A Quadratic Estimation Approach from Fading Measurements Subject to Deception Attacks

In this paper, using covariance information, the least-squares quadratic filtering and fixed-point smoothing problems are addressed under the assumption that the measurements are perturbed by both a multiplicative noise and a time-correlated additive noise. Additionally, they are affected by the fading phenomena and exposed to random deception attacks. In the least-squares quadratic estimation approach, the signal and observation vectors are augmented by combining the original vectors with their second-order Kronecker powers. Then, using the Kronecker algebra rules and under an innovation approach, the linear estimators of the original signal based on the augmented observations are obtained. These linear estimators provide the required quadratic estimators. A simulation example shows the feasibility of the proposed quadratic estimation algorithms; also, the superiority of the quadratic estimators over the conventional linear ones is illustrated and the influence of the deception attack success probabilities on the estimation accuracy is analyzed.