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

Maria Adam, Nicholas Assimakis and Alfonso Farina

Applied Mathematics and Computation, 2015, vol. 250, issue C, 817-831

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.

Keywords: Positive definite matrices; Riccati equation; Kalman filter; Lainiotis filter; Golden section; Fibonacci sequence (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:250:y:2015:i:c:p:817-831

DOI: 10.1016/j.amc.2014.11.022

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