Secure state estimation over Markov wireless communication channels (extended version)

TL;DR

This paper introduces a novel approach to secure state estimation in wireless control systems over Markov channels, ensuring bounded estimation error for legitimate users while keeping eavesdroppers' error unbounded, demonstrated on a pendulum example.

Contribution

It proposes the concept of optimal mean square expected secrecy over FSMCs and designs a secrecy parameter to achieve bounded user error and unbounded eavesdropper error.

Findings

Secrecy parameter effectively bounds user MSE.

Eavesdropper MSE remains unbounded under the proposed scheme.

Validated approach on an inverted pendulum system.

Abstract

This note studies state estimation in wireless networked control systems with secrecy against eavesdropping. Specifically, a sensor transmits a system state information to the estimator over a legitimate user link, and an eavesdropper overhears these data over its link independent of the user link. Each connection may be affected by packet losses and is modeled by a finite-state Markov channel (FSMC), an abstraction widely used to design wireless communication systems. This paper presents a novel concept of optimal mean square expected secrecy over FSMCs and delineates the design of a secrecy parameter requiring the user mean square estimation error (MSE) to be bounded and eavesdropper MSE unbounded. We illustrate the developed results on an example of an inverted pendulum on a cart whose parameters are estimated remotely over a wireless link exposed to an eavesdropper.