Structured Noise Adaptation for Sequential Bayesian Filtering with Embedded Latent Transfer Operators

Abstract: 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.

Submission Type: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission:

We have revised our manuscript based on the constructive feedback from viewers. Here, we summarize the major changes we made below.

**Clarified data assumptions:** We revised the manuscript to clarify that our method uses standard, noisy validation observations ($\boldsymbol{Y}^{\text{val}}$) and does not require (unobservable) noiseless ground truth.

**Added experiments:** We included the Lorenz-96 system to demonstrate our method’s scalability to high-dimensional problems, and the historical Canadian lynx and snowshoe hare dataset to highlight its application to real-world data where the ground truth is unknown.

**New baselines:** We added comparisons with recent Neural-Aided KFs: SPKF and CKFNet.

**Expanded ablation studies:** We added detailed analyses of computational complexity, kernel selection, block size, and embedding window size.

Assigned Action Editor: ~Mauricio_A_Álvarez1

Submission Number: 6998