This paper deals with mean square state estimation over sensor networks with a fixed topology. Attention is focused on designing local stationary state estimators with a general structure while accounting for the network communication topology. Two estimator design approaches are proposed. One is based on the observability Gramian, and the other on the controllability Gramian. The computation of the estimator state-space matrices is recast as off-line convex optimization problems and requires the system asymptotic stability and global knowledge of the network topology. Convergence of the estimation error variance is ensured at each network node and a guaranteed performance in the mean square sense is achieved. The proposed approaches are also extended for designing robust filters to handle polytopictype parameter uncertainty. (C) 2016 Elsevier Ltd. All rights reserved.