Covariance-Based Estimation for Clustered Sensor Networks Subject to Random Deception Attacks

Abstract

In this paper, a cluster-based approach is used to address the distributed fusion estimation problem (filtering and fixed-point smoothing) for discrete-time stochastic signals in the presence of random deception attacks. At each sampling time, measured outputs of the signal are provided by a networked system, whose sensors are grouped into clusters. Each cluster is connected to a local processor which gathers the measured outputs of its sensors and, in turn, the local processors of all clusters are connected with a global fusion center. The proposed cluster-based fusion estimation structure involves two stages. First, every single sensor in a cluster transmits its observations to the corresponding local processor, where least-squares local estimators are designed by an innovation approach. During this transmission, deception attacks to the sensor measurements may be randomly launched by an adversary, with known probabilities of success that may be different at each sensor. In the second stage, the local estimators are sent to the fusion center, where they are combined to generate the proposed fusion estimators. The covariance-based design of the distributed fusion filtering and fixed-point smoothing algorithms does not require full knowledge of the signal evolution model, but only the first and second order moments of the processes involved in the observation model. Simulations are provided to illustrate the theoretical results and analyze the effect of the attack success probability on the estimation performance.

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

“…k/k . The recursive relations (17) and (18) are immediately derived from (24) and (25), respectively, and Expression (19) is straightforward from (23) and (25).…”

“…The distributed H ∞ -consensus filtering problem for discrete-time systems with multiplicative noises and deception attacks over sensor networks was studied in [22]. A cluster-based approach was used in [23] to address the distributed fusion estimation problem for multi-sensor networked systems, when the measurements are subject to stochastic deception attacks, and the influence of unbounded false data injection attacks on state estimation processes was studied in [18].…”

“…Related work: Some of the most closely related papers in the literature are [9,14,23,25]. In [9], discrete-time linear systems with fading measurements over connected networks were considered and distributed filtering estimators with a specific structure were obtained, where the gain matrices were determined using the minimum variance criterion.…”

“…Furthermore, the estimation methodology is substantially different in both papers: a centralized Kalman filter was designed in [14], while least-squares distributed filtering estimators over a sensor network with a given topology are proposed in the current paper. In [23], networked systems subject to stochastic deception attacks, where the sensor nodes are grouped into clusters, were considered. Assuming that the sensors within each cluster are fully connected, least-squares linear distributed fusion estimators were obtained based on the measurements received from all the sensors in the same cluster.…”

“…Assuming that the sensors within each cluster are fully connected, least-squares linear distributed fusion estimators were obtained based on the measurements received from all the sensors in the same cluster. The main difficulty to address the distributed estimation problem in the current paper, compared to [23], was due to the fact that the sensor network was not fully connected, and the use of zeros to weight those measurements from non-connected sensors was commonly handled by using generalized inverses. However, as previously indicated, in this paper, an alternative matrix simplification methodology is employed to avoid the use of pseudo-inverses.…”