M
i - Ms Mi,   yij -
ys yij ġ δ zero ʽİ ȴ.
             ST = = y112 + y122 + + ykr02
             = ( M1y1 + M2y2 + + Mkyk ) / r
             r = r0 ( M12 + M22 + + Mk2 }
             S = ( M1y1 + M2y2 + + Mkyk )2 / r

: , Ի꿡 ϴ ͷκ ys 쿡 (kr0 - 1) Ǹ (kr0 - 2) ȴ. ׸ 꿡 ϴ Ϳʹ ͸ 쿡 kr0,
(kr
0 - 1) ȴ. ϰԴ ξ , 迡 ̰ ۱ Ͻ (kr0 - 1) ߴ.
 

 4) ʽ

÷ 󵵸 ϴ м SN Ѵ. ȣڷμ 4 󵵸 ǥؾ ߴ. м 5% ǥؾ ʽ Ͽ Ѵ. ڸ ٲپ2ȸ ǥ ͸ .  

 

켱 ͸ ó Ѵ. Ms = 5%
            
ys = ( 5.2 + 5.0 ) / 2 = 5.1
̹Ƿ ͷκ ͸ Ѵ. Ʒǥ .

 

лм Ѵ.
             ST = 0.12 + (- 0.1) 2 + + 15.22 = 722.350  (f = 8)
             r = 2 × ( 02 + 52 + 102 + 15 2 ) = 700
             S = ( 0 × 0 + 5 × 10.2 + 10 × 20.7 + 15 × 30.2 )2 / 700
                  = 711
2 / 700 = 722.173     (f = 1)
             Se = ST - S = 722.35 - 722.173 = 0.177     (f = 7)
             Ve = Se / 7 = 0.1771 / 7 = 0.025

̸ ϸ лмǥ ´.

   

SN
             = { ( 722.173 - 0.025 ) / 700 } / 0.025 = 40.76  (%)2
ȴ. ׸ ú ȯϸ
             = 10 log 40.76 = 16.10  (dB)
̴.

               = 711 / 700 = 1.015
Ǹ M y
             y - 5.1 = 1.015 (M - 5)
ȴ.
 

  1.4  1                                                                  

ȣڿ ̿ Ư 踦 ̴. M y 1
           y = + M
ϰ, Լ ʿ з ÿ Ͽ л ϴ ̴.

 1) 1  

1 ׽ · ٲپ  з͸ Ѵ.
             y = m + ( M -
M )                                                                                                                                ()

  
 
( M bar M ǥ )

з m Ϲݽ ȴ.
             m =
y
 
           = { y1 ( M1 -
M ) + y2 ( M2 - M ) + +yk ( Mk - M ) }/r                                        ()
             M = ( M1 + M2 + + Mk )/k
ȿ
             r = r0 { ( M1-
M )2 + ( M2 - M )2 + + ( Mk - M )2}                                                 ()
̴. Լ
             y = m + ( M -
M )
ȴ.

 

 2) 1 SN  

SN ϱ лм Ѵ. , Ϲݺ ȣ 1 ȿ Ϲݽ ȴ.
             ST = y112 + y122 + + ykr02
             Sm = (yij)2 / kr0
             S = { y1 ( M1 -
M ) + y2 ( M2 - M ) + + yk ( Mk - M ) }2 / r                                  ()
ȣ ذ  ƴ 쿡 ϹݽĿ Ͽ Ѵ. ȣ ذ  h 쿡 ȹ ηǥ ִ "׽ ǥ" ̿Ѵ.   k = 4
             S = (-3y1- y2 + y3 + 3y4 )2 / 20 r0
             r = 5 r0 h2
̴.

             Se = ST - Sm - S
л
             Ve = Se / ( kr0 - 2 )
̴. лмǥ ϸ, .

 

SN
            
= { ( S - Ve ) / r }/ Ve

ȴ.

 3) 1

öƽ ⼺ з ȣ Ͽ  ǰ ġ ϰ ִ. ý SN ϱ з ȭ ϰ ǰ2 ġ Ͽ ͸ . 쿡 迡 Ư ʰ 1 Ѵ.

 ǥ лм ϴ ( Mi - M ) ߴ. ⼭ M = 45 ̴.

  

лм Ѵ.
             ST = 4.6082 + 4.5902 + + 4.7022 = 173.552     (f = 8)
             Sm = ( 9.198 + + 9.420 )2 / 8 = 173.538     (f = 1)
             r = 2 ×{ (-15 )2 + ( -5 )2 + 52 + 152} = 1000
             S = { (-15 ) × 9.198 + +15 × 9.420 }2 / 1000
                  = 0.013      (f = 1)
             Se = ST - Sm - S  = 173.552 - 173.538 - 0.013
                 = 0.000516     (f = 6)
             Ve = Se / 6 = 0.000516 / 6 = 0.00009

̸ ϸ лмǥ ´.

   

SN
            
= {( 0.013-0.00009 ) / 1000 } / 0.00009 = 0.153 ȴ. ׸ ú ȯϸ
            
= 10 log 0.153 = -8.156  (dB)
̴.

հ m
             m = 37.26 / 8 = 4.66
              = 3.64 / 1000 = 0.0036
Ǹ, M y
             y = 4.66 + 0.0036 ( M-45 )
ȴ.

׸ S 꿡 ־, ʿ ȣ  Ƿ ׽ ִ. 쿡  k = 4, r0 = 2, h = 10 ̹Ƿ
             S = ( -3y1 - y2 + y3 + 3y4 )2 / ( 20 × r0 )
                 = { ( -3 ) × 9.198 - 9.290 + 9.352 + 3 × 9.420 }2 / ( 20 × 2 )
             r = 5 r0 h2 = 5 × 2 ×102 = 1000

ε ִ. лм .
 

   1.5 Ư