A Unified Filter Method for Jointly Estimating State and Parameters of Stochastic Dynamical Systems via the Ensemble Score Filter

TL;DR

This paper introduces the United Filter, a novel method combining an ensemble score filter and a direct parameter filter to improve joint state and parameter estimation in stochastic dynamical systems, addressing limitations of existing approaches.

Contribution

The paper presents the United Filter, integrating an ensemble score filter with a direct filter for online joint state-parameter estimation, enhancing accuracy and stability over AugEnKF.

Findings

Demonstrates improved accuracy in numerical experiments.

Shows enhanced stability compared to traditional methods.

Effectively estimates both states and parameters in complex systems.

Abstract

This paper tackles the intricate task of jointly estimating state and parameters in data assimilation for stochastic dynamical systems that are affected by noise and observed only partially. While the concept of ``optimal filtering'' serves as the customary approach to estimate the state of the target dynamical system, traditional methods such as Kalman filters and particle filters encounter significant challenges when dealing with high-dimensional and nonlinear problems. When we also consider the scenario where the model parameters are unknown, the problem transforms into a joint state-parameter estimation endeavor. Presently, the leading-edge technique known as the Augmented Ensemble Kalman Filter (AugEnKF) addresses this issue by treating unknown parameters as additional state variables and employing the Ensemble Kalman Filter to estimate the augmented state-parameter vector. Despite its considerable progress, AugEnKF does exhibit certain limitations in terms of accuracy and stability. To address these challenges, we introduce an innovative approach, referred to as the United Filter. This method amalgamates a remarkably stable and efficient ensemble score filter (EnSF) for state estimation with a precise direct filter dedicated to online parameter estimation. Utilizing the EnSF's generative capabilities grounded in diffusion models, the United Filter iteratively fine-tunes both state and parameter estimates within a single temporal data assimilation step. Thanks to the robustness of the EnSF, the proposed method offers a promising solution for enhancing our comprehension and modeling of dynamical systems, as demonstrated by results from numerical experiments.