论文标题
反向扩展卡尔曼滤波器 - 第二部分：高度非线性和不确定的系统
Inverse Extended Kalman Filter -- Part II: Highly Non-Linear and Uncertain Systems
论文作者
论文摘要
反逆转系统的设计问题最近激发了反向贝叶斯过滤器的发展。例如，最近已经制定了逆卡尔曼过滤器（I-KF），以估算对手的卡尔曼滤波器跟踪估计值，因此可以预测对手的未来步骤。本文和同伴论文（第一部分）的目的是通过提出反向扩展的卡尔曼过滤器（I-EKF）来解决非线性系统中的反过滤问题。同伴论文提出了I-EKF（有和没有未知输入）和I-KF（未知输入）的理论。在本文中，我们为高度非线性模型开发了这种理论，该模型采用了二阶，高斯总和和前向EKFS。特别是，我们使用有界的非线性方法来得出二阶EKF的理论稳定性保证。为了解决标准I-EKF的局限性，即防御者完全知道系统模型和正向过滤器，我们建议再现基于Hilbert Space基于空间的EKF来学习基于其观察值的未知系统动力学，这可以用作逆滤波器来推断对抗性的估计。数值实验证明了使用递归cramér-rao下限作为基准的递归的状态估计性能。
Counter-adversarial system design problems have lately motivated the development of inverse Bayesian filters. For example, inverse Kalman filter (I-KF) has been recently formulated to estimate the adversary's Kalman-filter-tracked estimates and hence, predict the adversary's future steps. The purpose of this paper and the companion paper (Part I) is to address the inverse filtering problem in non-linear systems by proposing an inverse extended Kalman filter (I-EKF). The companion paper proposed the theory of I-EKF (with and without unknown inputs) and I-KF (with unknown inputs). In this paper, we develop this theory for highly non-linear models, which employ second-order, Gaussian sum, and dithered forward EKFs. In particular, we derive theoretical stability guarantees for the inverse second-order EKF using the bounded non-linearity approach. To address the limitation of the standard I-EKFs that the system model and forward filter are perfectly known to the defender, we propose reproducing kernel Hilbert space-based EKF to learn the unknown system dynamics based on its observations, which can be employed as an inverse filter to infer the adversary's estimate. Numerical experiments demonstrate the state estimation performance of the proposed filters using recursive Cramér-Rao lower bound as a benchmark.
