Detectability Measure for State Estimation of Discrete Event Systems

Abstract

In this note, we investigate how to quantitatively evaluate the performance of state estimation for discrete event systems. We use a stochastic automaton to model a discrete event system. We say that an event sequence is detectable if we can determine the current and subsequent states after the occurrence of the sequence. We define the limit of the sum of probabilities of all detectable sequences when the length of the sequences goes to infinity as a quantitative indicator of goodness of state estimation. We call this indicator “detectability measure.” In order to calculate the detectability measure, we augment the discrete event system to include the information of its state estimates and then convert it into a Markov chain by removing all the event labels. Calculation of the detectability measure is then translated to calculation of the sum of probabilities of some states in the Markov chain, which can be done effectively. Finally, a practical example is used to illustrate these results.