Model-based diagnosis of discrete event systems (DESs) has attracted more and more attention in recent years. Online diagnosis based on actually emitted sequences of observations is very important for dynamic systems in practice. However, the observations are often uncertain. Especially, the received observation sequences may not be the actually emitted ones completely. In this paper, we use directed acyclic graphs (DAGs) for modeling the partial emission orders of received observations. Furthermore, combining the concept Two restricted Successive Temporal Windows proposed by Zhao and Ouyang [AI Commun. 21(4) (2008), 249–262], we present a novel method to online update the global emitted observation sequence DAG gradually. Experimental results show that we can reason out the emitted observation sequences by this approach effectively.