Lainiotis filter, golden section and fibonacci sequence

dc.contributor.author	Ασημάκης, Νικόλαος Δ.	el
dc.contributor.author	Αδάμ, Μαρία	el
dc.contributor.author	Τριανταφύλλου, Χρυσαυγή	el
dc.date.accessioned	2015-05-21T10:02:57Z
dc.date.available	2015-05-21T10:02:57Z
dc.date.issued	2015-05-21
dc.identifier.uri	http://hdl.handle.net/11400/10826
dc.rights	Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ηνωμένες Πολιτείες	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/us/	*
dc.source	http://www.sciencedirect.com/science/article/pii/S0165168412003349#	el
dc.subject	Random Walk
dc.subject	Riccati equation
dc.subject	Golden section
dc.subject	Lainiotis filter
dc.subject	Λαϊνιώτης φίλτρο
dc.subject	Εξίσωσης Riccati
dc.subject	Χρυσή τομή
dc.subject	Fibonacci sequence
dc.subject	Fibonacci ακολουθία
dc.title	Lainiotis filter, golden section and fibonacci sequence	en
heal.type	journalArticle
heal.classification	Electrical engineering
heal.classification	Mathematics
heal.classification	Ηλεκτρολογία Μηχανολογία
heal.classification	Μαθηματικά
heal.classificationURI	http://skos.um.es/unescothes/C01311
heal.classificationURI	http://zbw.eu/stw/thsys/70269
heal.classificationURI	N/A-Ηλεκτρολογία Μηχανολογία
heal.classificationURI	N/A-Μαθηματικά
heal.keywordURI	http://zbw.eu/stw/descriptor/19572-2
heal.keywordURI	http://id.loc.gov/authorities/subjects/sh85113861
heal.keywordURI	http://id.loc.gov/authorities/subjects/sh85055763
heal.identifier.secondary	doi:10.1016/j.sigpro.2012.09.014
heal.language	en
heal.access	free
heal.publicationDate	2013-04
heal.bibliographicCitation	Assimakis, N., Adam, M. and Triantafillou, C. (2013). Lainiotis filter, golden section and fibonacci sequence. "Signal Processing", 93(4), April 2013. pp. 721–730. Available from: http://www.sciencedirect.com/science/article/pii/S0165168412003349#. [Accessed 03/10/2012]	en
heal.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.	en
heal.journalName	Signal Processing	en
heal.journalType	peer-reviewed
heal.fullTextAvailability	true