Counter-Adversarial Learning with Inverse Unscented Kalman Filter

TL;DR

This paper introduces an inverse Unscented Kalman Filter (IUKF) for counter-adversarial systems, enabling nonlinear state estimation of adversaries' strategies with theoretical stability guarantees and near-optimal accuracy.

Contribution

It formulates inverse cognition as a nonlinear Gaussian state-space model and develops the IUKF with proven stochastic stability, addressing limitations of linear models.

Findings

IUKF estimation error converges over time.

IUKF closely approaches the recursive Cramér-Rao lower bound.

Theoretical guarantees ensure mean-squared boundedness of IUKF.

Abstract

In counter-adversarial systems, to infer the strategy of an intelligent adversarial agent, the defender agent needs to cognitively sense the information that the adversary has gathered about the latter. Prior works on the problem employ linear Gaussian state-space models and solve this inverse cognition problem by designing inverse stochastic filters. However, in practice, counter-adversarial systems are generally highly nonlinear. In this paper, we address this scenario by formulating inverse cognition as a nonlinear Gaussian state-space model, wherein the adversary employs an unscented Kalman filter (UKF) to estimate the defender's state with reduced linearization errors. To estimate the adversary's estimate of the defender, we propose and develop an inverse UKF (IUKF) system. We then derive theoretical guarantees for the stochastic stability of IUKF in the mean-squared boundedness sense. Numerical experiments for multiple practical applications show that the estimation error of IUKF converges and closely follows the recursive Cram\'{e}r-Rao lower bound.