This paper is concerned with the recursive secure filtering problem for a class of discrete-time systems subject to unreliable communication due to the security vulnerability of sensor networks. The unreliable communication, caused probably by denial-of-service cyber-attacks, is described by the well-known Gilbert-Elliott model. The addressed nonlinearities are applicable for some of the most investigated stochastic nonlinear models, including the well-known state-dependent multiplicative noises as special cases. The aim of this paper is to design a novel distributed filter that uses the information not only from the individual node itself but also from its neighboring nodes according to the given topology. In order to improve the security of designed filter, a $\chi ^2$ detector is utilized to detect abnormal innovations. By means of the failure and recovery rates of the Gilbert-Elliott channels, sufficient conditions are established to ensure the existence of an upper bound on the estimation error covariance, and then the desired filter parameters are designed by minimizing the trace of such an upper bound. The asymptotic boundedness of the estimation error covariance is subsequently investigated. Finally, a simulation example on the target tracking problem is employed to verify the effectiveness and the security of the proposed filtering scheme.

中文翻译：

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传感器网络中Gilbert-Elliott通道上的递归安全过滤：分布式案例

本文针对一类离散时间系统的递归安全过滤问题，该系统由于传感器网络的安全漏洞而受到不可靠的通信。众所周知的吉尔伯特·埃利奥特（Gilbert-Elliott）模型描述了可能由拒绝服务网络攻击引起的通信不可靠。所解决的非线性适用于一些研究最多的随机非线性模型，包括众所周知的与状态有关的乘性噪声作为特例。本文的目的是设计一种新颖的分布式滤波器，该滤波器不仅使用单个节点本身的信息，而且还根据给定的拓扑结构使用其相邻节点的信息。为了提高设计过滤器的安全性，$ \ chi ^ 2 $检测器用于检测异常创新。通过吉尔伯特-埃利奥特（Gilbert-Elliott）通道的故障率和恢复率，建立了充分的条件以确保估计误差协方差的上限存在，然后通过最小化此类上限的轨迹来设计所需的滤波器参数。随后研究估计误差协方差的渐近有界性。最后，以目标跟踪问题为例，验证了所提滤波方案的有效性和安全性。