Kullback-Leibler Divergence-Based Observer Design Against Sensor Bias Injection Attacks in Single-Output Systems

This paper considers observer-based detection of sensor bias injection attacks (BIAs) on linear cyber-physical systems with single output driven by white Gaussian noise. Despite their simplicity, BIAs pose a severe risk to systems with integrators, which we refer to as integrator vulnerability. Specifically, the residual generated by any linear observer is indistinguishable under attack and normal operation at steady state, making BIAs detectable only during transients. To address this, we propose a principled method based on Kullback-Leibler divergence to design a residual generator that significantly increases the signal-to-noise ratio against BIAs. For systems without integrator vulnerability, our method also enables a trade-off between transient and steady-state detectability. The effectiveness of the proposed method is demonstrated through numerical comparisons with three state-of-the-art residual generators.