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