We investigate state estimation of linear systems over channels having a finite state not known by the transmitter or receiver. We show that similar to memoryless channels, zero-error capacity is the right figure of merit for achieving bounded estimation errors. We then consider finite-state, worst-case versions of the common erasure and additive noise channels models, in which the noise is governed by a finite-state machine without any statistical structure. Upper and lower bounds on their zero-error capacities are derived, revealing a connection with the {\em topological entropy} of the channel dynamics. Separate necessary and sufficient conditions for bounded linear state estimation errors via such channels are obtained. These estimation conditions bring together the topological entropies of the linear system and the discrete channel.

翻译：我们调查在发射机或接收机不知道的有限状态的频道上对线性系统的状态估计。我们显示,与无记忆的频道相似,零性能是达到约束性估计错误的正确优点数字。然后我们考虑通用消化和添加噪音频道模型的有限状态、最坏情况版本,其中噪音由没有统计结构的有限状态机器控制。从零性能的上下限中得出,揭示了与频道动态的湿性表层昆虫的连接。通过这些渠道获得受约束的线性状态估计错误的单独必要和充分条件。这些估计条件将线性系统和离散通道的表层元素连接在一起。