On State Estimation with Bad Data Detection

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In this paper, we consider the problem of state estimation through observations possibly corrupted with 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. Through 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 performing bad data detections in nonlinear electrical power networks problems.