New Bayesian Filter Adapts to Non-Stationary Processes with Structured Noise

Kalman filters based on Embedded Latent Transfer Operators (ELTO) are emerging as valuable tools for sequential state estimation. However, a key limitation of these filters has been their reliance on simplified noise models, which often fail to adapt effectively to non-stationary processes where dynamics change over time. To overcome this, a new ELTO-based Bayesian filtering approach has been developed, featuring a structured parameterization for the filter's noise model. This innovative parameterization enables structured noise adaptation, which couples the data-driven learning of an optimal time-invariant noise model with dynamic parameter adjustments that respond to changes in process dynamics. Empirical evaluations demonstrate that this structured noise adaptation significantly enhances the filter's dynamic state estimation capabilities. It achieves improved performance in environments characterized by noise and time-varying conditions, offering a more robust solution for sequential state estimation.