Inverse Particle Filter

TL;DR

This paper introduces an inverse particle filter (I-PF) for inverse cognition in adversarial systems, capable of handling non-linear dynamics and unknown system information, with proven convergence and demonstrated effectiveness through numerical experiments.

Contribution

It develops a global inverse particle filter that overcomes limitations of Gaussian assumptions and local approximations, including a differentiable version for unknown system scenarios.

Findings

The I-PF converges to the optimal inverse filter under mild conditions.

Numerical experiments show effective estimation performance.

The proposed method handles non-linear dynamics and unknown system information.

Abstract

In cognitive systems, recent emphasis has been placed on studying the cognitive processes of the subject whose behavior was the primary focus of the system's cognitive response. This approach, known as inverse cognition, arises in counter-adversarial applications and has motivated the development of inverse Bayesian filters. In this context, a cognitive adversary, such as a radar, uses a forward Bayesian filter to track its target of interest. An inverse filter is then employed to infer the adversary's estimate of the target's or defender's state. Previous studies have addressed this inverse filtering problem by introducing methods like the inverse Kalman filter (KF), inverse extended KF, and inverse unscented KF. However, these filters typically assume additive Gaussian noise models and/or rely on local approximations of non-linear dynamics at the state estimates, limiting their practical application. In contrast, this paper adopts a global filtering approach and presents the development of an inverse particle filter (I-PF). The particle filter framework employs Monte Carlo (MC) methods to approximate arbitrary posterior distributions. Moreover, under mild system-level conditions, the proposed I-PF demonstrates convergence to the optimal inverse filter. Additionally, we propose the differentiable I-PF to address scenarios where system information is unknown to the defender. Using the recursive Cramer-Rao lower bound and non-credibility index (NCI), our numerical experiments for different systems demonstrate the estimation performance and time complexity of the proposed filter.