基于智能传感器在马尔可夫衰落信道上的远程状态估计
Remote State Estimation with Smart Sensors over Markov Fading Channels
AI总结：
针对LTI系统经$M$状态马尔可夫衰落信道的远程状态估计，提出基于估计周期的方法，得出均方稳定充要条件并验证其优于现有充分条件。
摘要：
我们考虑离散时间线性时不变（LTI）系统的一个基本远程状态估计问题。智能传感器通过时间相关的 $M$ 状态马尔可夫衰落信道将其本地状态估计转发给远程估计器，其中丢包概率随时间变化，并取决于当前衰落信道状态。我们建立了远程估计误差协方差均方稳定的充要条件，即 $ρ^2(\mathbf{A})ρ(\mathbf{DM})<1$，其中 $ρ(\cdot)$ 表示谱半径，$\mathbf{A}$ 是 LTI 系统的状态转移矩阵，$\mathbf{D}$ 是包含不同信道状态下丢包概率的对角矩阵，$\mathbf{M}$ 是马尔可夫信道状态的转移概率矩阵。为推导该结果，我们提出了一种新颖的基于估计周期的方法，并给出了矩阵幂的新的逐元素界。该稳定性条件由数值结果验证，并被证明比文献中现有的充分条件更有效。我们观察到，依据不同信道状态下丢包概率表示的稳定区域可以是凸的或凹的，这取决于转移概率矩阵 $\mathbf{M}$。数值结果表明，尽管智能传感器设置实现了更好的估计性能，但智能传感器与传统传感器（向远程估计器发送原始测量值）设置的远程估计稳定性条件可能一致。
英文摘要：
We consider a fundamental remote state estimation problem of discrete-time linear time-invariant (LTI) systems. A smart sensor forwards its local state estimate to a remote estimator over a time-correlated $M$-state Markov fading channel, where the packet drop probability is time-varying and depends on the current fading channel state. We establish a necessary and sufficient condition for mean-square stability of the remote estimation error covariance as $ρ^2(\mathbf{A})ρ(\mathbf{DM})<1$, where $ρ(\cdot)$ denotes the spectral radius, $\mathbf{A}$ is the state transition matrix of the LTI system, $\mathbf{D}$ is a diagonal matrix containing the packet drop probabilities in different channel states, and $\mathbf{M}$ is the transition probability matrix of the Markov channel states. To derive this result, we propose a novel estimation-cycle based approach, and provide new element-wise bounds of matrix powers. The stability condition is verified by numerical results, and is shown more effective than existing sufficient conditions in the literature. We observe that the stability region in terms of the packet drop probabilities in different channel states can either be convex or concave depending on the transition probability matrix $\mathbf{M}$. Our numerical results suggest that the stability conditions for remote estimation may coincide for setups with a smart sensor and with a conventional one (which sends raw measurements to the remote estimator), though the smart sensor setup achieves a better estimation performance.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
