Resilient State Estimation for Discrete-Time Linear Systems

TL;DR

This paper introduces a resilient state estimator for discrete-time linear systems that maintains bounded estimation error despite impulsive and dense measurement noise, leveraging convex optimization techniques.

Contribution

It presents a novel estimator design that ensures resilience against impulsive measurement noise, with explicit bounds related to system observability and performance functions.

Findings

Estimator achieves bounded error under unbounded noise

Resilience depends on system observability and chosen performance function

Simulation results confirm robustness against impulsive noise

Abstract

This paper proposes a resilient state estimator for LTI discrete-time systems. The dynamic equation of the system is assumed to be affected by a bounded process noise. As to the available measurements, they are potentially corrupted by a noise of both dense and impulsive natures. In this setting, we construct the estimator as the map which associates to the measurements, the minimizing set of an appropriate (convex) performance function. It is then shown that the proposed estimator enjoys the property of resilience, that is, it induces an estimation error which, under certain conditions, is independent of the extreme values of the (impulsive) measurement noise. Therefore, the estimation error may be bounded while the measurement noise is virtually unbounded. Moreover, the expression of the bound depends explicitly on the degree of observability of the system being observed and on the considered performance function. Finally, a few simulation results are provided to illustrate the resilience property.