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.

翻译：在对抗系统中，为推断智能对抗体的策略，防御方需要认知感知对手已获取的关于己方信息。以往研究采用线性高斯状态空间模型，通过设计逆随机滤波器解决这一逆认知问题。然而实际中对抗系统通常具有高度非线性。本文通过将逆认知建模为非线性高斯状态空间模型来处理此场景——其中对抗方采用无迹卡尔曼滤波（UKF）以减小线性化误差来估计防御方状态。为估计对手对防御方的估计量，我们提出并开发了逆无迹卡尔曼滤波（IUKF）系统。随后推导了IUKF在均方有界意义下随机稳定性的理论保证。针对多个实际应用场景的数值实验表明，IUKF的估计误差收敛并紧密遵循递归克拉美-罗下界。