A Two-Phase Distributed Filtering Algorithm for Networked Uncertain Systems with Fading Measurements under Deception Attacks.

In this paper, the distributed filtering problem is addressed for a class of discrete-time stochastic systems over a sensor network with a given topology, susceptible to suffering deception attacks, launched by potential adversaries, which can randomly succeed or not with a known success probability, which is not necessarily the same for the different sensors. The system model integrates some random imperfections and features that are frequently found in real networked environments, namely: (1) fading measurements; (2) multiplicative noises in both the state and measurement equations; and (3) sensor additive noises cross-correlated with each other and with the process noise. According to the network communication scheme, besides its own local measurements, each sensor receives the measured outputs from its adjacent nodes. Based on such measurements, a recursive algorithm is designed to obtain the least-squares linear filter of the state. Thereafter, each sensor receives the filtering estimators previously obtained by its adjacent nodes, and these estimators are all fused to obtain the desired distributed filter as the minimum mean squared error matrix-weighted linear combination of them. The theoretical results are illustrated by a simulation example, where the efficiency of the developed distributed estimation strategy is discussed in terms of the error variances.