Signal coding and compression based on discrete-time chaos: statistical approaches

In our previous paper we proposed to employ simple one-dimensional maps as sources of signal sequences which could be used as approximations to any real measured time series. The effectiveness of the approach depends on the procedures proposed for solving the inverse problem, formulated as finding initial conditions for a given map which then will reproduce a given signal (time series) with assumed accuracy. In this paper, we investigate the applicability and effectiveness of standard statistical approaches for estimation of initial conditions, which may find application in our signal compression scheme.