Secure distributed estimation via an average diffusion LMS and average likelihood ratio test

Secure distributed estimation algorithms are designed to protect against a spectrum of attacks by exploring different attack models and implementing strategies to enhance the resilience of the algorithm. These models encompass diverse scenarios such as measurement sensor attacks and communication link attacks, which have been extensively investigated in existing literature. This paper, however, focuses on a specific type of attack: the multiplicative sensor attack model. To counter this, the paper introduces the Average diffusion least mean square (ADLMS) algorithm as a viable solution. Furthermore, the paper introduces the Average Likelihood Ratio Test (ALRT) detector, which provides a straightforward detection criterion. In the presence of communication link attacks, the paper considers the manipulation attack model and presents an ALRT adversary detector. The analysis extends to these ALRT detectors, encompassing the calculation of adversary detection probability and false alarm probability, both achieved in closed form. The paper also provides the mean convergence analysis of the proposed ADLMS algorithm. Simulation results reveal that the proposed algorithms exhibit enhanced performance compared to the DLMS algorithm, while the incremental complexity remains only marginally higher than that of the DLMS algorithm.