Expressing stochastic filters via number sequences

Authors:
A. Capponi;A. Farina;C. Pilotto
Affiliations:
Department of Computer Science, California Institute of Technology, 91125 Pasadena, USA;Business Unit of Large Systems, SELEX Sistemi Integrati S.p.A., Rome, Italy;Department of Computer Science, California Institute of Technology, 91125 Pasadena, USA
Venue:
Signal Processing
Year:
2010

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Abstract

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.