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

TL;DR

This paper develops quadratic estimation techniques for stochastic systems affected by random uncertainties, correlated noise, and deception attacks, demonstrating improved performance over linear methods through covariance-based filtering and smoothing.

Contribution

It introduces a covariance-based quadratic filtering and smoothing approach for stochastic systems with random parameters, correlated noise, and deception attacks, filling a gap in existing estimation methods.

Findings

Quadratic estimators outperform linear ones in simulations.

The approach effectively handles random parameter matrices and deception attacks.

Simulation results demonstrate improved estimation accuracy.

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.