Clustering-based detection algorithm of remote state estimation under stealthy innovation-based attacks with historical data

Abstract

This paper investigates a security issue in cyber–physical systems (CPSs) concerning the performance of a multi-sensor remote state estimation under a novel attack called “Optimal Stealthy Innovation-Based Attacks with Historical Data”. The attacker is able to launch a linear attack to modify sensor measurements. The objective of the attacker is to maximize the deterioration of estimation performance while ensuring they remain undetected by the ${\chi }^2$ detector. To counteract this new type of attack, a remote state estimator equipped with a detection mechanism that utilizes a Gaussian mixture model (GMM) is employed. We derive the error covariances for the remote state estimator with and without a GMM detection mechanism in a recursive manner under Optimal Stealthy Innovation-Based Attacks with Historical Data. The experimental results demonstrate the superiority of the GMM detection mechanism. However, it is observed that the estimation performance of the GMM-based system deteriorates as the system dimension increases. In order to address this issue, we propose two dimensionality reduction methods, namely kernel principal component analysis (KPCA) and variational autoencoder (VAE), to enhance the estimation performance. Finally, the results are illustrated via the simulation examples.