Ahmet Hamdi KAYRAN, Ender Mete EKŞİOĞLU

Gerekirci diziler kullanarak doğrusal olmayan sistem tanılama

Bu çalışmada sınırlı doğrusalsızlık derecesine sahip Volterra süzgeçleri için yeni bir gösterilim geliştirilmekledir. Bu gösterilim kullanılarak Volterra süzgeçleri için kesin bir tanılama yöntemi sunulmaktadır. Bu yeni yöntem, giriş işareti olarak farklı seviyelere sahip impulslardan oluşan gerekirci diziler kullanmaktadır. Yeni tanılama yöntemi doğrusal, zamanla-değişmez sistemlerdeki birim impuls cevabının doğrusal olmayan sistemlere başarılı bir uyarlaması olarak düşünülebilir. Çalışmada sunulan tanılama yöntemi kesindir; böylece gözlem gürültüsü olmadığında Volterra çekirdeklerini hatasız kestirmektedir. Bilgisayar benzetimleriyle tanılama yönteminin literatürde yakın zamanda sunulmuş olan yöntemlerden daha iyi kestirim sonuçları verdiği gösterilmiştir.

Nonlinear system identification using deterministic multilevel sequences

In this paper we develop a new representation for the finite-order Volterra filters. This representation introduces a novel partitioning of the Volterra kernels. Using this representation, we formulate a novel exact identification method for Volterra filters, which uses deterministic sequences consisting of impulses with distinct levels. The identification method might be considered as a successful extension of the impulse response of the linear, time-invariant systems to the realm of nonlinear systems. The developed method indeed includes identification using the unit impulse response as a subcase when the system under consideration is a linear system. Our identification method is exact; hence, it calculates the exact Volterra kernels in the absence of noise for very short length input sequences. Our method calculates each Volterra kernel individually. The kernel estimates are not utilized in the calculation of further kernel estimates. This property hinders error propagation among kernel estimates. Our method calculates directly the Volterra kernels, instead of calculating first some intermediary representation such as the Wiener kernels, which do not have any directly interpretable results. Our method does not introduce and identify any kernels which are redundant for the regular Volterra filter. We demonstrate with simulations that the identification algorithm can produce better parameter estimates than some most recent algorithms in the literature.

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