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

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  • Adam, Maria
  • Assimakis, Nicholas
  • Farina, Alfonso

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.

Suggested Citation

  • Adam, Maria & Assimakis, Nicholas & Farina, Alfonso, 2015. "Golden section, Fibonacci sequence and the time invariant Kalman and Lainiotis filters," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 817-831.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:817-831
    DOI: 10.1016/j.amc.2014.11.022
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    References listed on IDEAS

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    1. Büyükkılıç, F. & Demirhan, D., 2009. "Cumulative growth with fibonacci approach, golden section and physics," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 24-32.
    2. Stakhov, A.P., 2005. "The Generalized Principle of the Golden Section and its applications in mathematics, science, and engineering," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 263-289.
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    Cited by:

    1. Florek, Wojciech, 2018. "A class of generalized Tribonacci sequences applied to counting problems," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 809-821.

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