Bayesian estimation of a class of chaotic signals

Chaotic signals are potentially attractive in a wide range of signal processing applications. This paper deals with Bayesian estimation of chaotic sequences generated by tent maps and observed in white noise. The existence of invariant distributions associated with these sequences makes the development of Bayesian estimators quite natural. Both maximum a posteriori (MAP) and minimum mean square error (MMSE) estimators are derived. Computer simulations confirm the expected performance of both approaches and show how the inclusion of a priori information produces in most cases an increase in performance over the maximum likelihood (ML) case