Table of Contents
ISRN Signal Processing
Volume 2012, Article ID 631873, 5 pages
http://dx.doi.org/10.5402/2012/631873
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.

Linked References

  1. A. Benavoli, L. Chisci, and A. Farina, “Fibonacci sequence, golden section, Kalman filter and optimal control,” Signal Processing, vol. 89, no. 8, pp. 1483–1488, 2009. View at Publisher · View at Google Scholar · View at Scopus
  2. A. Capponi, A. Farina, and C. Pilotto, “Expressing stochastic filters via number sequences,” Signal Processing, vol. 90, no. 7, pp. 2124–2132, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. J. Donoghue, “State estimation and control of the Fibonacci system,” Signal Processing, vol. 91, no. 5, pp. 1190–1193, 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. A. F. Horadam, “Complex Fibonacci numbers and Fibonacci quaternions,” The American Mathematical Monthly, vol. 70, no. 3, pp. 289–291, 1963. View at Google Scholar
  5. C. J. Harman, “Complex Fibonacci numbers,” The Fibonacci Quarterly, vol. 19, no. 1, pp. 82–86, 1981. View at Google Scholar
  6. S. Pethe and A. F. Horadam, “Generalised Gaussian Fibonacci numbers,” Bulletin of the Australian Mathematical Society, vol. 33, no. 1, pp. 37–48, 1986. View at Google Scholar
  7. H. Walser, The Golden Section, The Mathematical Society of America, Washington, DC, USA, 2001.
  8. I. J. Good, “Complex Fibonacci and Lucas numbers, continued fractions, and the square root of the golden ratio,” The Fibonacci Quarterly, vol. 31, no. 1, pp. 7–20, 1993. View at Google Scholar
  9. G. Berzsenyi, “Gaussian Fibonacci numbers,” The Fibonacci Quarterly, vol. 15, no. 3, pp. 233–236, 1977. View at Google Scholar
  10. D. Simon, Optimal State Estimation, John Wiley & Sons, Hoboken, NJ, USA, 2006.
  11. A. H. Sayed, Fundamentals of Adaptive Filtering, John Wiley & Sons, Hoboken, NJ, USA, 2003.
  12. G. Franklin, J. Powell, and M. Workman, Digital Control of Dynamic Systems, Addison-Wesley, Reading, Mass, USA, 2nd edition, 1990.
  13. P. J. deBruijn, “An extension of Fibonacci’s sequence,” The Fibonacci Quarterly, vol. 12, no. 3, pp. 251–258, 1974. View at Google Scholar
  14. F. J. Wunderlich, D. E. Shaw, and M. J. Jones, “Argand diagrams of extended Fibonacci and Lucas numbers,” The Fibonacci Quarterly, vol. 12, no. 3, pp. 233–234, 1974. View at Google Scholar
  15. A. F. Horadam and A. G. Shannon, “Fibonacci and Lucas curves,” The Fibonacci Quarterly, vol. 26, no. 1, pp. 3–13, 1988. View at Google Scholar