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.

翻译：在认知系统中，近期研究重点转向分析其行为构成系统认知响应主要关注对象的主体的认知过程。这种被称为逆认知的方法产生于对抗性应用场景，并推动了逆贝叶斯滤波器的发展。在此背景下，认知对抗体（如雷达）使用前向贝叶斯滤波器跟踪其关注目标。逆滤波器则被用于推断对抗体对目标或防御方状态的估计。先前研究通过引入逆卡尔曼滤波器（KF）、逆扩展KF和逆无迹KF等方法解决了这一逆滤波问题。然而，这些滤波器通常假设加性高斯噪声模型和/或依赖于状态估计处非线性动力学的局部近似，限制了其实际应用。相比之下，本文采用全局滤波方法，提出了逆粒子滤波器（I-PF）的构建方案。该粒子滤波器框架采用蒙特卡洛（MC）方法来近似任意后验分布。此外，在温和的系统级条件下，所提出的I-PF被证明能收敛至最优逆滤波器。我们还提出了可微分I-PF以应对防御方未知系统信息的场景。通过递归克拉美-罗下界和非可信度指数（NCI）的数值实验，我们在不同系统中验证了所提出滤波器的估计性能与时间复杂度。