用可逆变换构建高效贝叶斯滤波器，解决高维非线性系统建模难题。
Flow-based Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems
- 基于归一化流构建隐变量线性状态空间模型
- 在高维非线性系统中实现更高精度与更低计算开销
- 无需先验动力学模型，适合数据驱动场景
高维非线性随机动力系统的贝叶斯滤波是科学与工程中的基础但极具挑战性的问题。现有方法面临显著瓶颈：高斯类滤波难以处理非高斯分布，而序列蒙特卡洛方法计算量大且在高维下易出现粒子退化。尽管机器学习中的生成模型在建模高维非高斯分布方面取得进展，但其在线更新效率低，限制了在滤波任务中的应用。为此，我们提出一种基于流的贝叶斯滤波器（FBF），利用归一化流构建新的隐变量线性状态空间模型，以高斯滤波分布为基础。该框架通过归一化流提供的可逆变换实现高效密度估计与采样，并能以数据驱动方式构造滤波器，无需系统动力学或观测模型的先验知识。数值实验表明，FBF在精度和效率上均表现更优。
原文摘要 · Abstract (English)
Bayesian filtering for high-dimensional nonlinear stochastic dynamical systems is a fundamental yet challenging problem in many fields of science and engineering. Existing methods face significant obstacles: Gaussian-based filters struggle with non-Gaussian distributions, while sequential Monte Carlo methods are computationally intensive and prone to particle degeneracy in high dimensions. Although generative models in machine learning have made significant progress in modeling high-dimensional non-Gaussian distributions, their inefficiency in online updating limits their applicability to filtering problems. To address these challenges, we propose a flow-based Bayesian filter (FBF) that integrates normalizing flows to construct a novel latent linear state-space model with Gaussian filtering distributions. This framework facilitates efficient density estimation and sampling using invertible transformations provided by normalizing flows, and it enables the construction of filters in a data-driven manner, without requiring prior knowledge of system dynamics or observation models. Numerical experiments demonstrate the superior accuracy and efficiency of FBF.
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