We present an analysis of a heuristic for abrupt change detection of systems with bounded state variations. The proposed analysis is based on the Singular Value Decomposition (SVD) of a history matrix built from system observations. We show that monitoring the largest singular value of the history matrix can be used as a heuristic for detecting abrupt changes in the system outputs. We provide sufficient detectability conditions for the proposed heuristic. As an application, we consider detecting malicious cyber data attacks on power systems and test our proposed heuristic on the IEEE 39-bus testbed.
@cite_16 assume a Bayesian model on the state variables and consider a binary detection problem. In particular, they assume that the state variables have a zero-mean Gaussian distribution. @cite_4 impose a linear state-space representation on the power system state evolution and propose a decoder that corrects for the compromised meters. In their plant model, they assume they know the state transition and measurement matrices.
@cite_16 @cite_4
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We consider the problem of state-estimation of a linear dynamical system when some of the sensor measurements are corrupted by an adversarial attacker. The errors injected by the attacker in the sensor measurements can be arbitrary and are not assumed to follow a specific model (in particular they can be of arbitrary magnitude). We first characterize the number of attacked sensors that can be tolerated so that the state of the system can still be correctly recovered by any decoding algorithm. We then propose a specific computationally feasible decoding algorithm and we give a characterization of the number of errors this decoder can correct. For this we use ideas from compressed sensing and error correction over the reals and we exploit the dynamical nature of the problem. We show using numerical simulations that this decoder performs very well in practice and allows to correct a large number of errors. This paper studies the estimation of a high-dimensional vector signal where the observation is a known "sparse" linear transformation of the signal corrupted by additive Gaussian noise. A paradigm of such a linear system is code-division multiple access (CDMA) channel with sparse spreading matrix. Assuming a "semi-regular" ensemble of sparse matrix linear transformations, where the bi-partite graph describing the system is asymptotically cycle-free, it is shown that belief propagation (BP) achieves the minimum mean-square error (MMSE) in estimating the transformation of the input vector in the large-system limit. The result holds regardless of the the distribution and power of the input symbols. Furthermore, the mean squared error of estimating each symbol of the input vector using BP is proved to be equal to the MMSE of estimating the same symbol through a scalar Gaussian channel with some degradation in the signal-to-noise ratio (SNR). The degradation, called the efficiency, is determined from a fixed-point equation due to Guo and Verdu, which is a generalization of Tanaka's formula to arbitrary prior distributions.