Summary: This paper proposes a state estimation technique in a decentralized context for time dependent systems. The plant of the studied system is modeled by P-time labeled Petri nets (P-TLPN) and the set of events is partitioned into a set of observable and unobservable ones, leading to a partial observation configuration. Indeed, the observation is distributed over a set of distinct sites which have their own local vision of the system. Moreover, some event are indistinguishable as the same label can be associated with the same transition adding another source of non-determinism. Thus, thanks to a global coordinator helped by the consideration of the timing factor, the local information transmitted via the different sites will be exploited to assess the set of states consistent with the current considered observation. The developed technique is an iterative procedure coupled with a time feasibility analysis (i.e., schedulability) conducted for particular firing sequences allowing to explain the considered observation, called time explanations. A diagnosis procedure aiming at evaluating the occurrence of particular faults for each behavior is also provided.