Widely Linear Quaternion-Valued Least-Mean Kurtosis Algorithm

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dc.authoridMandic, Danilo/0000-0001-8432-3963
dc.contributor.authorMenguc, Engin Cemal
dc.contributor.authorAcir, Nurettin
dc.contributor.authorMandic, Danilo P.
dc.date.accessioned2024-11-07T13:34:38Z
dc.date.available2024-11-07T13:34:38Z
dc.date.issued2020
dc.departmentNiğde Ömer Halisdemir Üniversitesi
dc.description.abstractA widely linear quaternion-valued least-mean kurtosis (WL-QLMK) algorithm is introduced for adaptive filtering of quaternion-valued circular and noncircular signals. In the design, kurtosis-based cost function is first defined in the quaternion domain by integrating the widely linear model, and augmented statistics, and then minimized using the recently developed generalized Hamilton-real (GHR) calculus. In this way, the novel WL-QLMK algorithm is obtained for training quaternion-valued adaptive filter structures. Furthermore, its steady-state performance is theoretically analyzed to determine the bounds of the step size, which provides a theoretical justification for simulations. The simulation results over both benchmark system identification scenarios, and one-step-ahead predictions of real-world 4D pathological resting tremors show that the proposed WL-QLMK algorithm, by virtue of its newly defined cost function, significantly enhances the performance compared to the recently developed quaternion-valued algorithms, especially for noncircular signals.
dc.identifier.doi10.1109/TSP.2020.3029959
dc.identifier.endpage5922
dc.identifier.issn1053-587X
dc.identifier.issn1941-0476
dc.identifier.scopus2-s2.0-85105868095
dc.identifier.scopusqualityQ1
dc.identifier.startpage5914
dc.identifier.urihttps://doi.org/10.1109/TSP.2020.3029959
dc.identifier.urihttps://hdl.handle.net/11480/16077
dc.identifier.volume68
dc.identifier.wosWOS:000584793600001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherIEEE-Inst Electrical Electronics Engineers Inc
dc.relation.ispartofIeee Transactions on Signal Processing
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_20241106
dc.subjectQuaternions
dc.subjectSignal processing algorithms
dc.subjectCalculus
dc.subjectCovariance matrices
dc.subjectCost function
dc.subjectAdaptation models
dc.subjectAlgebra
dc.subjectAdaptive filters
dc.subjectcircular and noncircular quaternion signals
dc.subjectleast mean kurtosis
dc.subjectstrictly linear
dc.subjectwidely linear
dc.titleWidely Linear Quaternion-Valued Least-Mean Kurtosis Algorithm
dc.typeArticle

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