Asymptotically consistent identification of binary quantized systems under Poisson-distributed replay attacks

Yadong Wang; Wenyang Jiang; Wenke Liu; Yadong Wang; Wenyang Jiang; Wenke Liu

doi:10.3934/era.2026308

Electronic Research Archive

2026, Volume 34, Issue 10: 7118-7151. doi: 10.3934/era.2026308

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Research article

Asymptotically consistent identification of binary quantized systems under Poisson-distributed replay attacks

1.
School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China
2.
Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, Beijing 100083, China

Received: 06 June 2026 Revised: 31 July 2026 Accepted: 10 August 2026 Published: 18 August 2026

This paper investigated the identifiability of attack frequency and the parameter estimation problem in binary quantized finite impulse response (FIR) systems under Poisson-distributed replay attacks. First, the replay attack is modeled as a Poisson stochastic process, and the convergence properties of the attack frequency in the long-term statistical sense were analyzed, along with definitions and criteria for attack frequency identifiability. Under the assumption that the attack frequency is known, a compensated identification algorithm was established for parameter estimation, and the strong consistency and asymptotic normality of the estimators were established. Furthermore, for the case of unknown attack frequency, a joint estimation algorithm based on empirical statistics was proposed to achieve simultaneous identification of the attack frequency and system parameters. In addition, the optimal design criterion for the compensation ratio parameter was derived to reduce estimation errors. The proposed framework falls within the scope of resilient identification, where the estimator continues to recover system parameters from long-term statistics even under intermittent replay corruptions of the communication channel. Finally, numerical simulations under various attack frequencies, delay distributions, and noise levels were conducted to verify the effectiveness and robustness of the attack frequency identifiability analysis and the proposed algorithms.
- Poisson distribution,
- replay attack,
- attack frequency,
- identifiability,
- parameter estimation
Citation: Yadong Wang, Wenyang Jiang, Wenke Liu. Asymptotically consistent identification of binary quantized systems under Poisson-distributed replay attacks[J]. Electronic Research Archive, 2026, 34(10): 7118-7151. doi: 10.3934/era.2026308

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Abstract

This paper investigated the identifiability of attack frequency and the parameter estimation problem in binary quantized finite impulse response (FIR) systems under Poisson-distributed replay attacks. First, the replay attack is modeled as a Poisson stochastic process, and the convergence properties of the attack frequency in the long-term statistical sense were analyzed, along with definitions and criteria for attack frequency identifiability. Under the assumption that the attack frequency is known, a compensated identification algorithm was established for parameter estimation, and the strong consistency and asymptotic normality of the estimators were established. Furthermore, for the case of unknown attack frequency, a joint estimation algorithm based on empirical statistics was proposed to achieve simultaneous identification of the attack frequency and system parameters. In addition, the optimal design criterion for the compensation ratio parameter was derived to reduce estimation errors. The proposed framework falls within the scope of resilient identification, where the estimator continues to recover system parameters from long-term statistics even under intermittent replay corruptions of the communication channel. Finally, numerical simulations under various attack frequencies, delay distributions, and noise levels were conducted to verify the effectiveness and robustness of the attack frequency identifiability analysis and the proposed algorithms.

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