AI 中文总结
该研究提出基于PDE控制的环境时空场的定位框架，采用Rao-Blackwellized粒子滤波器分解车辆状态，仿真与实验表明其定位精度优于标准粒子滤波器，验证了环境场用于实际定位的可行性。
AI 中文摘要
本文提出了一种利用偏微分方程（PDE）控制的时空场作为定位特征的框架，考虑两类PDE：描述海岸与河流环境自由表面流动的浅水方程，以及模拟温度、盐度、溶解氧等标量输运与混合的平流-扩散方程。数值PDE求解器会生成区域内的预测场，多个场通道作为多模态测量值融合以提升定位精度。我们将该问题建模为Rao-Blackwellized粒子滤波器（RBPF），该滤波器将车辆状态划分为粒子采样的非线性分量，以及通过每个粒子的卡尔曼滤波器解析跟踪的线性传感器偏差分量。这种分解相较于标准粒子滤波器减少了所需粒子数量，同时考虑了实际传感器漂移。对两类PDE场景的仿真研究表明，在不同粒子数量下，RBPF在最终位置误差和均方根误差（RMSE）方面始终优于标准粒子滤波器；采用自主水面车辆测量盐度、温度和溶解氧的野外实验验证了，PDE控制的环境场提供了足够的空间变异性以用于实际定位，相关实验视频可在此httpsURL获取。
英文摘要
This paper proposes a localization framework that uses spatiotemporal fields governed by partial differential equations (PDEs) as localization signatures. Two PDE classes are considered: the shallow water equations, which describe free-surface flows in coastal and riverine environments, and the advection-diffusion equation, which models the transport and mixing of scalar quantities such as temperature, salinity, and dissolved oxygen. A numerical PDE solver provides predicted fields over the domain, and multiple field channels are fused as multimodal measurements to improve localization accuracy. We formulate the problem within a Rao-Blackwellized particle filter (RBPF) that partitions the vehicle state into a nonlinear component sampled by particles and a linear sensor bias component tracked analytically via per-particle Kalman filters. This factorization reduces the required number of particles compared to a standard particle filter while accounting for realistic sensor drift. Simulation studies on both PDE scenarios show that the RBPF consistently outperforms a standard particle filter in terms of final position error and Root Mean Square Error (RMSE) across varying particle counts. Field experiments with an autonomous surface vehicle measuring salinity, temperature, and dissolved oxygen validate that PDE-governed environmental fields provide sufficient spatial variability for practical localization. Related experimental videos are available at https://localization-environmental-pdes.github.io/.
CommentsAccepted to the 2026 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2026)
