Optimal estimation of a class of chaotic signals

Signals generated by iterating nonlinear maps are highly attractive in a wide range of signal processing applications. Among the different possible one-dimensional chaotic systems, an important class is composed of the so-called skew tent maps. In this paper, an algorithm for the optimal estimation of this class of signals in the presence of noise is developed based on the Maximum Likelihood (ML) method. The resulting algorithm is quite demanding computationally, so suitable suboptimal schemes are proposed that show good performance at a much reduced computational cost. Computer simulations are included, and the performance of the different approaches compared with the associated Cramer-Rao Lower Bound (CRLB).