Consensus-based distributed estimation schemes are becoming increasingly popular in sensor networks due to their scalability and fault tolerance capabilities. In a consensusbased state estimation framework, multiple neighboring nodes iteratively communicate with each other, exchanging their own local estimates of a target’s state with the goal of converging to a single state estimate over the entire network. However, the state estimation problem becomes challenging when a node has limited observability of the state. In addition, the consensus estimate is sub-optimal when the cross-covariances between the individual state estimates across different nodes are not incorporated in the distributed estimation framework. The crosscovariance is usually neglected because the computational and bandwidth requirements for its computation grow exponentially with the number of nodes. These limitations can be overcome by noting that, as the state estimates at different nodes converge, the information at each node becomes redundant. This fact can be utilized to compute the optimal estimate by proper weighting of the prior state and measurement information. Motivated by this idea, we propose information-weighted consensus algorithms for distributed maximum a posteriori parameter estimates, and their extension to the information-weighted consensus filter (ICF) for state estimation. We show both theoretically and experimentally that the proposed methods asymptotically approach the optimal centralized performance. Simulation results show that ICF is robust even when the optimality conditions are not met and has low communication requirements.