Stochastic stability for centralized Kalman filtering over a wireless sensor networkwith correlated fading channels is studied. On their route to the gateway, sensor packets, possiblyaggregated with measurements from several nodes, may be dropped because of fading links. Byassuming the network states to be Markovian, we establish sufficient conditions that ensure theKalman filter to be exponentially bounded in norm. In the one sensor case, this new stabilitycondition is shown to include previous results obtained in the literature as special cases. Theresults also hold when applying power control, where the transmission power of each node is anonlinear mapping of the network state and the channel gains.