In order to infer the strategy of an intelligent attacker, it is desired for the defender to cognitively sense the attacker's state. In this context, we aim to learn the information that an adversary has gathered about us from a Bayesian perspective. Prior works employ linear Gaussian state-space models and solve this inverse cognition problem through the design of inverse stochastic filters. In practice, these counter-adversarial settings are highly nonlinear systems. We address this by formulating the inverse cognition as a nonlinear Gaussian state-space model, wherein the adversary employs an unscented Kalman filter (UKF) to estimate our state with reduced linearization errors. To estimate the adversary's estimate of us, we propose and develop an inverse UKF (IUKF), wherein the system model is known to both the adversary and the defender. We also derive the conditions for the stochastic stability of IUKF in the mean-squared boundedness sense. Numerical experiments for multiple practical system models show that the estimation error of IUKF converges and closely follows the recursive Cram\'{e}r-Rao lower bound.
翻译:为了推算智能攻击者的战略, 防御者需要对攻击者状态进行认知感知感知感知。 在这方面, 我们的目标是从巴伊西亚角度了解对手收集的关于我们的信息。 先前的工程采用线性高斯国家空间模型, 并通过设计反视过滤器来解决反向认知问题。 实际上, 这些对抗性设置是高度非线性系统。 我们通过将反认知作为非线性高斯国家空间模型来解决这个问题, 敌人使用非线性卡尔曼过滤器( 乌克曼过滤器) 来用减少线性错误来估计我们的状况。 为了估计敌人对我们的估计, 我们提议并开发一个反UKF( 乌克罗夫) 系统模型, 对手和捍卫者都了解它。 我们还从中测出IUKF 的随机稳定性条件。 多个实用系统模型的数值实验显示, IUKF 的估算误差是更低的, 并紧随下拉夫 。