Distributed recursive filtering for stochastic systems under uniform quantizations and deception attacks through sensor networks

TLDR: In this paper, a distributed recursive filtering problem for a class of discrete time-delayed stochastic systems subject to both uniform quantization and deception attack effects on the measurement outputs is considered.

About: This article is published in Automatica.The article was published on 2017-04-01 and is currently open access. It has received 340 citations till now. The article focuses on the topics: Recursive filter & Filtering problem.

Figures

Fig. 1. Topological structure of the sensor network.

Fig. 4. The trace of filtering error covariance for different

Fig. 3. The system states and their estimation (two elements for considered system state).

Fig. 2. The measurements and the received signals.

Fig. 5. The trace of Π2,k|k for varying ᾱ on k = 100.

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Distributedrecursivefiltering for stochastic systemsunder uniformquantizations anddeceptionattacks through sensornetworks ⋆" ?

This paper is concerned with the distributed recursive filtering problem for a class of discrete time-delayed stochastic systems subject to both uniform quantization and deception attack effects on the measurement outputs. Furthermore, by utilizing the mathematical induction, a sufficient condition is established to ensure the asymptotic boundedness of the sequence of the error covariance. 

Q2. What future works have the authors mentioned in the paper "Distributedrecursivefiltering for stochastic systemsunder uniformquantizations anddeceptionattacks through sensornetworks ⋆" ?

Further research topics would be to extend the main results of this paper to other more complex systems ( e. g. [ 5, 10, 14, 33–35 ] ). Along the trajectory of system ( 1 ), it can be derived that Xk+1 = BkB T k + r∑ s=0 { Πi, k+1|kC T 0, k+1 +K2i, k+1 ( ( ~iin ) 2 ( 1− ᾱ ) 2C0, k+1 ×Πi, k+1|kC T 0, k+1 +Ψ 23 i, k+1 ) = 0 which can be further simplified as follows: K1i, k+1S 1 i, k+1 + ( 1 − ᾱ ) ( ~ i in ) 2K2i, k+1S 0 i, k+1 − ~iinΠi, k+1|kC T 0, k+1 = 0, K2i, k+1S 2 i, k+1 + ( 1 − ᾱ ) ( ~ i in ) 2K1i, k+1S 0 i, k+1 − ( 1 − ᾱ ) ~iinΠi, k+1|kC Therefore, taking ( 20 ) - ( 22 ) into consideration, the authors can obtain the desired filter gain matrices. 

Q3. What is the main purpose of the paper?

In this paper, the mathematical induction method combined with the properties of matrix analysis is utilized to overcome the difficulties and obtain the desired sufficient conditions that are related to both the quantization and the attack. 

Q4. What is the boundedness of the system parameter matrices?

There are positive real constants f̄i, f̄ d i , b, b̄, d, d̄ and c̄i (i = 0, 1, 2, · · · , r) such that the system parameter matrices are bounded: 

Q5. What is the main contribution of this paper?

The main contribution of this paper is threefold: 1) a novel structure of distributed filters is designed to adequately utilize the available innovations from not only itself (credible measurements) but also its neighbouring sensors which could be subject to deception attacks; 2) the developed filter design algorithm is of a form suitable for distributed recursive computation in online applications via solving two Riccati-like difference equations; and 3) a sufficient condition is proposed to show the asymptotic boundedness of the filtering error covariance through intensive stochastic analysis. 

Q6. What is the main topic of research in the area of cyber-security?

In the research area of cyber-security, the success ratio of the launched attacks has recently become an emerging topic of research from the defenders’ perspectives. 

Q7. How is the filtering error covariance calculated?

In addition, by utilizing the mathematical induction method, a sufficient condition has been proposed under which the filtering error covariance is bounded as time trends to infinity. 

Q8. What is the focus of this paper?

Summarizing the above discussions, the focus of this paper is on the parameter design and performance analysis of distributed recursive filtering with uniform quantization and intermittent deception attacks. 

Q9. What is the general context of networked control systems?

In the general context of networked control systems, so far, much progress has been made on the security control/filtering problems by employing the techniques of dynamic programming or Lyapunov stability theory, see e.g. [1, 21] for denial-of-service (DoS) attacks and [6, 7, 11, 16, 26] for deception attacks. 

Q10. What is the boundedness of the sequence i,k|k?

In this section, for obtained filter gains, the authors will propose a sufficient condition ensuring the boundedness of the sequence Πi,k|k with respect to the filtering error covariance. 

Q11. what is the upper bound for the filtering error covariance?

the upper bound for the filtering error covariance Πi,k+1|k+1 is recursively calculated by Riccati-like difference equation (11). 

Q12. what is the gain matrices of the recursive filter?

For the addressed system (1) with measurements (3) suffering from attacks (4), the gain matrices of the recursive filter (5a) and (5b) are given as followsK1i,k+1 = ~ i in 

Q13. What are the main reasons for the lack of stability and minimum data transmission rate issues?

The launched attacks by the adversaries may not always be successful for mainly three reasons: 1) only a relatively small amount of attacks could pass through the detectors (with anti-attack countermeasures) for systems equipped with protection devices or software; 2) the attacks cannot be persistently (or arbitrarily) launched by the adversaries due to unavoidable limited resource(e.g. energy); and 3) the attacks sent through the networks with limited bandwidth are subject to randomly fluctuated condition changes (e.g. network load, network congestion and network transmission rate) and therefore cannot arrive at the desired end.