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Golden section, Fibonacci sequence and the time invariant Kalman and Lainiotis filters.

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Title: Golden section, Fibonacci sequence and the time invariant Kalman and Lainiotis filters.
Authors: Adam, Maria1 madam@dib.uth.gr, Assimakis, Nicholas1,2 assimakis@mail.teiste.gr, Farina, Alfonso3 alfonso.farina@selex-es.com
Source: Applied Mathematics & Computation. Jan2015, Vol. 250, p817-831. 15p.
Subjects: Golden ratio, Fibonacci sequence, Kalman filtering, Stochastic analysis, Dynamical systems
Abstract: We consider the discrete time Kalman and Lainiotis filters for multidimensional stochastic dynamic systems and investigate the relation between the golden section, the Fibonacci sequence and the parameters of the filters. Necessary and sufficient conditions for the existence of this relation are obtained through the associated Riccati equations. A conditional relation between the golden section and the steady state Kalman and Lainiotis filters is derived. A Finite Impulse Response (FIR) implementation of the steady state filters is proposed, where the coefficients of the steady state filter are related to the golden section. Finally, the relation between the Fibonacci numbers and the discrete time Lainiotis filter for multidimensional models is investigated. [ABSTRACT FROM AUTHOR]
Copyright of Applied Mathematics & Computation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: <searchLink fieldCode="DE" term="%22Golden+ratio%22">Golden ratio</searchLink><br /><searchLink fieldCode="DE" term="%22Fibonacci+sequence%22">Fibonacci sequence</searchLink><br /><searchLink fieldCode="DE" term="%22Kalman+filtering%22">Kalman filtering</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+analysis%22">Stochastic analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink>
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  Data: We consider the discrete time Kalman and Lainiotis filters for multidimensional stochastic dynamic systems and investigate the relation between the golden section, the Fibonacci sequence and the parameters of the filters. Necessary and sufficient conditions for the existence of this relation are obtained through the associated Riccati equations. A conditional relation between the golden section and the steady state Kalman and Lainiotis filters is derived. A Finite Impulse Response (FIR) implementation of the steady state filters is proposed, where the coefficients of the steady state filter are related to the golden section. Finally, the relation between the Fibonacci numbers and the discrete time Lainiotis filter for multidimensional models is investigated. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Applied Mathematics & Computation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.amc.2014.11.022
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      – Code: eng
        Text: English
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        PageCount: 15
        StartPage: 817
    Subjects:
      – SubjectFull: Golden ratio
        Type: general
      – SubjectFull: Fibonacci sequence
        Type: general
      – SubjectFull: Kalman filtering
        Type: general
      – SubjectFull: Stochastic analysis
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      – SubjectFull: Dynamical systems
        Type: general
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      – TitleFull: Golden section, Fibonacci sequence and the time invariant Kalman and Lainiotis filters.
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              Text: Jan2015
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