  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.
