  In this paper, we consider the problems of state estimation and false data
injection detection in smart grid when the measurements are corrupted by
colored Gaussian noise. By modeling the noise with the autoregressive process,
we estimate the state of the power transmission networks and develop a
generalized likelihood ratio test (GLRT) detector for the detection of false
data injection attacks. We show that the conventional approach with the
assumption of Gaussian noise is a special case of the proposed method, and thus
the new approach has more applicability. {The proposed detector is also tested
on an independent component analysis (ICA) based unobservable false data attack
scheme that utilizes similar assumptions of sample observation.} We evaluate
the performance of the proposed state estimator and attack detector on the IEEE
30-bus power system with comparison to conventional Gaussian noise based
detector. The superior performance of {both observable and unobservable false
data attacks} demonstrates the effectiveness of the proposed approach and
indicates a wide application on the power signal processing.
