What did your adversary believeƒ Optimal Filtering and Smoothing in Counter-Adversarial Autonomous Systems

Abstract

We consider fixed-interval smoothing problems for counteradversarial autonomous systems. An adversary deploys an autonomous filtering and control system that i) measures our current state via a noisy sensor, ii) computes a posterior estimate (belief) and iii) takes an action that we can observe. Based on such observed actions and our knowledge of our state sequence, we aim to estimate the adversary's past and current beliefs -this forms a foundation for predicting, and counteracting against, future actions. We derive the optimal smoother for the adversary's beliefs (we treat the problem in a Bayesian framework). Moreover, we demonstrate how the smoother can be computed for discrete systems even though the corresponding backward variables do not admit a finite-dimensional characterization. Finally, we illustrate our results in numerical simulations.

Inverse Filtering for Hidden Markov Models with Applications to Counter-Adversarial Autonomous Systems

“…The latter is of crucial importance when applying inverse filtering algorithms in counter-adversarial scenarios [4]- [6]. In such, an adversary is trying to estimate our state (via Bayesian filtering) and does not, in general, have access to our transition kernel -recall the setup from Fig.…”

“…Hence, its filtering system is mismatched (e.g., a maximum likelihood estimate P computed by the adversary is used instead of the true P ). Compared to [5], [6] that aim to estimate information private to the adversary, the present work does not assume knowledge of the adversary's filter parameters, nor that its filtering system is matched.…”

“…Consider an adversary that employs an autonomous filtering and control system that estimates our state and takes actions based on a control policy. The goal in the design of a counteradversarial autonomous (CAA) system is to infer information private to the adversary, and to predict and guard against its future actions [4]- [6].…”

“…In order to leverage these results for Problem 3, we first need to obtain the adversary's posterior distributions from its actions. This is discussed to a longer extent in [5], [6], in a Bayesian framework, and in [34] in an analytic setting. We will use, and briefly recap, the main results of [34] below.…”

“…, y N . An important motivating application is the design of counter-adversarial systems [4]- [6]: Given measurements of the actions of a sophisticated autonomous adversary, how to remotely calibrate (i.e., estimate) its sensors and predict, so as to guard against, its future actions? We refer the reader to Fig.…”