Efficient Secure State Estimation against Sparse Integrity Attack for System with Non-derogatory Dynamics

TL;DR

This paper introduces a computationally efficient secure state estimation method for linear Gaussian systems under sparse integrity attacks, achieving optimal resilience when the system is 2p-sparse detectable and the unstable eigenvalues are non-derogatory.

Contribution

It proposes a novel secure estimation scheme that is resilient to integrity attacks under specific spectral conditions and provides a fundamental limit for secure dynamic estimation.

Findings

Estimation scheme is resilient to attacks if system is 2p-sparse detectable.

The proposed estimator coincides with Kalman filter in absence of attacks.

The detection and estimation processes are computationally efficient.

Abstract

We consider the problem of estimating the state of a time-invariant linear Gaussian system in the presence of integrity attacks. The attacker can compromise $p$ out of $m$ sensors, the set of which is fixed over time and unknown to the system operator, and manipulate the measurements arbitrarily. Under the assumption that all the unstable eigenvalues of system matrix $A$ have geometric multiplicity 1 (unstable part of $A$ is non-derogatory), we propose a secure estimation scheme that is resilient to integrity attack as long as the system is $2p$-sparse detectable, which is proved to be the fundamental limit of secure dynamic estimation. In the absence of attack, the proposed estimation coincides with Kalman estimation with a certain probability that can be adjusted to trade-off between performance with and without attack. Furthermore, the detectability condition checking in the designing phase and the estimation computing in the online operating phase are both computationally efficient. A numerical example is provided to corroborate the results and illustrate the performance of the proposed estimator.