Bayesian estimation of chaotic signals generated by piecewise-linear maps

Chaotic signals are potentially attractive in a wide range of signal processing applications. This paper deals with Bayesian estimation of chaotic sequences generated by piecewise-linear (PWL) maps and observed in white Gaussian 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 (MS) 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.

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