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Expressing stochastic filters via number sequences

Capponi, A. and Farina, A. and Pilotto, C. (2010) Expressing stochastic filters via number sequences. Signal Processing, 90 (7). pp. 2124-2132. ISSN 0165-1684.

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We generalize the results presented in [1] regarding the relation between the Kalman filter and the Fibonacci sequence. We consider more general filtering models and relate the finite dimensional Kalman and Benes filters to the Fibonacci sequence and to the Golden Section. We also prove that Fibonacci numbers may be expressed as the convolution of the Fibonacci and Padovan sequence, thus extending the connection between stochastic filtering and Fibonacci sequence to the Padovan sequence.

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Additional Information:© 2010 Elsevier B.V. Received 3 August 2009; revised 13 January 2010; accepted 15 January 2010. Available online 20 January 2010. Alfonso Farina would like to thank his colleagues N. Gogin, P. Costa, L. Chisci, A. Benavoli, D. Benvenuti and S. Giompapa for fruitful discussions.
Subject Keywords:Kalman filter; Benes filter; Fibonacci sequence; Padovan sequence; Filtering gain
Issue or Number:7
Record Number:CaltechAUTHORS:20100603-131206402
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:18552
Deposited By: Tony Diaz
Deposited On:18 Jun 2010 17:53
Last Modified:03 Oct 2019 01:44

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