Estimation of a certain class of chaotic signals: An em-based approach

Maximum-likelihood estimation of chaotic signal generated by iterating piecewise-linear maps on the unit interval exhibits an exponential increase in computational cost with the register length. This paper considers iterative estimation algorithms based on the Expectation-Maximization (EM) algorithm and related space alternating methods. This approach is inspired in the parallelism that may be drawn between chaotic estimation and multiuser detection, which also becomes prohibitively complex as the number of users increases. The resulting algorithms are based on an iterative updating of estimates of the chaotic signal itinerary. Computer simulations show that the proposed algorithms achieve the performance of the ML estimator for short data registers and improve the computationally feasible (suboptimal) estimators for long records.