基于不良数据检测的状态估计
On State Estimation with Bad Data Detection
摘要：
本文考虑了通过可能受到坏数据和加性观测噪声破坏的观测进行状态估计的问题。采用混合的$\ell_1$和$\ell_2$凸规划方法从观测值中分离稀疏坏数据和加性噪声。利用线性子空间的几乎欧几里德性质，得到了稀疏坏数据和加性观测噪声下状态估计误差的一个新的性能界。我们的主要贡献是提供尖锐的界限几乎欧几里德性质的线性子空间，使用“逃逸通过一个网格”定理从几何泛函分析。我们还提出了一种迭代凸规划方法，并进行了数值评估，在非线性电力网络问题中进行不良数据检测。
英文摘要：
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.
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