Table of Contents
ISRN Signal Processing
Volume 2012, Article ID 631873, 5 pages
Research Article

The Kalman Filter for Complex Fibonacci Systems

Department of Electrical and Computer Engineering, Cleveland State University, 2121 Euclid Avenue, Cleveland, OH 44115, USA

Received 19 March 2012; Accepted 22 April 2012

Academic Editors: Y.-S. Chen and Y. Xiang

Copyright © 2012 John Donoghue. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper investigates the characteristics of the Kalman filter for a broad class of complex Fibonacci systems and represents an extension to the complex domain of the state estimation problem for the real-valued Fibonacci system. Complex Fibonacci systems are obtained by modifying the real-valued Fibonacci recurrence relation to include complex coefficients, control and noise inputs, and a noisy output-measurement equation. Analytic expressions for the Kalman filter’s steady-state gain and error covariance matrices are obtained, and it is found that for a broad subclass of these complex systems the elements of the matrices are functions of the golden ratio.