Generative Bayesian Filtering Improves State Estimation

This paper introduces Generative Bayesian Filtering (GBF), a novel framework for state estimation in dynamic systems where latent modes govern observable behavior. Traditional filtering methods, such as Kalman filters, typically rely on simplistic observation models (e.g., linear-Gaussian) that struggle with the complex, nonlinear, and high-dimensional patterns found in modern sensor data. GBF addresses this limitation by substituting these restrictive models with powerful pretrained conditional generative models, specifically conditional variational autoencoders (CVAEs). For online inference, GBF employs a Bayesian prediction-update recursion. The crucial measurement update step is reframed as a posterior sampling problem, which effectively combines the dynamical prior with the likelihood derived from the CVAE. This transformation converts the filtering problem into a score-based sampling problem, allowing GBF to leverage the flexibility of generative models while retaining the uncertainty quantification capabilities inherent in ensembling. Experimental results on synthetic datasets and real-world applications, including manufacturing system monitoring and arrhythmia diagnosis, demonstrate that GBF significantly enhances state estimation accuracy and robustness. It outperforms baseline approaches by better characterizing complex observation patterns, making it suitable for scenarios where high-dimensional and heterogeneous sensor signals are prevalent.