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

arXiv: https://arxiv.org/abs/2606.14195 · HTML: https://mlsanity.com/paper/2606.14195/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 33 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Builds on (most cited first, 9 of 9)

- [Recurrent Kalman Networks: Factorized Inference in High-Dimensional Deep Feature Spaces](https://mlsanity.com/paper/1905.07357/) (2019)
- [On Particle Methods for Parameter Estimation in State-Space Models](https://mlsanity.com/paper/1412.8695/) (2014)
- [Outlier-robust Kalman Filtering through Generalised Bayes](https://mlsanity.com/paper/2405.05646/) (2024)
- [Adaptive Adjustment of Noise Covariance in Kalman Filter for Dynamic State Estimation](https://mlsanity.com/paper/1702.00884/) (2017)
- [Optimization or Architecture: How to Hack Kalman Filtering](https://mlsanity.com/paper/2310.00675/) (2023)
- [Adaptive Uncertainty-Guided Model Selection for Data-Driven PDE Discovery](https://mlsanity.com/paper/2308.10283/) (2023)
- [Sigma-point Kalman Filter with Nonlinear Unknown Input Estimation via Optimization and Data-driven Approach for Dynamic Systems](https://mlsanity.com/paper/2306.12361/) (2023)
- [Learning Stochastic Nonlinear Dynamics with Embedded Latent Transfer Operators](https://mlsanity.com/paper/2501.02721/) (2025)
- [CKFNet: Neural Network Aided Cubature Kalman filtering](https://mlsanity.com/paper/2508.09727/) (2025)

## Abstract (arXiv)

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.