ESTIMATING THE INITIAL CONDITION OF CHAOTIC ORBITS: PERFORMANCE BOUNDS

We derive the Cramér-Rao lower bound associated with the estimation of the initial condition of noise-embedded chaotic signals produced by general one-dimensional maps. We relate its asymptotic behaviour to the chaotic attractor's Lyapunov number. These results can be used to choose the chaotic generator more suitable for applications on chaotic digital communication systems.