We consider distributed systems modeled as communicating finite state machines with reliable unbounded FIFO channels. As an essential sub-routine for control, monitoring and diagnosis applications, we provide an algorithm that computes, during the execution of the system, an estimate of the current global state of the distributed system for each local subsystem. This algorithm does not change the behavior of the system; each subsystem only computes and records a symbolic representation of the state estimates, and piggybacks some extra information to the messages sent to the other subsystems in order to refine their estimates. Our algorithm relies on the computation of reachable states. Since the reachability problem is undecidable in our model, we use abstract interpretation techniques to obtain regular overapproximations of the possible FIFO channel contents, and hence of the possible current global states. An implementation of this algorithm provides an empirical evaluation of our method.