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    This study analyzes replay attacks on distributed filtering systems. We found that for stable systems, estimation errors remain bounded, while unstable systems may experience diverging errors, necessitating detectability conditions.

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    Area of Science:

    • Control Systems Engineering
    • Cybersecurity
    • Distributed Computing

    Background:

    • Consensus-based distributed filtering is crucial for networked systems.
    • Replay attacks pose a significant threat by manipulating sensor data.
    • Understanding attack impact on estimation performance is vital.

    Purpose of the Study:

    • To analyze the security of consensus-based distributed filtering against replay attacks.
    • To quantify the stealthiness and impact of replay attacks on estimation error.
    • To develop conditions for detecting replay attacks in unstable systems.

    Main Methods:

    • Analysis of distributed estimation performance under replay attacks.
    • Utilizing Kullback-Leibler (K-L) divergence to measure attack stealthiness.
    • Employing Lyapunov equations to analyze error bounds in stable systems.
    • Investigating error covariance in unstable systems.

    Main Results:

    • For stable systems, estimation errors are bounded and can reach a steady state, with replay attacks proven to be $\epsilon$-stealthy.
    • For unstable systems, estimation error covariance is lower bounded by an exponential function, indicating potential divergence.
    • A sufficient condition for detecting replay attacks in unstable systems was established.

    Conclusions:

    • Replay attacks degrade distributed estimation performance, with varying impacts on stable and unstable systems.
    • The stealthiness of replay attacks can be quantified using K-L divergence.
    • Detectability conditions are crucial for securing distributed filtering against sophisticated replay attacks.