Research On Event-triggered State Estimation Under Multiple Attacks

State estimation is an important method for online monitoring,network sensing,and control.It is widely used in smart cities,Intelligent Traffic Systems,and other fields.Most of the current research on state estimation assumes that the noise is Gaussian distributed,but modeling errors or multipath propagation in the data transmission process makes these noises follow non-Gaussiandistributiond with heavy-tailed.The design of estimators under non-Gaussian noise needs to be studied.At the same time,the sensor needs to transmit a large number of data in a short,which is limited by the constraints of communication bandwidth.It is likely to lead to channel blockage,and the loss of measurement data,resulting in reduced system estimation accuracy.In addition,due to the presence of malicious or unintentional attackers in the communication network,the transmission process of measurement data may face multiple types of attacks,which may compromise the security and integrity of the data and affect the state estimation accuracy.Therefore,this paper investigates a resilient attack-resistant state estimation method to address the problems of heavy-tailed and non-Gaussian noise,limited channel bandwidth,and multiple malicious attacks in stochastic nonlinear systems,and the main contents of this paper are given as follows:(1)For a stochastic nonlinear system with a heavy-tailed and non-Gaussian distribution of process noise and measurement noise,the state estimation problem of a system with multiple physical attacks is considered,and an event-triggered resilient Student’s t extended Kalman filtering method is designed.Firstly,the Student’s t distribution is used to approximate the probability density function of the noise;secondly,an event-triggered mechanism based on the amount of measurement change as a threshold is designed to reduce the number of measurement transmissions and improve transmission efficiency;and the introduction of two mutually independent binary random variables to characterize the attacks.Minimizing the estimation error covariance is used as the optimization principle to design an anti-attack filter under event triggering and realizing the state estimation under multiple attacks;finally,a sufficient condition for the estimation state error to be bounded is given.The effectiveness of the designed filter is verified by simulation comparison.(2)For a nonlinear system with a bandwidth constraint and a heavy-tailed nonGaussian characteristic of the noise,an event-triggered resilient Student’s t filter based on the Bayesian criterion is designed by considering the state estimation problem under multiple attacks with a known attack rate.Assuming the probability of an attack is known,the measured probability density function under multiple attacks is calculated,and the state update process is derived based on the Bayesian criterion to obtain the Student’s t filter under multiple attacks with an event-triggered mechanism.A sufficient condition for the boundedness of estimation error is proposed,and the effectiveness of the designed filter is verified by simulation comparison and cart trajectory tracking experiments.(3)The adaptive Student’s t Unscented Kalman Filter is designed for the state estimation of stochastic nonlinear systems with multi-sensor measurements under time-varying multiple attacks with unknown attack probabilities,to achieve accurate estimation of unknown states and unknown attack rates.Firstly,the probability likelihood function of the measurement under attacks is calculated;secondly,the variational approximation of the prior and posterior probability density functions is calculated according to the variational Bayesian principle;then,the state estimation and the estimation of the attack probability are obtained based on the fixed-point iteration method.The measurement noise adaptive method is proposed.Finally,the stability of the designed adaptive Student’s t Unscented Kalman Filter is analyzed.The effectiveness of the designed filter is verified by simulation comparison and the trajectory tracking experiment of the cart.