A localized particle filter for geophysical data assimilation

2025-07-09

AI Summary

Particle filtering in high-dimensional geophysical systems—such as numerical weather prediction and ocean modeling—suffers from prohibitive computational cost and severe particle degeneracy. To address these challenges, this paper proposes a spatially localized particle filter. The method partitions the state space into non-overlapping local regions, where particle weight updates and independent resampling are performed separately, incorporating only locally available observations. This localization mitigates both the curse of dimensionality and particle degeneracy. Numerical experiments using the rotating shallow-water model demonstrate that, under partial-observation scenarios, the proposed method significantly reduces root-mean-square error (RMSE) and improves estimation stability compared to standard particle filters. Moreover, its computational complexity is reduced from *O*(*N*²) to approximately *O*(*N*), enhancing scalability and practicality for large-scale, highly nonlinear geophysical dynamical systems.

Technology Category

• Intelligent Robots: State Estimation
• Search and Optimization: Local Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

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• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Particle filters are computational techniques for estimating the state of dynamical systems by integrating observational data with model predictions. This work introduces a class of Localized Particle Filters (LPFs) that exploit spatial localization to reduce computational costs and mitigate particle degeneracy in high-dimensional systems. By partitioning the state space into smaller regions and performing particle weight updates and resampling separately within each region, these filters leverage assumptions of limited spatial correlation to achieve substantial computational gains. This approach proves particularly valuable for geophysical data assimilation applications, including weather forecasting and ocean modeling, where system dimensions are vast, and complex interactions and nonlinearities demand efficient yet accurate state estimation methods. We demonstrate the methodology on a partially observed rotating shallow water system, achieving favourable performance in terms of algorithm stability and error estimates.

Problem

• Reducing computational costs in high-dimensional geophysical systems
• Mitigating particle degeneracy via spatial localization techniques
• Improving state estimation for weather and ocean modeling

Innovation

• Localized Particle Filters reduce computational costs
• Partition state space for separate weight updates
• Effective for high-dimensional geophysical systems