Quadratic estimation for stochastic systems in the presence of random parameter matrices, time-correlated additive noise and deception attacks

TL;DR

The paper tackles state estimation in linear systems with random parameter matrices and time-correlated additive noise, further complicated by random deception attacks. It proposes a covariance-based LS quadratic framework that augments observations with second-order Kronecker powers, recasts the problem as a linear estimation in the augmented space, and derives recursive quadratic filtering and fixed-point smoothing algorithms via an innovations approach. Theoretical results include explicit dynamics and second-order statistics for the augmented processes, plus structured recursive procedures for both filtering and smoothing, with linear estimators provided as baselines. Simulations demonstrate that the LS quadratic estimators outperform traditional LS linear methods and quantify how attack and missing-measurement probabilities degrade performance, highlighting the practical robustness of the proposed approach in secure networked systems.

Abstract

Networked systems usually face different random uncertainties that make the performance of the least-squares (LS) linear filter decline significantly. For this reason, great attention has been paid to the search for other kinds of suboptimal estimators. Among them, the LS quadratic estimation approach has attracted considerable interest in the scientific community for its balance between computational complexity and estimation accuracy. When it comes to stochastic systems subject to different random uncertainties and deception attacks, the quadratic estimator design has not been deeply studied. In this paper, using covariance information, the LS quadratic filtering and fixed-point smoothing problems are addressed under the assumption that the measurements are perturbed by a time-correlated additive noise, as well as affected by random parameter matrices and exposed to random deception attacks. The use of random parameter matrices covers a wide range of common uncertainties and random failures, thus better reflecting the engineering reality. The signal and observation vectors are augmented by stacking the original vectors with their second-order Kronecker powers; then, the linear estimator of the original signal based on the augmented observations provides the required quadratic estimator. A simulation example illustrates the superiority of the proposed quadratic estimators over the conventional linear ones and the effect of the deception attacks on the estimation performance.

Figures (4)

• Figure 1: Estimation error variance comparison of the linear and quadratic filtering and smoothing estimators when $\overline{\theta}=\overline{\lambda}=0.5$.
• Figure 2: Simulated signal, linear and quadratic filtering and fixed-point smoothing estimates when $\overline{\theta}=\overline{\lambda}=0.5$.
• Figure 3: Linear and quadratic filtering and smoothing error variances versus $\overline{\theta}$, when $\overline{\lambda}=0.5$.
• Figure 4: Linear and quadratic filtering and smoothing error variances versus $\overline{\lambda}$, when $\overline{\theta}=0.5$.

Theorems & Definitions (10)

• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Remark 5
• Theorem 3.1
• Proposition 3.2
• Proposition 3.3
• Remark 6
• Theorem 4.1