This article develops a novel design principle for the observer of timed discrete event systems behaving under specific time semantics. Observers devoted to discrete event systems usually ignore the timing aspects of underlying systems but this can have implications to many applications, in particular, for refinement of estimation and inference tasks. The techniques of this article use the time stamps of observations to refine the state estimation process for a class of labeled and timed automata where events occur based on constant time values. The resulting timed observer is beneficial for refining privacy and security issues. Current-state opacity is discussed as a promising application of the timed observer.