State estimation for a class of nonlinear non‐Gaussian cyber–physical systems under false data injection attacks

This paper addresses a distributed nonlinear filtering issue based on maximum correntropy for dealing with randomly occurring hybrid cyber‐attacks in non‐Gaussian environment. The types of cyber‐attacks include denial of service attacks and deception attacks. First, a modified distributed unscented Kalman filter is proposed, using Cauchy kernel‐based maximum correntropy criterion instead of the traditional mean square error criterion, against cyber‐attacks and non‐Gaussian noise. Then based on fixed‐point iterative rules and information fusion strategy, the update equations of state estimates and covariance matrices of the proposed filter are obtained. Furthermore, the sufficient condition guaranteeing its convergence and computational complexity are also given. Finally, an illustrative example is presented to verify the effectiveness of the proposed filter under hybrid cyber‐attacks in non‐Gaussian environment.

Distributed maximum correntropy unscented Kalman filter under hybrid attacks in non‐Gaussian environment

Liu,

Ma,

Huang

et al. 2024

Maximum weighted correntropy filters for nonlinear non‐Gaussian systems

Liu,

Zhang,

Song

2024

In this paper, we focus on the filtering issue for nonlinear non‐Gaussian systems. Considering the limitations of the Gaussian function with a single kernel bandwidth, we design a novel extended version called weighted Gaussian function, which consists of a weighting coefficient and two distinct kernel bandwidths. The additional coefficient can directly balance two kernel bandwidths, which improves the flexibility and performance of the correntropy. We develop a cost function utilizing the suggested weighted Gaussian function and statistical linearization method, followed by deriving a maximum weighted correntropy filter based on the maximum correntropy criterion. The proposed algorithm is demonstrated to converge to a Gaussian filter as the kernel bandwidths approach infinity. In addition, we derive the corresponding information filter, which takes the form of information matrix and information vector. It is computationally efficient and easier to generalize to multisensor systems. The performance of the proposed algorithms is compared with other filters based on the third‐order spherical cubature rule and the fixed point iteration technique in a target tracking system. Simulation results confirm the effectiveness of the new approaches.

Recursive multi‐sensor fusion estimation under the coding‐based relay network

Zhang,

Liu,

Deng

2024

This paper studies the recursive fusion estimation issue for a class of linear time‐varying multi‐sensor systems with amplify‐and‐forward (AF) relays. The AF relay is located between the sensor and the estimator to forward measurement signals for facilitating long‐distance transmission. A binary encoding scheme is used to regulate signal transmission via a digital network where the signal is encoded into a bit string and decoded at the endpoint of the receiver. Because of the uncertainty of the network and the existence of channel noises, a set of Bernoulli distributed random variables is introduced to characterize the random bit flip phenomenon. The purpose of the addressed problem is to design a fusion estimator to simultaneously reflect the impact of multiplicative noises, the AF relay, the binary encoding scheme, and the random bit flip on the filtering error covariance. First of all, an upper bound for the filtering error covariance of the local estimator can be acquired, and by minimizing such an upper bound, the parametric form of the gain matrix is obtained. Subsequently, the fusion estimation is given based on the covariance intersection fusion strategy. Finally, a simulation example is presented to verify the effectiveness of the proposed multi‐sensor fusion estimation.