Bibliographic Details
| Title: |
Golden section, Fibonacci sequence and the time invariant Kalman and Lainiotis filters. |
| Authors: |
Adam, Maria1 madam@dib.uth.gr, Assimakis, Nicholas1,2 assimakis@mail.teiste.gr, Farina, Alfonso3 alfonso.farina@selex-es.com |
| Source: |
Applied Mathematics & Computation. Jan2015, Vol. 250, p817-831. 15p. |
| Subjects: |
Golden ratio, Fibonacci sequence, Kalman filtering, Stochastic analysis, Dynamical systems |
| 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. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
