AI 中文总结
本文提出重中心域 Yau-Yau 滤波器（RD-YYF），通过在固定大小局部窗口内求解 FKE 实现高效非线性目标跟踪，经实验其跟踪误差低于 EKF 和 PF，且推理效率高。
AI 中文摘要
Yau-Yau 滤波器将非线性状态估计重新表述为受正向柯尔莫哥洛夫方程（FKE）控制的概率密度传播。然而，将其应用于目标跟踪需要在有限计算域上对 FKE 进行高效近似。本文提出一种重中心域 Yau-Yau 滤波器（RD-YYF），该滤波器在以最新状态估计为中心的固定大小局部窗口内求解 FKE，此设计将数值分辨率集中在主导后验密度附近。离线阶段，物理信息神经网络（PINNs）生成 FKE 解快照，同时主成分分析构建密度演化的低维表示；轻量级残差代理将初始条件系数和域中心映射到终态解系数。在线阶段，预训练的代理预测重中心窗口内的密度演化，随后进行观测更新和状态估计。对两个受几何约束的目标跟踪示例的实验表明，RD-YYF 比扩展卡尔曼滤波器（EKF）和粒子滤波器（PF）实现更低的跟踪误差，同时保持每时间步的高效推理； ablation 结果显示，域重中心可提升高概率区域的密度近似效果并加速离线 PINN 收敛。这些结果证明了 RD-YYF 在高效非线性目标跟踪中的应用潜力。
英文摘要
The Yau-Yau filter reformulates nonlinear state estimation as probability-density propagation governed by the Forward Kolmogorov equation (FKE). Applying it to target tracking, however, requires efficient FKE approximation on a finite computational domain. This paper proposes a Recentered-Domain Yau-Yau Filter (RD-YYF), which solves the FKE within a fixed-size local window centered at the latest state estimate. This design concentrates numerical resolution near the dominant posterior density. Offline, physics-informed neural networks (PINNs) generate FKE solution snapshots, while principal component analysis constructs a low-dimensional representation of density evolution. A lightweight residual surrogate maps the initial-condition coefficients and domain center to the terminal-solution coefficients. Online, the pretrained surrogate predicts density evolution within the recentered window, followed by observation update and state estimation. Experiments on two geometrically constrained target-tracking examples show that RD-YYF achieves lower tracking errors than the extended Kalman filter (EKF) and particle filter (PF), while retaining efficient per-timestep inference. Ablation results indicate that domain recentering improves density approximation in high-probability regions and accelerates offline PINN convergence. These results demonstrate the potential of RD-YYF for efficient nonlinear target tracking
