[Paper Review] Interacting particle filters for simultaneous state and parameter estimation

David Angwenyi, Jana de Wiljes+1 more|arXiv (Cornell University)|Sep 26, 2017

Target Tracking and Data Fusion in Sensor Networks6 references3 citations

TL;DR

This paper proposes a hybrid interacting particle filter that combines the ensemble Kalman-Bucy filter (EnKBF) for continuous-time state estimation with an extended ensemble transform particle filter (ETPF) for intermittent parameter updates in high-dimensional stochastic dynamical systems. The method efficiently handles joint state-parameter estimation by exploiting the near-Gaussianity of state conditionals and non-Gaussianity of parameters, demonstrating accurate recovery of unknown wave velocity in a stochastic wave equation with minimal computational overhead via parallelized filtering and adaptive resampling.

ABSTRACT

Simultaneous state and parameter estimation arises from various applicational areas but presents a major computational challenge. Most available Markov chain or sequential Monte Carlo techniques are applicable to relatively low dimensional problems only. Alternative methods, such as the ensemble Kalman filter or other ensemble transform filters have, on the other hand, been successfully applied to high dimensional state estimation problems. In this paper, we propose an extension of these techniques to high dimensional state space models which depend on a few unknown parameters. More specifically, we combine the ensemble Kalman-Bucy filter for the continuous-time filtering problem with a generalized ensemble transform particle filter for intermittent parameter updates. We demonstrate the performance of this two stage update filter for a wave equation with unknown wave velocity parameter.

Motivation & Objective

• To address the computational challenge of simultaneous state and parameter estimation in high-dimensional, nonlinear stochastic dynamical systems.
• To overcome limitations of standard particle filters and ensemble Kalman filters in handling non-Gaussian parameter distributions while maintaining efficiency in high-dimensional state spaces.
• To develop a scalable, parallelizable filtering framework that separates state and parameter updates using distinct particle filter strategies.
• To enable accurate estimation of unknown parameters in systems where state distributions are approximately Gaussian but parameter posteriors are non-Gaussian.

Proposed method

• The method employs a two-stage filtering approach: the ensemble Kalman-Bucy filter (EnKBF) for continuous state updates and an extended ensemble transform particle filter (ETPF) for discrete, intermittent parameter updates.
• The EnKBF is applied to each ensemble member conditioned on fixed parameter values, enabling efficient, parallelized state estimation using feedback particle flow dynamics.
• The ETPF is used to update the parameter ensemble when the effective sample size drops below a threshold, ensuring diversity and accuracy in non-Gaussian parameter posteriors.
• The algorithm uses a Wasserstein barycenter problem to align state ensembles across different parameter realizations, preserving cross-ensemble correlation.
• A hybrid ansatz is used to approximate the joint conditional density by decoupling the state and parameter dynamics, avoiding full joint filtering in high-dimensional space.
• The method supports localization and ensemble inflation techniques to improve performance in spatially extended systems.

Experimental results

Research questions

• RQ1 Can a hybrid particle filter combining EnKBF and ETPF achieve accurate joint state-parameter estimation in high-dimensional stochastic PDEs with few unknown parameters?
• RQ2 How does the performance of the proposed method compare to a direct EnKBF approach when the parameter distribution is non-Gaussian?
• RQ3 To what extent does the use of a Wasserstein barycenter improve the correlation between state ensembles across different parameter realizations?
• RQ4 Can the method maintain accuracy and stability in long-time simulations of nonlinear, high-dimensional systems like the stochastic wave equation?
• RQ5 What is the computational cost of the ETPF-based parameter update relative to standard resampling, and can it be reduced via efficient solvers like the Sinkhorn algorithm?

Key findings

• The proposed hybrid filter successfully estimates the true wave velocity parameter in a stochastic wave equation, converging to the correct value within a short assimilation window.
• The method outperforms a direct EnKBF approach for both states and parameters when the parameter posterior is non-Gaussian, as the ETPF better captures the true parameter distribution.
• The use of the Wasserstein barycenter for state ensemble alignment maintained sufficient correlation between state and parameter ensembles without requiring frequent reorganization.
• The algorithm demonstrated robustness and stability over 400 time steps with a 100-point spatial discretization, achieving accurate state and parameter tracking.
• The computational cost of the ETPF-based parameter update is higher than standard resampling but remains feasible, especially with efficient implementations such as the Sinkhorn algorithm.
• The method enables scalable, parallelized filtering by decoupling state and parameter updates, making it suitable for high-dimensional systems with few unknown parameters.