Cramer-Rao alt sınırı ile AR metodunda parametre kestirim performansının analizi

Bu çalışmada, kutup, varyans ve ortalama karesel hata gibi istatistiksel ölçümlerin değerlendirilmesi ile minimum varyanslı kutupsuz kestirim metodlarının belirlenmesi incelenmiştir, Kutupsuz kestirirn metodlarında Gramer-Rao alt sınırının hesaplanması ile kestirim metodlarının varyansları belirlenmiştir. Parametrjk metodlarda işaretin, nedensel, sıfır-kutup, ayrık, girişi beyaz gürültü olan filtrenin çıkışı olarak modellenmesi ve, bu modelin parametre kestirimi açıklanmıştır. Bu çalışmada kullanılan test işaretinin AR parametrelerinin kestirimi, Yule-Walker AR metodu ve en küçük kareler AR metodu ile yapılmıştır. Kestirim sonuçlarından Yule-Walker AR metodu ve en küçük kareler AR metodunun asimptotik olarak kutupsuz kestirim metodu oldukları gösterilmiştir. AR parametre kestiriminin asimptotik Cramer-Rao alt sınırı hesaplanmış ve böylece kestirim metodunun performansı belirlenmiştir.

Performance analysis of parameter estimation in AR method with Cramer-Rao lower bound

In this study, determination of minimum variance unbiased estimation methods was examined by the evaluation of statistical measurements such as bias, variance and mean square error. Variances of estimation methods were determined by calculation of Cramer-Rao lower bound in unbiased estimation methods. In parametric methods, modeling the signal as output of causal, zero-pole, discrete filter that has white noise input and parameter estimation of this model were explained. AR parameter estimation of test signal used in this study was done by Yule-Walker AR method and least square AR method. From the results of estimation it was indicated that Yule-Walker AR method and least square AR method were asymptotically unbiased estimation methods. Asymptotic Cramer-Rao lower bound of AR parameter estimation was calculated and thus performance of estimation method was determined.

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