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Lainiotis filter, golden section and Fibonacci sequence

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Title: Lainiotis filter, golden section and Fibonacci sequence
Authors: Assimakis, Nicholas1 assimakis@teilam.gr, Adam, Maria2 madam@ucg.gr, Triantafillou, Chrissavgi3 chrtriantafillou@teilam.gr
Source: Signal Processing. Apr2013, Vol. 93 Issue 4, p721-730. 10p.
Subjects: Riccati equation, Estimation theory, Stochastic systems, Random walks, Mathematical analysis, Finite impulse response filters
Abstract: Abstract: The relation between the discrete time Lainiotis filter on the one side and the golden section and the Fibonacci sequence on the other is established. As far as the random walk system is concerned, the relation between the Lainiotis filter and the golden section is derived through the Riccati equation since the steady state estimation error covariance is related to the golden section. The relation between the closed form of the Lainiotis filter and the Fibonacci sequence is also derived. It is shown that the steady state Lainiotis filter computes the state estimate using a linear combination of the previous estimate and of the current measurement with coefficients related to the golden section. A Finite Impulse Response (FIR) implementation of the steady state Lainiotis filter is also proposed, where the filter computes the state estimate as a linear combination of a well-defined set of the last measurements with coefficients which are powers of the golden section. Finally, the scalar generic stochastic dynamic system is considered and the relation between its parameters and the golden section is investigated. [Copyright &y& Elsevier]
Copyright of Signal Processing 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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DbLabel: Engineering Source
An: 84477622
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  Data: Lainiotis filter, golden section and Fibonacci sequence
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  Data: <searchLink fieldCode="AR" term="%22Assimakis%2C+Nicholas%22">Assimakis, Nicholas</searchLink><relatesTo>1</relatesTo><i> assimakis@teilam.gr</i><br /><searchLink fieldCode="AR" term="%22Adam%2C+Maria%22">Adam, Maria</searchLink><relatesTo>2</relatesTo><i> madam@ucg.gr</i><br /><searchLink fieldCode="AR" term="%22Triantafillou%2C+Chrissavgi%22">Triantafillou, Chrissavgi</searchLink><relatesTo>3</relatesTo><i> chrtriantafillou@teilam.gr</i>
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  Data: <searchLink fieldCode="JN" term="%22Signal+Processing%22">Signal Processing</searchLink>. Apr2013, Vol. 93 Issue 4, p721-730. 10p.
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  Data: <searchLink fieldCode="DE" term="%22Riccati+equation%22">Riccati equation</searchLink><br /><searchLink fieldCode="DE" term="%22Estimation+theory%22">Estimation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+systems%22">Stochastic systems</searchLink><br /><searchLink fieldCode="DE" term="%22Random+walks%22">Random walks</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+impulse+response+filters%22">Finite impulse response filters</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: Abstract: The relation between the discrete time Lainiotis filter on the one side and the golden section and the Fibonacci sequence on the other is established. As far as the random walk system is concerned, the relation between the Lainiotis filter and the golden section is derived through the Riccati equation since the steady state estimation error covariance is related to the golden section. The relation between the closed form of the Lainiotis filter and the Fibonacci sequence is also derived. It is shown that the steady state Lainiotis filter computes the state estimate using a linear combination of the previous estimate and of the current measurement with coefficients related to the golden section. A Finite Impulse Response (FIR) implementation of the steady state Lainiotis filter is also proposed, where the filter computes the state estimate as a linear combination of a well-defined set of the last measurements with coefficients which are powers of the golden section. Finally, the scalar generic stochastic dynamic system is considered and the relation between its parameters and the golden section is investigated. [Copyright &y& Elsevier]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Signal Processing 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.sigpro.2012.09.014
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      – Code: eng
        Text: English
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        PageCount: 10
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    Subjects:
      – SubjectFull: Riccati equation
        Type: general
      – SubjectFull: Estimation theory
        Type: general
      – SubjectFull: Stochastic systems
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      – SubjectFull: Random walks
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      – SubjectFull: Mathematical analysis
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      – SubjectFull: Finite impulse response filters
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      – TitleFull: Lainiotis filter, golden section and Fibonacci sequence
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              M: 04
              Text: Apr2013
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