We propose a state estimator for linear discrete-time systems composed by coupled subsystems affected by bounded disturbances. The architecture is distributed in the sense that each subsystem is equipped with a local state estimator that exploits suitable pieces of information from parent subsystems. Furthermore, each local estimator reconstructs the state of the corresponding subsystem only. Differently from methods based on moving horizon estimation, our approach does not require the on-line solution to optimization problems. Our state-estimation scheme, which is based on the notion of practical robust positive invariance developed in (Rakovic et al., 2011), also guarantees satisfaction of constraints on local estimation errors and it can be updated with a limited computational effort when subsystems are added or removed.