The Estimation of Chaotic Signal Initial Value

Chaotic signal has abroad applications in communication. Most such applications require an accurate estimation of initial values of actual chaotic sequence from a noisy signal so as to recover the Chaotic signal to realize the correct receiving in the terminal. Some algorithms are currently available which are limited to ideal situations with very high signal-to-noise ratios (SNRpsilas). This paper presents a modified minimum mean squares estimate algorithm to estimate the initial condition of a chaotic signal in a wide range of SNRpsilas down to -3 dB. Take the logistic map as an example, we have simulated and validated the new method.