In this paper we propose a novel partition-based state estimator for linear discrete-time systems composed of physically coupled subsystems affected by bounded disturbances. The proposed scheme is distributed in the sense that each local state estimator exploits suitable pieces of information from parent subsystems. Moreover, differently from schemes based on moving horizon estimation, it does not require the on-line solution to optimization problems. Our method also guarantees the satisfaction of constraints on local estimation errors. We achieve our aims exploiting the notion of practical robust positive invariance developed in (Rakovic et al, 2012). As an example, we illustrate the use of the distributed state estimator for reconstructing the states of a power network system.