Kalman filters based on the Embedded Latent Transfer Operators (ELTO) emerge as novel statistical tools for sequential state estimation. However, a critical limitation stems from their use of simplified noise models, which fail to dynamically adapt to non-stationary processes. To address this limitation, we introduce an ELTO-based Bayesian filtering approach with a new structured parameterization for the filter's noise model. This parameterization enables structured noise adaptation, which couples the data-driven learning of an optimal time-invariant noise model with dynamic parameter adaptation that responds to changes in dynamics within non-stationary processes. Empirical results show that our structured noise adaptation improves the filter's dynamic state estimation performance in noisy, time-varying environments.

翻译：基于嵌入潜传递算子（ELTO）的卡尔曼滤波器是序列状态估计的新型统计工具。然而，其关键局限在于采用简化的噪声模型，无法动态适应非平稳过程。为解决该局限，我们提出一种基于ELTO的贝叶斯滤波方法，该方法对滤波器的噪声模型采用新型结构化参数化方案。该参数化使结构化噪声自适应成为可能，它将基于数据驱动的最优时不变噪声模型学习与针对非平稳过程中动态变化进行响应的动态参数自适应相结合。实验结果表明，我们的结构化噪声自适应方法在含噪时变环境中提升了滤波器的动态状态估计性能。