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We consider the problem of state estimation through observations corrupted by both bad data and additive observation noises. A mixed 1 and 2 convex programming is used to separate both sparse bad data and additive noises from the observations. Using the almost Euclidean property for a linear subspace, we derive a new performance bound for the state estimation error under sparse bad data and additive observation noises. Our main contribution is to provide sharp bounds on the almost Euclideandoi:10.1109/cdc.2011.6161214 dblp:conf/cdc/XuWT11 fatcat:nvz3bi6qxvcfbbu3z7d7ojhwim