This paper deals with state estimation in networked scenarios. We focus on a situation where the output of an LTI system is measured over an erasure channel and design a class of switched state estimators. In the considered class, the estimators use the channel output and instantaneous information on the channel state, to construct both a state estimate and, when data dropouts occur, an estimate of the missing data. Our focus is on stationary performance and present explicit expressions for the optimal designs that minimize the stationary state estimation error variance. A toy-example is provided to illustrate our results. © 2011 IEEE.