In this paper, we focus on for in a dense time context, i.e., the time constraints of the automata can be given according to real numbers. Given a sequence of timed observations (i.e., pairs of logical observations with their time stamps) collected from a system within a finite time window, a state estimation method is proposed to find the set of states in which the system might reside by the end of the time window. By using both labeling and timing information as well as the structure of the system, we can express any finite time evolution from one state to another into (CSPs). This structural analysis is independent of all collected sequences of timed observations and can be achieved offline, although its cost is exponential with respect to the number of states in the system. Consequently, two algorithms are designed to perform state estimation under a single observation and no observation, respectively, by solving a finite number of CSPs generated according to the system’s structural information. Both algorithms can be jointly used in an iterative approach to perform state estimation for any sequence of timed observations. In such a case, the number of generated CSPs in the algorithms increases linearly with respect to the length of the observed sequence.

中文翻译：

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密集时间下恒定时间标记自动机的状态估计


在本文中，我们关注的是密集时间上下文中的情况，即自动机的时间约束可以根据实数给出。给定在有限时间窗口内从系统收集的一系列定时观测（即带有时间戳的逻辑观测对），提出了一种状态估计方法来查找系统在结束时可能所处的状态集。时间窗口。通过使用标签和计时信息以及系统结构，我们可以将从一种状态到另一种状态的任何有限时间演化表达为（CSP）。这种结构分析独立于所有收集的定时观察序列，并且可以离线实现，尽管其成本相对于系统中的状态数量呈指数级增长。因此，设计了两种算法分别在单次观测和无观测下进行状态估计，通过求解根据系统结构信息生成的有限数量的CSP。这两种算法可以在迭代方法中联合使用，以对任何定时观察序列执行状态估计。在这种情况下，算法中生成的 CSP 数量相对于观察序列的长度线性增加。