Secure State Estimation against Sparse Attacks on a Time-varying Set of Sensors

TL;DR

This paper introduces a secure state estimation method for linear systems that remains accurate despite sparse, time-varying sensor attacks, using decentralized observers and optimization-based fusion.

Contribution

It proposes a novel decentralized observer scheme with optimization-based fusion for secure state estimation under sparse, time-varying sensor attacks.

Findings

Estimation error is bounded by a system-dependent constant.

The method successfully detects and resets compromised sensors.

Application on IEEE 14-bus system demonstrates effectiveness.

Abstract

This paper studies the problem of secure state estimation of a linear time-invariant (LTI) system with bounded noise in the presence of sparse attacks on an unknown, time-varying set of sensors. In other words, at each time, the attacker has the freedom to choose an arbitrary set of no more that $p$ sensors and manipulate their measurements without restraint. To this end, we propose a secure state estimation scheme and guarantee a bounded estimation error subject to $2p$-sparse observability and a mild, technical assumption that the system matrix has no degenerate eigenvalues. The proposed scheme comprises a design of decentralized observer for each sensor based on the local observable subspace decomposition. At each time step, the local estimates of sensors are fused by solving an optimization problem to obtain a secure estimation, which is then followed by a local detection-and-resetting process of the decentralized observers. The estimation error is shown to be upper-bounded by a constant which is determined only by the system parameters and noise magnitudes. Moreover, we optimize the detector threshold to ensure that the benign sensors do not trigger the detector. The efficacy of the proposed algorithm is demonstrated by its application on a benchmark example of IEEE 14-bus system.