This paper proposes an efficient marking estimation method for a subclass of time labeled Petri nets (TLPNs), in which each transition is associated with an infinite upper bound delay. The unobservable subnet of the considered subclass of TLPNs is backward-conflict-free, and all the output transitions of each conflict place are observable. The highlight of this method is that the markings set consistent with a given observation can be determined by a linear algebraic system based on the so-called slow-bound marking and fast-bound marking pairs. An algorithm to compute an online estimator is provided, and an example is given. By this method, the exhaustive construction of the full state space including the state class graph is avoided. This approach provides guidelines of sensor deployment in the design stage so that the online marking estimation problem can be efficiently solved.

中文翻译：

---

一类时间标记Petri网的标记估计

本文针对时间标记 Petri 网 (TLPN) 的子类提出了一种有效的标记估计方法，其中每个转换都与无限的上限延迟相关联。所考虑的 TLPN 子类的不可观察子网是无后向冲突的，并且每个冲突位置的所有输出转换都是可观察的。该方法的亮点在于与给定观察一致的标记集可以由基于所谓的慢边界标记和快速边界标记对的线性代数系统确定。提供了一种计算在线估计量的算法，并给出了一个示例。通过这种方法，避免了包括状态类图的完整状态空间的详尽构造。