The Kalman Filter for Complex Fibonacci Systems. (19th June 2012)

• Record Type: Journal Article
• Authors: Donoghue, John
• Other Names: Chen Y.-S. Academic Editor.; Xiang Y. Academic Editor.
• Is Part Of: ISRN signal processing. Volume 2012(2012)
• Publication Date: 2012-06-19
• Subjects: Signal processing -- Periodicals; Signal processing; Periodicals; 621.3822
• DOI: 10.5402/2012/631873
• Languages: English
• ISSNs: 2090-5041

Abstract

Abstract : 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.