AI 中文总结
该研究提出扩展Perron-Frobenius算子滤波器（PFOF），结合扩展动态模态分解（eDMD）学习相关算子，处理非线性系统的非高斯分布，经数值验证可高效且高精度地完成非线性状态估计。
AI 中文摘要
我们提出一种用于非线性状态估计的扩展Perron-Frobenius算子滤波器（PFOF）。该方法利用扩展动态模态分解（eDMD）学习Perron-Frobenius算子，这是一种完全保留非线性动力系统特性的无限维线性算子。这使我们能在线性算子表示中明确考虑非线性系统呈现的非高斯分布，同时保留在eDMD中选择基函数的自由度。通过两个数值示例，我们表明扩展PFOF通过利用eDMD中基函数选择的灵活性，实现了高计算效率和高估计精度。
英文摘要
We propose an extended Perron--Frobenius Operator Filter (PFOF) for nonlinear state estimation. The method learns the Perron--Frobenius operator, an infinite-dimensional linear operator fully preserving properties of a nonlinear dynamical system, using the extended Dynamic Mode Decomposition (eDMD). This enables us to explicitly account for non-Gaussian distributions exhibited by the nonlinear system within a linear-operator representation, while retaining the freedom to choose basis functions in eDMD. Through two numerical examples, we show that the extended PFOF achieves high computational efficiency and high estimation accuracy by exploiting the flexibility in the choice of basis functions in eDMD.
CommentsSubmitted to Nonlinear Theory and Its Applications, IEICE (NOLTA), 9 pages, 5 figures, 2 tables
