Quickest Detection of Time-Varying False Data Injection Attacks in Dynamic Linear Regression Models
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Motivated by the sequential detection of false data injection attacks (FDIAs) in a dynamic smart grid, we consider a more general problem of sequentially detecting time-varying FDIAs in dynamic linear regression models. The unknown time-varying parameter vector in the linear regression model and the FDIAs impose a significant challenge for designing a computationally efficient detector. We first propose two Cumulative-Sum-type algorithms to address this challenge. One is called generalized Cumulative-Sum (GCUSUM) algorithm, and the other one is called relaxed generalized Cumulative-Sum (RGCUSUM) algorithm, which is a modified version of the GCUSUM. It can be shown that the computational complexity of the proposed RGCUSUM algorithm scales linearly with the number of observations. Next, considering Lordon's setup, for any given constraint on the expected false alarm period, a lower bound on the threshold employed in the proposed RGCUSUM algorithm is derived, which provides a guideline for the design of the proposed RGCUSUM algorithm to achieve the prescribed performance requirement. In addition, for any given threshold employed in the proposed RGCUSUM algorithm, an upper bound on the expected detection delay is also provided. The performance of the proposed RGCUSUM algorithm is also numerically studied in the context of an IEEE standard power system under FDIAs.
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