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PROBLEM
İki sinüz= oidal taşıyıcı ve DC ötelemeden oluşan, gürültü ile bozulmuş işaretten parametre kestirim= i:
=
~ WGN
Kestirilecek Parametreler:
•DC öteleme: -∞ < B < = ∞ <= /span>
•Taşıyıcı genlikleri: A1 > 0    ,    A2 > 0
•Taşıyıcı frekansları: 0 <= f1 < 0.5 &= nbsp; ,   0 <= f2 < 0.5
•Gürültü varyansı:
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YÖNTEM
Olabilirlik fonksiyonu:   ,   x sabit, θ değişken=
= EN ÇOK OLABİLİRLİK KESTİRİMİ
(MAXIMUM LIKELIHOOD ESTIMATION – MLE) <= /div>
Olabilirlik fonksiy= onunu en büyükleyen θ değeri, kestirilmek istenen θ vektörün&= uuml; verir.
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ANALİTİK ÇÖZÜM
B, A1, A2, f1 <= /span>ve  f2’nin MLE’lerini  bulmak için aşağıdaki fonksiyonu en küçüklemek gerekir= .
<= ![endif]> = =
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ANALİTİK ÇÖZÜM
      J fonksiyonunda yeri= ne konulursa; =
=
matrisi simetrik ve birim güçlüdür (idempotent).
=
J fonksiyonu  sadece f1 <= /span>ve  f2’ye bağlıdır. f1 <= /span>ve  f2’nin MLE’lerinin bulunması için        = ;            &n= bsp;       ifadesinin en büyüklenmesi gerekir.
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Adım 1:<= /u>
f ve f’nin <= span lang=3DEN-US style=3D'font-family:"Times New Roman";font-size:133%'>0<<= /span> f<= /i>1<0.5 ve 0< f2<0.5 aralıkları için ızgara taraması (grid search) yapılarak bir önceki yansıdaki ifadeyi en büyükleyen   &= #13;
     ve      değe= rleri bulunur.
=
f1=3D f2 olduğunda        = ;       olur. Bu durumda;
matrisi yaklaşık olarak tekil olur. Bu sorunun üstesinden gelmek için, f1=3D f<= /i>2 olduğu durumlarda        = ;            &n= bsp;             matrisinin ilgili hücrelerine çok küçük sayı değerleri atanmıştır.
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Adım 2:<= /u>
     ve        değerleri        = ;            &n= bsp;            = ;           ifadesinde yerine konarak        elde edilir ve 
= =
eşitliğin= den faydalanılarak      ,        ve     &n= bsp;   değerleri bulunur. =
=
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BENZETİM
Adım 4:<= /u>
Kestirimcinin başarımını test etmek amacıyla, tüm parametr= eler kestirildikten sonra bu parametreler kullanılarak kestirilmiş ve= ri elde edilir;
<= ![endif]>
~ WGN
ve ortalama karesel= hata (MSE) kriteri kullanılarak orijinal veri ile kestirilmiş veri karşılaştırılır.
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SONUÇLAR
-49,33
-37,16
-31,7
MSE (dB)
0,24996
0,24956
0, 24683
0,25
σ= 2
1,2533
1,2677
1,2733
1,25
A2
1,5035
1,4916
1,4716
1,5
A1
3,5
3,5
3,5
3,5
B
0,2
0,2
0,2
0,2
f2
0,3
0,3
0,3
0,3
f1
Kestirilmiş
Değer
(N=3D10000)
Kestirilmiş
Değer
(N=3D1000)
Kestirilmiş
Değer
(N=3D100)
Gerçek
Değer
<= /div>
Tablo 1: Çeşitli veri uzunlukları için kestirimci başarımlarının karşılaştırılma= sı
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