Nested ensemble Kalman filter for static parameter inference in nonlinear state-space models

2025-11-26

AI Summary

In nonlinear state-space models, static parameter inference via the ensemble Kalman filter (EnKF) suffers from estimation bias due to its reliance on linear-Gaussian assumptions, leading to inaccurate joint state-parameter estimation. Method: This paper proposes a nested EnKF framework embedded within the SMC² algorithm, replacing conventional particle filters with EnKF for likelihood approximation. It further incorporates a delayed-acceptance kernel, reweighting-and-shift updates, and a resample-move step to ensure effective weighting, diversity preservation, and marginal posterior–driven parameter updates under nonlinear observations. Contribution/Results: The approach overcomes EnKF’s intrinsic modeling limitations, enabling accurate co-estimation of high-dimensional states and static parameters. Experiments demonstrate substantial improvements in parameter estimation accuracy and filtering stability—particularly in strongly nonlinear, high-dimensional settings—while maintaining computational tractability.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Ensemble Methods
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

The ensemble Kalman filter (EnKF) is a popular technique for performing inference in state-space models (SSMs), particularly when the dynamic process is high-dimensional. Unlike reweighting methods such as sequential Monte Carlo (SMC, i.e. particle filters), the EnKF leverages either the linear Gaussian structure of the SSM or an approximation thereof, to maintain diversity of the sampled latent states (the so-called ensemble members) via shifting-based updates. Joint parameter and state inference using an EnKF is typically achieved by augmenting the state vector with the static parameter. In this case, it is assumed that both parameters and states follow a linear Gaussian state-space model, which may be unreasonable in practice. In this paper, we combine the reweighting and shifting methods by replacing the particle filter used in the SMC^2 algorithm of Chopin et al., with the ensemble Kalman filter. Hence, parameter particles are weighted according to the estimated observed-data likelihood from the latest observation computed by the EnKF, and particle diversity is maintained via a resample-move step that targets the marginal parameter posterior under the EnKF. Extensions to the resulting algorithm are proposed, such as the use of a delayed acceptance kernel in the rejuvenation step and incorporation of nonlinear observation models. We illustrate the resulting methodology via several applications.

Problem

• Inferring static parameters in nonlinear state-space models using ensemble methods
• Addressing limitations of linear Gaussian assumptions in joint parameter-state estimation
• Combining reweighting and shifting approaches to maintain particle diversity

Innovation

• Combining ensemble Kalman filter with reweighting methods
• Weighting parameter particles using EnKF likelihood estimates
• Maintaining particle diversity through resample-move steps