Analysis of resilience for a State Estimator for Linear Systems

Abstract

This paper proposes to analyze the resilient properties of a specific 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 define an 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.

An Optimization Framework for Resilient Batch Estimation in Cyber-Physical Systems

“…We now recall from [16] a technical lemma which will play a fundamental role in analyzing the properties of the estimator (8). In particular, our proof of well-definedness relies on this lemma.…”

“…Since 0 ∈ Fr, a consequence of property (16) is that E(Y ) = {X}, which follows from (16) for F = 0. This fact expresses correctness of the estimator in a nominal situation, i.e., its ability to recover the true state matrix X in the absence of any uncertainty in the a priori known model.…”

“…Note also that no statistical significance is attached to the uncertainties modeled by noise. In this setting, by generalizing our previous work reported in [16], the current paper proposes a general (robust) estimation framework for the state of LTV systems. We propose a class of state estimators constructed as the set-valued maps which associate to the output measurements, the minimizing set of some appropriate performance functions.…”