Quaternion Kalman Filter for False Data Injection Attacks

Quaternion Kalman filter (QKF) can deal with the estimation issues existing in three/four dimensional space, effectively. However, when the measurements are attacked by multiplicative or/and additive false data injection (FDI), the performance of traditional QKF will be degraded dramatically. To this end, this brief first remodels the quaternion measurement equation with consideration of FDI attacks. Then, a novel QKFs to combat multiplicative or/and additive FDI attacks are developed using the quaternion linear estimation and generalized Hamilton real (GHR) calculus theories. Finally, simulations illustrate the high filtering accuracy of the proposed quaternion algorithms under FDI attacks.