A localized particle filter for geophysical data assimilation

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.