Bayesian estimation of discrete chaotic signals by MCMC

This paper considers Markov Chain Monte Carlo (MCMC) methods for the estimation in Additive White Gaussian Noise (AWGN) of discrete chaotic signals generated iterating any unimodal map. In particular, the Metropolis-Hastings (MH) algorithm is applied to the estimation of signals generated by iteration of the logistic map. Using this technique, Bayesian Minimum Mean Square Error (MS) and Maximum a Posteriori (MAP) estimators have been developed for any unimodal map. Computer simulations show that the proposed algorithms attain the Cramer-Rao Lower Bound (CRLB), and outperform the existing alternatives.