Introducing the Golden Section to Computer Science
ICCI '02 Proceedings of the 1st IEEE International Conference on Cognitive Informatics
Number theoretic transforms over the golden section quadratic field
IEEE Transactions on Signal Processing
Object tracking using the Gabor wavelet transform and the golden section algorithm
IEEE Transactions on Multimedia
Optimum search for the location of the maximum of a unimodal function
IEEE Transactions on Information Theory
The golden code: a 2×2 full-rate space-time code with nonvanishing determinants
IEEE Transactions on Information Theory
On Robustness Properties of Beta Encoders and Golden Ratio Encoders
IEEE Transactions on Information Theory
IEEE Communications Magazine
On the Average Growth Rate of Random Compositions of Fibonacci and Padovan Recurrences
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Expressing stochastic filters via number sequences
Signal Processing
State estimation and control of the Fibonacci system
Signal Processing
Lainiotis filter, golden section and Fibonacci sequence
Signal Processing
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A connection between the Kalman filter and the Fibonacci sequence is developed. More precisely it is shown that, for a scalar random walk system in which the two noise sources (process and measurement noise) have equal variance, the Kalman filter's estimate turns out to be a convex linear combination of the a priori estimate and of the measurements with coefficients suitably related to the Fibonacci numbers. It is also shown how, in this case, the steady-state Kalman gain as well as the predicted and filtered covariances are related to the golden ratio @f=(5+1)/2. Furthermore, it is shown that, for a generic scalar system, there exist values of its key parameters (i.e. system dynamics and ratio of process-to-measurement noise variances) for which the previous connection is preserved. Finally, by exploiting the duality principle between control and estimation, similar connections with the linear quadratic control problem are outlined.