Detection algorithm for data integrity attacks in quantized FIR system identification

Jingrong Liu; Shuying Sun; Qingxiang Zhang; Jingrong Liu; Shuying Sun; Qingxiang Zhang

doi:10.3934/era.2026353

Electronic Research Archive

2026, Volume 34, Issue 11: 8328-8362. doi: 10.3934/era.2026353

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Research article

Detection algorithm for data integrity attacks in quantized FIR system identification

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: 09 July 2026 Revised: 15 September 2026 Accepted: 20 September 2026 Published: 24 September 2026

Targeting data integrity security threats, this paper investigates the anomaly detection and performance evaluation problems of data integrity attacks for finite impulse response systems with binary quantized observations. Breaking through the limitations of existing detection methods that highly depend on precise prior models and struggle with quantization non-linearity, we start from the inherent mechanisms of parameter identification and fully exploit the persistent excitation property of the system input. By cleverly designing and partitioning the observation dataset into two independent full-rank subsets, a novel detection residual is constructed. Without relying on prior knowledge of attack types, this method can provide unified and effective anomaly detection and early warning for whether the system is suffering from denial of service attacks, tampering attacks, or replay attacks. Furthermore, to measure the detection performance of the algorithm, we strictly prove the asymptotic normality of the detection residuals under both attack-free and various attack environments and derive explicit calculation expressions for the false alarm rate and missed detection rate. Finally, the impacts of factors on the algorithm's performance are analyzed. Numerical simulations verify the effectiveness of the proposed detection algorithm and the accuracy of the theoretical derivations.
- attack detection,
- quantization,
- system identification,
- data integrity attacks
Citation: Jingrong Liu, Shuying Sun, Qingxiang Zhang. Detection algorithm for data integrity attacks in quantized FIR system identification[J]. Electronic Research Archive, 2026, 34(11): 8328-8362. doi: 10.3934/era.2026353

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Abstract

Targeting data integrity security threats, this paper investigates the anomaly detection and performance evaluation problems of data integrity attacks for finite impulse response systems with binary quantized observations. Breaking through the limitations of existing detection methods that highly depend on precise prior models and struggle with quantization non-linearity, we start from the inherent mechanisms of parameter identification and fully exploit the persistent excitation property of the system input. By cleverly designing and partitioning the observation dataset into two independent full-rank subsets, a novel detection residual is constructed. Without relying on prior knowledge of attack types, this method can provide unified and effective anomaly detection and early warning for whether the system is suffering from denial of service attacks, tampering attacks, or replay attacks. Furthermore, to measure the detection performance of the algorithm, we strictly prove the asymptotic normality of the detection residuals under both attack-free and various attack environments and derive explicit calculation expressions for the false alarm rate and missed detection rate. Finally, the impacts of factors on the algorithm's performance are analyzed. Numerical simulations verify the effectiveness of the proposed detection algorithm and the accuracy of the theoretical derivations.

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