A Pretrained Model for Bayesian Filtering in Heterogeneous Dynamical Systems

Abstract

Filtering has not yet had its foundation-model moment: state estimation is still dominated either by online Bayesian filtering algorithms that require known dy- namics as inputs, or by learning-based neural filters trained from scratch for a single system or parametric family. The core challenge is structural heterogene- ity: dynamical systems differ in their governing dynamics, physical scales, and noise levels, precluding a shared representation space for a reusable filter. To bridge this gap, we introduce FilterFM, the first pretrained model for Bayesian filtering that estimates latent states across heterogeneous dynamical systems with a single checkpoint. FilterFM employs a hierarchical two-level observation se- quence encoder and a prior-to-posterior state-reconstruction module that together handle varying observation and state dimensions across heterogeneous systems, while modeling state uncertainty via quantile prediction. Trained on a mixture of heterogeneous filtering tasks, FilterFM exhibits superior in-domain performance, delivering significant gains in estimation accuracy, runtime efficiency, and noise robustness compared to existing baselines. Beyond in-domain performance, it marks the first model to successfully enable zero-shot filtering on unseen dynamics, bridging the generalization gap in state estimation. Furthermore, we uncover clear scaling behaviors in foundation-model-based Bayesian filtering, which combined with comprehensive component ablation studies, validate the structural optimality of our design and broaden the generalization scope for this research field.