We consider the problem of parameter estimation, based on noisy chaotic signals, from the viewpoint of twisted modulation for waveform communication. In particular, we study communication systems where the parameter to be estimated is conveyed as the initial condition of a chaotic dynamical system of a certain class and we examine its estimation performance in terms of the expectation 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 a lower bound on the weak-noise estimation error for this class of chaotic modulators, and argue that it can be outperformed by using the itinerary signal associated with the chaotic system instead of the main chaotic output signal.

翻译：我们从波形通信的扭曲调制视角，研究基于噪混沌信号的参数估计问题。具体而言，我们考察一类通信系统：待估计参数以某类混沌动力系统初始条件的形式传递。在要求异常概率保持较小的条件下，我们于高信噪比场景分析该系统的估计性能——以给定凸函数形式的估计误差期望为度量。针对此类混沌调制器，我们推导了弱噪声估计误差的下界，并论证：利用与该混沌系统关联的轨迹信号替代主混沌输出信号，可获得更优的估计性能。