ABSTRACT
This chapter shows how asymptotically optimal estimators, developed for the estimation of chaotic signals generated by discrete chaotic maps and corrupted by additive white Gaussian noise (AWGN), can be applied to improve the performance of digital chaotic communication schemes. It also focuses on chaotic sequences generated by the discrete-time iteration of unidimensional (1D) piecewise linear (PWL) chaotic maps. Although this choice may look too restritive, one-dimensional discrete-time chaotic maps, described by a non-linear difference equation, seem to possess all the interesting features of higher-dimensional continuous-time systems, defined through non-linear differential equations. The maximum likelihood estimator(MLE) of chaotic sequences corrupted by AWGN was formulated originally in, where two suboptimal approaches for finding the MLE, based on dynamic programming and the Kalman filter, respectively, were proposed. Due to the computational complexity of the MLE, many suboptimal algorithms have been proposed for estimating chaotic signals corrupted by AWGN.
