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

2026-06-12

AI Summary

Existing Kalman filters based on the Embedding Linear Time-invariant Operator (ELTO) rely on simplified noise models that struggle to capture dynamic variations in non-stationary processes. This work proposes a Bayesian filtering approach that integrates structured noise modeling within the ELTO framework, simultaneously learning an optimal time-invariant noise structure and adaptively adjusting its parameters in real time. By introducing a data-driven parameterization mechanism for structured noise, the method effectively couples static noise characterization with dynamic environmental adaptability. This integration significantly enhances the accuracy and robustness of state estimation under conditions of high noise levels and time-varying dynamics.

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.

Problem

• structured noise adaptation
• sequential Bayesian filtering
• non-stationary processes
• noise model
• Embedded Latent Transfer Operators

Innovation

• Structured Noise Adaptation
• Embedded Latent Transfer Operators
• Bayesian Filtering
• Non-stationary Processes
• Dynamic State Estimation