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Secure Event-Triggered Distributed Kalman Filters for State Estimation over Wireless Sensor Networks

Aquib Mustafa, Majid Mazouchi, Hamidreza Modares

TL;DR

This work addresses secure state estimation over wireless sensor networks using an event-triggered distributed Kalman filter (DKF) by revealing how an attacker can exploit the triggering mechanism to cause non-triggering or continuous-triggering misbehavior, compromising connectivity and observability. It introduces a Gaussian-free attack detector based on KL divergence estimated via $k$-NN to detect attacks on sensors and communication channels, and a meta-Bayesian second-order inference framework that yields confidence and trust values to discard corrupted data and mitigate impacts. The main contributions are (i) a rigorous analysis of triggering-based attack paths, (ii) an entropy-based, non-Gaussian detector, and (iii) a confidence-trust based resilient estimation mechanism validated through simulations on AUV dynamics. The results significantly advance practical resilience for distributed state estimation in CPS under deception attacks, enabling reliable operation in energy-constrained WSNs.

Abstract

In this paper, we analyze the adverse effects of cyber-physical attacks as well as mitigate their impacts on the event-triggered distributed Kalman filter (DKF). We first show that although event-triggered mechanisms are highly desirable, the attacker can leverage the event-triggered mechanism to cause non-triggering misbehavior which significantly harms the network connectivity and its collective observability. We also show that an attacker can mislead the event-triggered mechanism to achieve continuous-triggering misbehavior which not only drains the communication resources but also harms the network's performance. An information-theoretic approach is presented next to detect attacks on both sensors and communication channels. In contrast to the existing results, the restrictive Gaussian assumption on the attack signal's probability distribution is not required. To mitigate attacks, a meta-Bayesian approach is presented that incorporates the outcome of the attack detection mechanism to perform second-order inference. The proposed second-order inference forms confidence and trust values about the truthfulness or legitimacy of sensors' own estimates and those of their neighbors, respectively. Each sensor communicates its confidence to its neighbors. Sensors then incorporate the confidence they receive from their neighbors and the trust they formed about their neighbors into their posterior update laws to successfully discard corrupted information. Finally, the simulation result validates the effectiveness of the presented resilient event-triggered DKF.

Secure Event-Triggered Distributed Kalman Filters for State Estimation over Wireless Sensor Networks

TL;DR

This work addresses secure state estimation over wireless sensor networks using an event-triggered distributed Kalman filter (DKF) by revealing how an attacker can exploit the triggering mechanism to cause non-triggering or continuous-triggering misbehavior, compromising connectivity and observability. It introduces a Gaussian-free attack detector based on KL divergence estimated via -NN to detect attacks on sensors and communication channels, and a meta-Bayesian second-order inference framework that yields confidence and trust values to discard corrupted data and mitigate impacts. The main contributions are (i) a rigorous analysis of triggering-based attack paths, (ii) an entropy-based, non-Gaussian detector, and (iii) a confidence-trust based resilient estimation mechanism validated through simulations on AUV dynamics. The results significantly advance practical resilience for distributed state estimation in CPS under deception attacks, enabling reliable operation in energy-constrained WSNs.

Abstract

In this paper, we analyze the adverse effects of cyber-physical attacks as well as mitigate their impacts on the event-triggered distributed Kalman filter (DKF). We first show that although event-triggered mechanisms are highly desirable, the attacker can leverage the event-triggered mechanism to cause non-triggering misbehavior which significantly harms the network connectivity and its collective observability. We also show that an attacker can mislead the event-triggered mechanism to achieve continuous-triggering misbehavior which not only drains the communication resources but also harms the network's performance. An information-theoretic approach is presented next to detect attacks on both sensors and communication channels. In contrast to the existing results, the restrictive Gaussian assumption on the attack signal's probability distribution is not required. To mitigate attacks, a meta-Bayesian approach is presented that incorporates the outcome of the attack detection mechanism to perform second-order inference. The proposed second-order inference forms confidence and trust values about the truthfulness or legitimacy of sensors' own estimates and those of their neighbors, respectively. Each sensor communicates its confidence to its neighbors. Sensors then incorporate the confidence they receive from their neighbors and the trust they formed about their neighbors into their posterior update laws to successfully discard corrupted information. Finally, the simulation result validates the effectiveness of the presented resilient event-triggered DKF.

Paper Structure

This paper contains 19 sections, 6 theorems, 89 equations, 11 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions and outline
  4. Notations and Preliminaries
  5. Notations
  6. Process Dynamics and Sensor Models
  7. Overview of Event-triggered Distributed Kalman Filter
  8. Attack Modeling
  9. Effect of Attack on Triggering Mechanism
  10. Non-triggering Misbehavior
  11. Continuous-triggering Misbehavior
  12. Attack Detection
  13. Secure Distributed Estimation Mechanism
  14. Confidence of sensor nodes
  15. Trust of sensor nodes about their incoming information
  16. ...and 4 more sections

Key Result

Theorem 1

Consider the process dynamics ZEqnNum820040 with compromised sensor model ZEqnNum973066. Let the state estimation equation be given by ZEqnNum120276 in the presence of attacks modeled by $f_{i}^{a}(k)$ in ZEqnNum499212. Then, the corrupted posterior state estimation error covariance $\hat{P}_{i}^{a} where $\Sigma _{i}^{f}(k)$ and $\Xi _{f} (k)$ denote the attacker's input dependent covariance matr

Figures (11)

  • Figure 1: Effect of non-triggering misbehavior on sensor nodes $\{$5,6$\}$ cluster the graph ${\rm {\mathcal{G}}}$ in the two isolated graphs ${\rm {\mathcal{G}}}_{1}$ and ${\rm {\mathcal{G}}}_{2}.$
  • Figure 2: The scenario of distributed estimating of the position and velocity of an AUV.
  • Figure 3:
  • Figure 4:
  • Figure 6:
  • ...and 6 more figures

Theorems & Definitions (15)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • proof
  • Theorem 3
  • proof
  • Theorem 4
  • proof
  • Theorem 5
  • ...and 5 more