State estimation for constant-time labeled automata under dense time

In this paper, we focus on state estimation for constant-time labeled automata 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 constraint satisfaction problems (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.