Distributed Subspace Projection Graph Signal Estimation with Anomaly Interference

Abstract

The estimation of graph signal is a vital problem in many distributed networks, such as vehicular networks, smart grids, unmanned aerial vehicles (UAVs), and the Internet of Things. In those networks, anomaly interference widely exists, such as network attack, noise, device fault, which will hazard the healthy of the entire system. In the paper, the estimation of graph signals with anomaly interference is investigated. We show that the graph signal estimation problem can be treated as a bandlimited subspace optimization problem, and propose a distributed subspace projection graph signal estimation algorithm based on the graph filter (DispGF), which can achieve better performance with less communication burden. In addition, a graph filter matrix that produces subspace projection is proposed to replace the nonsparse projection matrix, which guarantees distributed implementation and projection accuracy. Different from previous work, here, graph signal estimation is studied with no prior anomaly information. To this end, for FDI attack, random attack, noise interference, we propose anomaly detection and node localization scheme based on smoothness, that can achieve similar performance compared with the case of prior anomaly information known. Numerical experiments verify the effectiveness of the proposed DispGF algorithm. The convergence of the algorithm is theoretically analyzed.