On State Estimation with Bad Data Detection

TL;DR

This paper introduces a convex programming method for robust state estimation that effectively separates sparse bad data and noise, providing sharp theoretical bounds and practical algorithms for nonlinear power network applications.

Contribution

It develops new performance bounds based on the almost Euclidean property and proposes an iterative convex approach for bad data detection in nonlinear systems.

Findings

Sharp bounds on the almost Euclidean property of linear subspaces.

Effective separation of bad data and noise using mixed convex programming.

Numerical validation in nonlinear power network scenarios.

Abstract

In this paper, we consider the problem of state estimation through observations possibly corrupted with both bad data and additive observation noises. A mixed $\ell_1$ and $\ell_2$ 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.