Consistent Identification of Wiener Systems with Quantized Data Under Replay Attacks

This paper studies parameter estimation of Wiener systems with quantized inputs and multiple-valued observations in the presence of replay attacks. The proposed approach effectively addresses the destruction of the data temporal structure caused by replay attacks as well as the information loss induced by multiple-valued observations, thereby achieving consistent parameter estimation of Wiener systems under constrained observation conditions. First, the influence of replay attacks on the consistency of parameter estimation is theoretically analyzed. It is shown that the attack-free estimation algorithm converges to a biased limit under replay attacks, and an explicit expression of this limit is derived. To address this issue, two classes of consistent estimation algorithms are proposed. When the attack strategy is known, a compensation matrix is constructed to correct the compromised data, thereby eliminating the bias introduced by replay attacks and achieving consistent parameter estimation. When the attack strategy is unknown, a data preprocessing mechanism with structured markers is designed to estimate the attack strategy, based on which a compensated parameter estimation method is further developed. Moreover, the statistical properties of the proposed algorithms are analyzed, and the asymptotic normality of the estimators is established together with analytical expressions for the covariance matrices. On this basis, an optimization problem aimed at minimizing the estimation variance is formulated, yielding the optimal design parameters for the consistent estimation algorithms. Simulation results demonstrate that the proposed methods can effectively suppress the influence of replay attacks on system identification and achieve accurate and consistent parameter estimation for Wiener systems under multiple-valued observation.