Piecewise-linear maps

Chaotic signals generated by iterating piecewise-linear (PWL) maps on the unit interval are highly attractive in a wide range of signal processing applications. In this letter, optimal estimation algorithms for signals generated by iterating PWL maps and observed in white noise are derived based on the method of maximum likelihood (ML). It is shown how the phase space of the map may be decomposed into a number of regions and how the estimation problem is linear in each of these regions. The final ML estimate is obtained as the best performing of these "local" solutions.