This paper presents a procedure to construct distributed observers for a system consisting in a perturbed linear time-invariant plant being observed by a network of sensor nodes. Based on local measurements of the plant and the information of its neighbours, every node builds an estimation of the plant states. Remarkably, each node can be designed to estimate a subspace of the plant, either because the observation attributes of the node impose a physical restriction or because of a free-design criterion. This relaxes the usual requirement of collective observability. The method presents features of suboptimal H-2/H performance, as the upper bound of a cost index is minimised, given a prescribed disturbance attenuation level. The computational cost as well as energy and bandwidth usage are reduced compared to existing solutions. Simulation results are presented to show the applicability of the results.