Secure Filtering against Spatio-Temporal False Data Attacks under Asynchronous Sampling

TL;DR

This paper proposes a decentralized, secure state estimation method for asynchronous, large-scale control systems that withstands various false data attacks by leveraging $$ regularization and time synchronization.

Contribution

It introduces a novel decentralized estimation algorithm that maintains security against complex false data attacks in asynchronous sampling environments.

Findings

The proposed method achieves secure state estimation with bounded error under attack.

It recovers optimal Kalman estimates in attack-free scenarios.

Validated effectiveness on IEEE 14-bus system benchmark.

Abstract

This paper addresses the secure state estimation problem for continuous linear time-invariant systems with non-periodic and asynchronous sampled measurements, where the sensors need to transmit not only measurements but also sampling time-stamps to the fusion center. This measurement and communication setup is well-suited for operating large-scale control systems and, at the same time, introduces new vulnerabilities that can be exploited by adversaries through (i) manipulation of measurements, (ii) manipulation of time-stamps, (iii) elimination of measurements, (iv) generation of completely new false measurements, or a combination of these attacks. To mitigate these attacks, we propose a decentralized estimation algorithm in which each sensor maintains its local state estimate asynchronously based on its measurements. The local states are synchronized through time prediction and fused after time-stamp alignment. In the absence of attacks, state estimates are proven to recover the optimal Kalman estimates by solving a weighted least square problem. In the presence of attacks, solving this weighted least square problem with the aid of $\ell_1$ regularization provides secure state estimates with uniformly bounded error under an observability redundancy assumption. The effectiveness of the proposed algorithm is demonstrated using a benchmark example of the IEEE 14-bus system.