Secure State Estimation against Sensor Attacks in the Presence of Noise

TL;DR

This paper introduces a secure state estimation method for noisy linear systems under sensor attacks, combining Kalman filtering, SMT techniques, and coding theory to improve robustness and efficiency.

Contribution

It presents a novel secure estimation algorithm that handles noise and adversarial sensor attacks, with optimal error bounds and efficient subset search methods.

Findings

Achieves optimal bounds on estimation error under sensor attack constraints.

Develops an efficient sensor subset search algorithm using SMT techniques.

Provides a coding theoretic perspective on attack detection and estimation.

Abstract

We consider the problem of estimating the state of a noisy linear dynamical system when an unknown subset of sensors is arbitrarily corrupted by an adversary. We propose a secure state estimation algorithm, and derive (optimal) bounds on the achievable state estimation error given an upper bound on the number of attacked sensors. The proposed state estimator involves Kalman filters operating over subsets of sensors to search for a sensor subset which is reliable for state estimation. To further improve the subset search time, we propose Satisfiability Modulo Theory based techniques to exploit the combinatorial nature of searching over sensor subsets. Finally, as a result of independent interest, we give a coding theoretic view of attack detection and state estimation against sensor attacks in a noiseless dynamical system.