Browsing by Subject "Linear estimation"

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    Optimal linear MMSE estimation in presence of correlation uncertainty under restricted Bayesian framework
    (2023-06) Topaloğlu, Süleyman Taylan
    A restricted Bayes approach is proposed for the linear estimation of a scalar random parameter based on a scalar observation under uncertainty regarding the correlation between the parameter and the observation. In particular, the optimal linear estimator that minimizes the average mean-squared error (MSE) is derived under a constraint on the worst-case MSE by considering possible values of the correlation coefficient and its probability distribution. A closed-form expression is derived for the optimal linear estimator in the proposed restricted Bayesian framework by considering a generic statistical characterization of the correlation coefficient. The performance of the proposed estimator is evaluated via numerical examples and its benefits are illustrated in various scenarios. The proposed framework is also extended to the case of vector-valued observation and the properties of the optimal linear estimator are characterized.
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    Optimal linear mmse estimation under correlation uncertainty in restricted bayesian framework
    (Institute of Electrical and Electronics Engineers, 2023-01-31) Dulek, B.; Topaloğlu, Süleyman Taylan; Gezici, Sinan
    A restricted Bayes approach is proposed for linear estimation of a scalar random parameter based on a scalar observation under uncertainty regarding the correlation between the parameter and the observation. In particular, the optimal linear estimator that minimizes the average mean-squared error (MSE) is derived under a constraint on the worst-case MSE by considering possible values of the correlation coefficient and its probability distribution. A closed-form expression is derived for the optimal linear estimator in the proposed restricted Bayesian framework by considering a generic statistical characterization of the correlation coefficient. Performance of the proposed estimator is evaluated via numerical examples and its benefits are illustrated in various scenarios. The proposed framework is also extended to the case of vector-valued observation and the properties of the optimal linear estimator are characterized.
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    Yapısal veri belirsizlikleri altında yarışmacı doğrusal MMSE kestirim
    (IEEE, 2014-04) Vanlı, N. Denizcan; Sayın, Muhammed Ö.; Kozat, Süleyman S.
    Bu bildiride, yapısal veri belirsizlikleri altında doğrusal kestirim problemi incelenmektedir. Maliyet fonksiyonu olarak ortalama karesel hata (MSE) düşünülmüştür ve sınırlı belirsizlikler altında gürbüz bir algoritma önerilmiştir. Sunulan yöntem yarışmacı algoritma yapısına sahiptir ve bu yapıya ulaşmak için doğrusal kestiricinin performansı, bilinmeyen veri belirsizliklerine göre ayarlanmış doğrusal enküçük MSE (MMSE) kestiricisinin performansına göreceli olarak tanımlanmıştır.Daha sonra, bu göreceli performans ölçütünü en kötü durumdaki sistem modeline göre enküçülten doğrusal kestirici bulunmuştur. Bu yarışmacı kestiriciyi bulmak için çözülmesi gereken problemin yarı-kesin programlama (SDP) problemi olarak düşünülebileceği gösterilmiştir. Ayrıca, teorik sonuçları izah etmek için sayısal örnekler sunulmuştur.