On state estimation with bad data detection

We consider the problem of state estimation through observations corrupted by both bad data and additive observation noises. A mixed ℓ₁ and ℓ₂ 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 Euclidean property of a linear subspace, using the “escape-through-a-mesh” theorem from geometric functional analysis. We also propose and numerically evaluate an iterative convex programming approach to solve bad data detection problems in electrical power networks.