Sampled Observability and State Estimation of Linear Discrete Ensembles
Sampled Observability and State Estimation of Linear Discrete Ensembles
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DOI：
10.1109/tac.2016.2613478
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发表时间：
2017-05
影响因子：
6.8
通讯作者：
Shen Zeng;H. Ishii;F. Allgöwer
中科院分区：
文献类型：
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作者：
Shen Zeng;H. Ishii;F. Allgöwer
我们考虑在离散时间步长和匿名方式接收单个系统的输出测量的情况下，重构结构相同的线性系统的有限组的初始状态的问题：虽然我们知道组中单个系统的所有输出测量，但我们不知道哪个输出测量对应于哪个系统。这个状态估计问题解决了种群状态估计问题的本质，其中单个系统的输出测量仅作为统计量给出。我们采用了一种测量理论的方法，在该方法中，该集团是由一个LTI系统描述的结构的个人系统和一个初始状态，这是由一个离散的措施表示。在此框架下，我们得到了一个几何特征的状态估计，承认一个唯一的解决方案，结合的结果，在不规则采样下的线性系统的可观性，产生一个充分条件的采样可观的离散集成。作为我们的理论研究结果的补充，我们通过模拟的例子提供插图。此外，我们考虑实际的状态估计问题下的噪声输出测量。
We consider the problem of reconstructing the initial states of a finite group of structurally identical linear systems in the situation that output measurements of the individual systems are received at discrete time steps and in an anonymized manner: While we do know all output measurements of the individual systems in the group, we do not know which output measurement corresponds to which system. This state estimation problem addresses the essence of state estimation problems for populations, in which the output measurements of the individual systems are given only as statistics. We adopt a measure theoretical approach in which the group is modelled by an LTI system describing the structure of the individual systems and an initial state which is expressed by a discrete measure. In this framework we derive a geometric characterization for the state estimation to admit a unique solution, which combined with a result on the observability of linear systems under irregular sampling, yields a sufficient condition for the sampled observability of discrete ensembles. As a supplement to our theoretical findings, we provide illustrations by means of simulation examples. Furthermore we consider the practical state estimation problem under noisy output measurements.