Generative Bayesian Filtering for State Estimation

生成式贝叶斯滤波：用于状态估计

Abstract: The state of a dynamic system evolves over time, switching among several latent modes that govern its observable behavior. Filtering methods infer the latent state from observations. Classical filtering approaches, including Kalman filters, typically rely on simple observation models, such as linear-Gaussian models, that are incapable of characterizing the increasingly nonlinear and heterogeneous patterns in high-dimensional sensor signals.

摘要： 动态系统的状态随时间演变，并在控制其可观测行为的多个潜在模式之间切换。滤波方法旨在从观测数据中推断潜在状态。传统的滤波方法（包括卡尔曼滤波）通常依赖于简单的观测模型（如线性高斯模型），这些模型无法刻画高维传感器信号中日益复杂的非线性和异构模式。

To tackle the challenge, we propose Generative Bayesian Filtering (GBF), a filtering framework that replaces restrictive observation models with pretrained conditional generative models parametrized by conditional variational autoencoders (CVAE). For online inference, GBF performs a Bayesian prediction-update recursion in which the measurement update is formulated as a posterior sampling problem that combines the dynamical prior with the CVAE-induced likelihood.

为了应对这一挑战，我们提出了生成式贝叶斯滤波（Generative Bayesian Filtering, GBF）。该滤波框架用预训练的条件生成模型（由条件变分自编码器 CVAE 参数化）取代了限制性的观测模型。在在线推断中，GBF 执行贝叶斯预测-更新递归，其中测量更新被表述为一个后验采样问题，将动态先验与 CVAE 诱导的似然函数相结合。

The resulting filtering problem is then transformed into a score-based sampling problem, which naturally inherits the flexibility from generative models and the uncertainty quantification capabilities from ensembling. Experiments on synthetic datasets and real-world applications involving manufacturing system monitoring and arrhythmia diagnosis demonstrate that GBF improves state estimation accuracy and robustness relative to baseline approaches.

由此产生的滤波问题被转化为一个基于分数的采样问题，这自然地继承了生成模型的灵活性以及集成学习的不确定性量化能力。在合成数据集以及涉及制造系统监控和心律失常诊断的实际应用中，实验结果表明，与基准方法相比，GBF 提高了状态估计的准确性和鲁棒性。