Dynamical Low-Rank Ensemble Kalman filter for State/Parameter estimation

TL;DR

This paper introduces a Dynamical Low-Rank Ensemble Kalman Filter that efficiently estimates states and parameters in high-dimensional systems by evolving a low-dimensional subspace, improving computational efficiency and robustness.

Contribution

The paper extends the DLR-ENKF to joint state-parameter estimation, incorporating a novel time-integration scheme and hyper-reduction for nonlinear evaluations.

Findings

Effective in benchmark problems

Robust and computationally efficient

Accurate filtering with reduced basis evolution

Abstract

We propose a Dynamical Low-Rank Ensemble Kalman Filter (DLR-ENKF) for efficient joint state-parameter estimation in high-dimensional dynamical systems. The method extends the DLR-ENKF formulation of arXiv:2509.11210 to the augmented state-parameter framework, tracking the filtering density within a dynamically evolving low-dimensional subspace. Key developments include a time-integration strategy that combines the Basis Update & Galerkin scheme with forecast/analysis discretisation, and a DEIM-based hyper-reduction technique for efficient evaluation of nonlinear terms. We demonstrate the effectiveness, robustness, and computational advantages of the proposed approach on benchmark problems. The results highlight the potential of dynamically evolving reduced bases to achieve accurate filtering and parameter estimation at reduced computational cost.