In this paper we address the problem of distributed state estimation of continuous- and discrete-time stable, LTI systems. The classical observer canonical form representation of the system dynamics is used to identify the observable states for each node (agent). The main novelty of our contribution is to obviate the need of the asymptotically (or finite-time) local Luenberger observers. Instead, following the generalized parameter estimation-based observer design approach, we use the state transition matrix of the system to translate the problem of reconstruction of the observable states into one of parameter estimation---namely, the initial conditions of the associated trajectory. Exploiting the local observability property of the agents we prove that, with a simple sample-and-hold or finite summation operation, it is possible to estimate these parameters algebraically. Consensus strategies are then used to fuse the parameter estimates of all agents to reconstruct the complete state vector. Asymptotic or finite convergence time of the observer are established for several scenarios for the graph, including time-varying, switching and with transmission delays.

中文翻译：

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具有时变通信图的连续和离散时间线性时不变系统的代数分布式状态观察器

在本文中，我们解决了连续和离散时间稳定 LTI 系统的分布式状态估计问题。系统动力学的经典观察者规范形式表示用于识别每个节点（代理）的可观察状态。我们贡献的主要新颖之处在于消除了渐近（或有限时间）局部 Luenberger 观察者的需要。相反，遵循基于广义参数估计的观察者设计方法，我们使用系统的状态转移矩阵将可观察状态的重建问题转化为参数之一估计——即相关轨迹的初始条件。利用代理的局部可观察性特性，我们证明，通过简单的采样保持或有限求和操作，可以以代数方式估计这些参数。然后使用共识策略融合所有代理的参数估计以重建完整的状态向量。观察者的渐近或有限收敛时间是为图的几种情况建立的，包括时变、切换和传输延迟。