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We consider the problem of parameter estimation, based on noisy chaoticsignals, from the viewpoint of twisted modulation for waveform communication.In particular, we study communication systems where the parameter to beestimated is conveyed as the initial condition of a chaotic dynamical system ofa certain class and we examine its estimation performance in terms of theexpectation of a given convex function of the estimation error at high SNR,under the demand that the probability of anomaly is kept small. We derive alower bound on the weak-noise estimation error for this class of chaoticmodulators, and argue that it can be outperformed by using the itinerary signalassociated with the chaotic system instead of the main chaotic output signal.

Trade-offs Between Weak-Noise Performance and Probability of Anomaly in Parameter Estimation from Noisy Chaotic Signals